PhD Projects

Simulating Rare Events

Dr. Rosalind Allen (Edinburgh)

“Rare events” happen very infrequently, but have dramatic consequences — for example, earthquakes, stock market crashes or the spontaneous nucleation of an ice crystal. Special techniques are needed to study rare events using computer simulations, since in normal simulations there is not enough time in the simulation run to observe the event. One of these methods is the forward flux sampling (or FFS) method, which was developed by Dr. Allen and coworkers in 2006. This method can speed up simulations of rare events by many orders of magnitude. Basically, FFS involves pushing the system from an initial state to a final state.

Although FFS works well for some rare event processes in soft matter and biological physics (such as genetic switch flipping and some crystal nucleation processes), there are many important problems for which it works less well (such as protein folding and glass formation). This project will involve developing new rare event simulation methods which do work for these problems, and applying them to exciting and challenging physical systems. The problems chosen will depend on the student, but might include simulating cage hopping in glasses or the dynamics of biological membranes.

Understanding osmotic and hydrostatic pressure using simulations

Dr. Rosalind Allen and Dr. Davide Marenduzzo (Edinburgh)

It is well-known that when the concentration of a solute is unbalanced across a semipermeable membrane, the result is an osmotic pressure on the membrane, which leads to a difference in hydrostatic pressure between the solvents on the two sides of the membrane. However, the molecular details of how this comes about are virtually unknown, despite it being a key fundamental concept in condensed matter physics. This project will use Molecular Dynamics and Lattice Boltzmann simulations to shed light on the origins of osmotic pressure. Despite their obvious importance, few simulations have been done in this area. You will first use simulations to determine the basic physical mechanisms giving rise to osmotic pressure, and how osmotic and hydrostatic pressure are connected. Later you will carry out more advanced simulations on the relation between hydrostaic pressure in complex nonequilibrium systems such as active, polymer producing colloids.

Open Quantum Systems

Dr. Erika Andersson (Heriot-Watt)

No physical system is truly isolated. An open quantum system is a quantum system whose dynamics are determined both by interactions internal to the system and by influences from an environment. Markovian behaviour arises when the environment is essentially "memory-less", leading, roughly speaking, to exponential decay of the quantities involved. The non-Markovian case is much less well understood, but is becoming increasingly relevant as our ability to control quantum systems experimentally develops.

Non-Markovian behavior is encountered in many areas of condensed matter physics. An example, relevant to experiments performed in the group of Prof Richard Warburton at Heriot-Watt, is a quantum dot coupled to a spin bath. Error correction in quantum computing, implemented using quantum dots or otherwise, may not be adequately handled by assuming that the errors are Markovian. In order to model and understand quantum systems in tailored and finite environments and at short time scales we need an understanding of non-Markovian effects. Experimental progress is rapid, e.g. in the field of quantum control, and makes this an increasingly relevant objective.

Open physical systems, that is, systems coupled to an environment, are described using master equations. Master equations have been extensively used to describe phenomena in condensed matter systems ranging from semiconductor and spin physics to a quantum mechanical description of Brownian motion. At the moment, however, it is not even known what a non-Markovian master equation should look like in general in order to be compatible with physical time evolution. This project will investigate the derivation and use of non-Markovian master equations to describe quantum systems in condensed matter physics.

Molecular dynamics simulations of tricomponent liquid mixtures

Prof. Simon Bates (Edinburgh)

The production of alcohols to act as fuel additives to petroleum offers the potential for both enhancing the octane-rating of the fuel, whilst at the same time being capable of being produced from renewable sources. But there are real challenges associated with a seemingly-simple system; not just with the production of the alcohols from biomass, but also because hydrocarbons and alcohols don't mix particularly well. And the presence of even a small amount of water makes matters much worse, causing the two phases to separate.

This project will use atomistic computer simulations to investigate the structure and dynamics of a three-components liquid mixtures: water, alcohol and hydrocarbons. Despite being a relatively simple 3-component mixture, a detailed understanding of the structure and dynamics at the molecular level of the alcohol-hydrocarbon-water system is still missing, and recent studies of alcohol-water mixtures have shown that these systems can be anything but simple [1]. This project will attempt to elucidate the nature of this system at an atomistic level and also identify how this may influence the liquid-phase separations on a macroscopic level. It will used a variety of different computational codes (both classical and quantum mechanical) on machines as diverse as a simple desktop to IBMs Blue Gene system, managed by the Edinburgh Parallel Computing Centre.

[1] S. Dixit, J. Crain, W.C.K. Poon, J.L. Finney and A.K. Soper, Nature 416 ( 2002)

Spectroscopic STM studies of unconventional superconductors

Dr Felix Baumberger, Dr Anna Tamai (St. Andrews)

The first goal of this project is to commission a brand new low-temperature (< 1K) Scanning Tunneling Microscope (STM), which will be delivered in September 2010. Once fully operational, you will use the instrument for local spectroscopic studies of topical strongly correlated electron systems. The scientific focus of the project will be on the recently discovered family of iron-chalcogenide superconductors Fe(Se/Te), where we plan to investigate the influence of excess iron on the electronic structure and on superconductivity. These experiments will be performed in close collaboration with other group members performing complementary angle resolved photoemission (ARPES) studies on the same samples and promise unique insight into a family of materials with intriguing properties.

Category: Experimental Hard Condensed Matter

Laser based ARPES from ultra-pure correlated electron systems

Dr Felix Baumberger (St. Andrews)

The goal of this project is to investigate the electronic structure of strongly correlated metallic oxides with unprecedented accuracy. To this end you will use a novel highly intense UV laser source to perform ultrahigh resolution angle resolved photoemission (ARPES) studies on ruthenates and related materials. ARPES is a uniquely powerful spectroscopic technique for electronic structure measurements. However, reaching the minute energy and temperature scales of some of the most intriguing phenomena in condensed matter systems remains a challenge. In this project you will commission a new laser based UV light source with significantly higher brilliance than today's best synchrotron beamlines and explore the potential of this instrument for very high resolution photoelectron spectroscopy using our existing state-of-the-art electron spectrometer.

Category: Experimental Hard Condensed Matter

Nonequilibrium Phase Transitions

Dr. Richard Blythe and Prof. Martin Evans (Edinburgh)

A major question concerning non-equilibrium systems is how their properties differ from systems in thermal equilibrium and in particular what is the nature of non-equilibrium phase transitions. A major achievement of our work in Edinburgh has been the realisation that phase transitions and, in particular, spontaneous symmetry breaking may occur in one-dimensional (1d) systems as opposed to equilibrium systems where phase transitions cannot occur in 1d. Such systems are realised, for example, by traffic and granular flow. A related non-equilibrium phase transition is ‘real-space condensation’ the characteristic feature of which is that above a critical density of the microscopic constituents a finite fraction of constituents ‘condense’ onto one site of the corresponding lattice model. The project is to extend our understanding of these and other non-equilibrium phase transitions through numerical and analytical studies.

Bicontinuous Gels Stabilised Using Nanoparticles or Nanorods

Dr. Paul Clegg (Edinburgh)

A composite material can be trapped out of equilibrium due to a superstructure which prevents the other constituents from reorganizing themselves. We have developed such a material where a liquid-liquid interface laden with colloidal particles prevents two liquids from fully phase separating. The resulting composite, known as a bijel, has a novel morphology and the resulting composite, known as a bijel, has a novel morphology and may be employed for a range of applications. Recent computer simulations suggest that if our colloidal particles are replaced by nanoparticles then the composite may be able to ‘break out ’ of the trap. Curious behaviour is also predicted if the spherical particles are replaced by long rods. You will explore these scenarios experimentally primarily using fluorescence confocal microscopy.

Colloidal Particles in a Blue Phase Liquid Crystal

Dr. Paul Clegg (Edinburgh)

Soft matter has constituents whose size is larger than normal molecules and smaller than macroscopic objects (those visible to the naked eye). This intermediate size is called the mesoscale and it makes these materials soft and their dynamics slow. New and surprising properties can emerge when two constituents are combined that are both characterized by intermediate length scales. In this project you will combine colloidal particles with the liquid crystalline blue phase. Both are characterized by length scales close to the wavelength of light. The blue phase is an exotic state in which defects in the arrangement of a chiral material crystallize in a similar way to atoms in a solid. You will use light scattering and confocal microscopy to characterize the constituents and the resulting composite samples. Your experimental studies will be complemented by computer simulations by in-house collaborators.

Nonequilibrium Steady States

Prof. Martin Evans (Edinburgh)

The development of statistical mechanics has allowed a deep understanding of systems in thermal equilibrium. However, particularly in the biophysical arena, most real-world systems are not in equilibrium! Their steady states are not described by the usual Boltzmann distribution and one is still very much in the dark about the nature of non-equilibrium steady states. To make progress we study simple mathematical models which may admit exact solution. Major successes have been the identification of models with factorised steady states and steady states of matrix product form. The project is to extend these exact analytical solutions through the calculation of non-equilibrium correlation functions, for example, and to identify new exactly solvable cases.

Physics and modelling Organic Semiconductor Devices

Prof. Ian Galbraith (Heriot-Watt)

Great strides have been made over the last ten years in realising the enormous potential of organic semiconductor materials in that they are cheap, flexible and easily processed. The development of early polymer lasers and amplifiers today is following a similar trajectory to that of inorganic optoelectronic devices in the 1980’s. At that time the first generation of bulk lasers had given way to a second generation based on quantum well heterostructures. Key to this development was a quantitative theoretical understanding of the influence of the underlying microscopic physics such as electronic bandstructure and carrier-carrier scattering losses. This led, for example, to the incorporation of strained hetereostructure layers into lasers which greatly enhanced their performance.

Organic (Polymer) photonics devices are currently sufficiently developed that we can credibly begin to search for the same level of understanding and potentially reap similarly high rewards. To model the optical response of the system requires knowledge not only of the population of any excitations in the system but also of the induced polarisations, as these are the sources for the propagating electric field. In inorganic semiconductor devices these can be calculated using a so-called Equation of Motion approach. This approach has been extremely successful in providing a quantitative description of inorganic semiconductor lasers and amplifiers. It has been widely adopted in academic research and increasingly, in the commercial sector. The Heriot-Watt Semiconductor Theory group has substantial experience with this Equation of Motion techniques. The major objective of this project is to develop an analogous set of physically appealing equations applicable to polymer semiconductor devices and test them against experiment. Clearly the usual periodic Bloch-like states are an inappropriate set of basis states to use for the localised excitations involved in the optics of polymer chains. Thus we use Density functional theory to compute the electronic states of the polymer which then form the basis set for the equations of motion. A further challenge is to quantify, in this basis, the dominant scattering mechanisms that determine the relaxation between the states and the damping of the optically induced polarisation. Inclusion of the light propagation involves coupling the equation for the induced polarization to the wave equation and thereby following the evolution of a real pulse as it transits the sample. The resulting pulse will be directly comparable to the measured pulses obtained by our experimental collaborators at the University of St. Andrews (Prof. I. Samuel & Dr. G. Turnbull). Success this ambitious project would lead to equations which are as key to modelling, understanding and optimising polymer devices as the semiconductor Bloch equations have proven to be in inorganic ones.

Quantum Monte Carlo simulations of Realistic Semiconductor Nanostructures

Prof. Ian Galbraith (Heriot-Watt)

Recent progress in growth of semiconductor materials has enabled the growth of semiconductor quantum dots and rings. Understanding the behaviour of electrons and holes confined to these nanostructures requires sophisticated modelling. In such dots, electrons (and holes) are confined into a small volume (having ~10nm radius) which determines the quantum states which the electrons can occupy. Similarly quantum rings can be grown (like a polo-mint!) which also display very novel physical properties. Experiments on such dots and rings are underway (in the Nano-optics group Prof. Richard Warburton here at Heriot-Watt) but the results require sophisticated microscopic modelling before they can be reliably interpreted. What makes this fascinating is that the electrons and/or holes interact strongly via the Coulomb interaction as well as being localized by the material structure. So a dot with two electrons inside shows a different energy-level structure than a dot containing only a single electron because of their mutual repulsion. From a practical point of view quantum nanostructures are widely used in making semiconductor lasers and are prime candidates for implementation of quantum information processing systems. As such, understanding the underlying physics of how electrons and holes behave in these dots is of both theoretical and practical importance. There are many energy scales in the problem which are rather similar; the Coulomb interaction energy between two carriers in the dot is about 30meV, the thermal energy at room temperature is about 25meV, the phonon energy of lattice vibrations is about 35meV and the separation of the energy levels for a single carrier in the dot (like the particle-in-a-box problem) is also about 25meV. So we need a nonperturbative technique which can handle these interactions without approximation and deal with the complex geometry of the quantum dot or ring.

One technique which meets these conditions is Path integral - Quantum Monte Carlo (PI-QMC), a powerful tool used for solving many-body quantum problems in a wide range of physical situations from Liquid He to semiconductors. Based on Richard Feynman’s Path integral formulation of quantum mechanics it involves the numerical sampling of interacting quantum trajectories for each particle. Specifically this project will build on our existing PI QMC simulations for a few particles with simple interactions to move them into the realm of more realistic simulations. To achieve this we need to make progress in two areas. Firstly when two indistinguishable particles (say two electrons with the same spin) are being modelled the overall wavefunction of the system must be antisymmetric in the exchange of the co-ordinates of the two particles. However this leads to a numerical difficulty, called the fermion sign problem, as the contribution of a given path and its antisymmetric partner have opposite signs and almost (but not quite) cancel. One of the aims of this project would be to address this issue. Secondly, and related to the above, the sampling of the differing paths is most efficiently done using non-trivial changes to the locations of more than one particle at a time. This leads to a better coverage of the required ‘path-spac’ than simple schemes. The second aim of the project would be to explore the influence of such approaches on the quantum dot simulations. Tackling both of these issues will involve understanding the theoretical foundations of the QMC method and computer coding of the simulations, where possible exploiting parallel processing on our new 320 CPU cluster. All the while we would expect to be in close collaboration with the experimental team in helping to interpret their results and in suggesting fresh experiments.

Hole spin in semiconductor quantum dots

Dr. Brian Gerardot, Dr. Paul Dalgarno and Prof. Richard Warburton (Heriot-Watt)

Spin, a fundamental quantum phenonenom, is crucial to many properties of materials such as semiconductors. Manipulating individual spins is now becoming possible experimentally and the exquisite sensitivity is throwing new light onto old problems. Furthermore, a highly coherent spin is a natural qubit with applications in quantum information processing: in the search for a qubit in the solid-state, a single spin confined to a quantum dot is so attractive as spin interacts only weakly with the phonons, the traditional source of dephasing in the solid-state. However, once the interaction with the phonons has been suppressed, the interaction of the spin with the nuclear spins in the host material, the hyperfine interaction, becomes important. For an electron spin, the hyperfine interaction is the main stumbling block. An alternative is to use not an electron but a hole which has a p-like atomic wave function, conveniently going to zero at the location of the nuclei. The project will probe and manipulate single hole spins in single quantum dots, using optical techniques to write and read-out spin information. The key goal is to demonstrate coherent manipulation of a hole spin.

Experimental and Theoretical Investigation of Spatially Modulated Magnetic Phases Near to Quantum Criticality

Dr Andrew Green (St. Andrews) and Prof Andrew Huxley (Edinburgh)

The possibility of magnetic spin-crystals formed by the superposition of helical spin modulations with different wave-vectors has been a subject of much recent experimental and theoretical work. Signatures of phases with this property have been found in an array of materials including MnSi and Sr3Ru2O7. On the theoretical side, there are several ways in which such states might form. These include the formation of spiral modulation due to a Dzyalosinskii-Moriya spin-orbit interaction in itinerant magnets, residual, small-wavevector nesting due to the electron dispersion in a lattice [1,2] and from competing interactions that can give rise to a series of transitions forming a Devil's Staircase [3]. Perhaps the most intriguing suggestion - and one that has most captured the imagination of condensed matter theorists of late - is that an itinerant system on the brink of a quantum phase transition might possess an intrinsic instability to the formation of modulated magnetic phases [4]. In any particular material, one or more of these effects may operate with the possibility of a complicated interplay between them.

This project aims to investigate the phenomenon of spatially modulated magnetism from both an experimental and theoretical perspective. We will use techniques of quantum many-body physics and field theory to investigate the possibility of spatially modulated magnetism in real systems. These investigations will be carried out in concert with neutron scattering experiments to provide inspiration for and validate this theory. The experimental part will include growing the crystals for these experiments as well as performing the measurements. We anticipate that a student will spend approximately 2/3 of their time on theory and 1/3 on experimental work, working both in Edinburgh and St Andrews as well as at international facilities.

[1] A. M. Berridge, A. G. Green, S. A. Grigera and B. D. Simons "A Magnetic Analogue of the of the FFLO state: Inhomogeneous Instabilities Near to Tricritical Points" Physical Review Letters 102, 149903 (2009).
[2] G. J. Conduit, A. G. Green, and B. D. Simons, "Inhomogeneous phase formation on the border of itinerant ferromagnetism" Physical Review Letters 103, 207201 (2009) [spotlighted in Physics 2, 93 (2009)]
[3] P. Bak & J. von Boehm, "Ising model with solitons, phasons, and 'the devil's staircase'", Phys Rev B 21 5297 (1980)
[4] J. Rech C.Pépin, V.Chubukov, "Quantum critical behaviour in intinerant electron systems: Eliashberg theory and instability of a ferromagentic quantum critical point" Phys Rev B 74 195126 (2006)

Hot Dense Hydrogen

Dr. Eugene Gregoryanz (Edinburgh)

The behaviour of hydrogen, the most abundant element in the Universe, at high densities has been widely explored in recent years both experimentally and theoretically. These studies have yielded a wealth of information on the material, but detailed static compression experiments have generally been limited to low-temperatures (<300 K) and maximum pressures of ~300GPa. However, there are now numerous questions regarding the behaviour of hydrogen at high pressures and temperatures, the answers to which will have important implications for both fundamental physics and planetary science. In this project, optical spectroscopy will be used to constrain the behaviour of H₂ (D₂) at extreme compressions and elevated temperatures, searching for the predicted transition to a metallic superfluid state.

Nanofabrication as a Route to Ultrahigh Pressures

Dr. Eugene Gregoryanz (Edinburgh)

Pressures above 1 million atmospheres (100GPa) can be generated routinely using a diamond anvil pressure cell. The current maximum pressure obtained with such a device is 400GPa, but pressures well beyond that might be generated by using nano-fabrication techniques to miniaturise both the diamond anvils and sample. In this project, focused ion beam technology will be used to "sculpt" diamond anvils to micron dimensions to achieve pressures beyond those currently achievable. The new technology will be used to study simple systems e.g. H₂, Li, Na, N₂, and O₂ to explore phenomena at extreme densities.

Next generation superconducting single photon detectors

Dr. Robert Hadfield and Prof. Richard Warburton (Heriot-Watt)

Quantum information science and technology, where information is encoded and manipulated on single quantum objects such as photons, is a field which promises to revolutionize computing and communications in the 21st century. Advanced quantum information applications place stringent demands on detector technologies. Superconducting nanowire single photon detectors offer improved performance over conventional photon-counting technologies. The goal of this PhD project is to create a new generation of superconducting nanowire single photon detectors with near-unity efficiency and photon number resolution. This challenging project will encompass device design, fabrication and low temperature nano-optical testing. The research will be carried out in a under the supervision of Dr Robert Hadfield and Professor Richard Warburton in collaboration with UK and international partners (University of Cambridge, UK and MIT, USA).

Exotic Kondo effects in tunable nanostructures

Dr. Chris Hooley (St. Andrews)

When a magnetic impurity (such as iron) is placed in a good metal, it causes anomalously strong scattering of the conduction electrons below a certain characteristic temperature. This effect is called the Kondo effect, and the associated temperature is therefore called the Kondo temperature. We now understand that what the magnetic impurity is trying to do is to bind the conduction electrons into a spin-singlet, and at sufficiently low temperatures, this is achieved. In 1998, the effect was observed for the first time in nanophysical systems, with a quantum dot playing the role of the magnetic impurity, and the two electrical leads playing the role of the conduction sea. Quantum dot systems are, however, much more tunable than the metals and impurities offered to us by chemistry: even the dimensionality of the leads can in principle be altered. This is an exciting prospect, since we know that in one dimension the interacting electron system adopts an unusual strongly correlated state called a Luttinger liquid, and that the theory of the Kondo effect with Luttinger liquid leads is quite different to that in the normal metal case. This theoretical project aims to address the following questions:

• Can the Luttinger-liquid Kondo effect be realised in quantum dot systems?
• How do its properties relate to those of the soft-gap Anderson model?
• What is its behaviour at bias voltages well above the Kondo scale?
• Does it have a critical point, and if so, can this be characterised?

Established relations with several experimental groups active in the field (e.g. the Grayson group at the Walter Schottky Institute, the Marcus group at Harvard, and the Kouwenhoven group at Delft) are expected to provide fruitful and up-to-date experimental information. The majority of the work will consist of pen-and-paper calculations, perhaps supplemented by some computational analysis.

Non-equilibrium and non-adiabatic effects in Bose-Einstein condensates

Dr. Chris Hooley (St. Andrews)

When a gas of bosonic atoms is cooled to very low temperatures, it undergoes a phase transition in which a macroscopic fraction of the atoms enters the lowest single-particle state of the system. This effect, called Bose-Einstein condensation, was predicted in 1924, but not directly observed until 1995 - the main difficulty being, of course, that gases don't tend to stay gaseous down to microkelvin temperatures unless cooled with great care! To this end, ingenious devices involving electromagnetic trapping and laser- and evaporative cooling have been devised. Recent experiments involve subjecting the atom cloud to laser standing waves (so-called “optical lattices”) as well as the background trapping potential that stops the atoms from leaving the system. One of the most exciting opportunities presented by these set-ups is the opportunity to study quantum processes far from equilibrium: since the characteristic time-scales of the Bose gas are rather long, it's easy to make a “sudden” change in the laser field. Indeed, the study of such non-equilibrium effects is vital, as they are in fact the key to measuring the properties of such gases in the first place (via “time-of-flight” experiments). This theoretical project aims to put our understanding of non-equilibrium processes in trapped Bose- and Fermi gases on a firmer footing, addressing such issues as:

• atom-atom correlations during cloud expansion;
• anti-bound states from sudden quenching of the condensate;
• growth models for low-temperature Bose-Einstein fluids;
• measuring the BCS state for fermions.

Established relations with several experimental groups active in the field (e.g. the Inguscio group in Florence, the Hinds group at Imperial, and the Schmiedmayer group at Heidelberg) are expected to provide fruitful and up-to-date experimental information. The majority of the work will consist of pen-and-paper calculations, perhaps supplemented by some computational analysis.

New Quantum states in perfectly stoichiometric high-quality single crystals

Prof Andrew Huxley and Dr D. Sokolov (Edinburgh)

Despite many of the complexities of real metals a description of their electronic and magnetic properties in terms of a collection of weakly-interacting identical free-electron-like particles usually works well at low enough temperatures. This is because the number of electrons excited above the Fermi surface becomes small as the temperature is decreased. However when metals are tuned to points known as quantum critical points the number of low energy excitations no longer vanishes sufficiently rapidly with decreasing temperature and it is believed that a unique ground state can only be achieved if the electrons assemble into new types of coherent quantum states. The formation of these coherent ground states, however, requires that the metals are defect free over the length scales characterising these more complex wavefunctions. The project aims to discover experimental examples of such states.

This will be achieved by developing innovative apparatus for tuning the composition of single crystals to achieve the exceptional degree of materials perfection required. These crystals will then be studied at very low temperatures, both in-house with our high-field millikelvin dilution refrigerator and with central facilities located in the UK, France and Germany.

The project offers the opportunity to gain skills in materials physics and a wide range of measurement techniques, in designing and building new apparatus, and in investigating fascinating fundamental physics. These skills are highly valued by employers in industry and for academic research.

Neutron and X-ray scattering studies of novel magnets and unconventional superconductors

Prof. Andrew Huxley and Dr D. Sokolov (Edinburgh / St. Andrews)

Near the absolute zero of temperature where magnetic order is suppressed by pressure or magnetic field, new exotic states of matter such as unconventional superconductivity, modulated spin and charge orderings may form. However, interactions that drive formation of such states remain poorly understood. The project is to study the dynamics of the electronic and magnetic excitations with different scattering methods.

Neutron scattering is a direct probe of magnetism and will be used in conjunction with high pressure and/or high magnetic field to study magnetism in solids. Charge and orbital orderings will be probed with X-ray scattering. The project aims to establish how novel magnetic and electronic ground states are formed from studying the spectra of excitations and their modification when the ground state changes. These studies will build on our continuing work on UGe2, URhGe, and other ferromagnets.

The experimental work will comprise synthesis of single crystals of 4f and 5f electron materials using Czochralski and Bridgman methods, subsequent neutron diffraction and inelastic neutron scattering at extremes of pressure and magnetic fields; work to be performed at the Rutherford Appleton Laboratory in Oxfordshire, FRMII in Germany and X-ray magnetic circular dichroism measurements at ESRF, France. The student will become expert in crystal growth methods and various state-of-the-art neutron and X-ray scattering techniques in combination with high-pressure instrumentation.

Investigating the interplay of magnetism and superconductivity in thin film devices using advanced neutron, muon and synchrotron techniques

Prof. Steve Lee (St. Andrews)

Nanomagnetic devices are present in many high technology systems, a classical example being hard disk drives, where they find use in both the recording media and the magnetoresistive read heads. There is currently an enormous effort in the area of ‘spintronics’, where idealized thin film structures are fabricated to create spin-polarised currents that could find application in a new generation of electronic devices. These devices, such as ‘spin valves’, typically combine juxtaposed layers of magnetic metals and normal metals each of typical thickness a few 10’s of nanometers.

In this project we extend the notion of spintronic devices to include magnetic and superconducting elements. Superconductivity and magnetism are frequently mutually exclusive and in instances where they do coexist in close proximity this usually implies some exotic ground state for the system. In superconducting spintronic devices one could envisage the magnetic switch controlling the superconducting wavefunction (amplitude and possibly phase) that could used to exploit quantum properties in future electronics and computing. We have also recently demonstrated that the superconducting state can also influence the magnetic state of the system. We are using traditional neutron techniques combined with a completely novel and unique technique, the low energy muon (LEM) facility at the Paul Scherrer Institute (PSI), Switzerland, to study the delicate interplay of magnetism and superconductivity in superconducting spin-valve and related systems. We have already been able to demonstrate the coexistence of superconductivity and a spin density wave using this approach, which is attracting attention from theorists working in this area.

The PhD position offers a great opportunity for a highly motivated student to receive outstanding training in advanced techniques at some of the world’s leading central facilities in France, Switzlerland, Germany and the UK. The work is carried out in collaboration with the world renowned group in Leiden headed by Professor Jan Aarts. The work is currently supported under an EU facilities user programme at PSI and via the EPSRC direct access programme at the Institut Laue Langevin in Grenoble, France and at ISIS, UK. Further support is soon to be sought from the EPSRC to enlarge the scope of the programme.

Studying Magnetic Recording Media using Neutrons and Synchrotron Radiation

Prof. Steve Lee (St. Andrews)

We are currently working in a close collaboration with Hitachi Research Labs, San Hose, CA to look at the magnetic structure of magnetic recording media at the sub-10 nm length scale. Magnetic recording media, used in magnetic disk drives, are of extreme commercial and technological importance and lie at the centre of many common devices including computers, video recorders and ipods. The smallest functional magnetic element in these materials, the magnetic grain, is typically about 10 nm in diameter, yet there are very few techniques that can probe the magnetic structure at these length scales. Among these are neutron and synchrotron radiation techniques. The group at St Andrews has a long reputation of carrying out high quality research using some of the world's best facilities for condensed matter research. This includes the use of international facilities for the generation of neutrons and muons such as the Institut Laue Langevin in Grenoble, France, or the Paul Scherrer Institute, Switzerland. This project with Hitachi is supported by an EPSRC grant of £420K over the next three years which includes a PhD project studentship which will be available from early 2007. The student will work closely with an experienced post-doctoral researcher employed on the same grant. We aim to bring the scientific rigour and attention to detail that we use in our fundamental research to this more applied project. This has already brought us to the forefront of worldwide research in this area and there is great opportunity for the further exploitation of the approaches we have developed. We are currently working on the very latest research materials from Hitachi and thus have the possibility of making valuable contributions to future materials development that could impact directly on technology.

The PhD position offers a great opportunity for a highly motivated student to receive outstanding training in advanced techniques at some of the world’s leading central facilities in France, Switzlerland, Germany and the UK. There also exists the possibility to spend periods at the Hitachi research centre in San Jose.

Gas Hydrates

Dr. John Loveday (Edinburgh)

Under modest pressures many simple gases form solid hydrates when mixed with water. As one example, a third of the Earth's methane is found at the bottom of the oceans in the form of methane hydrate. The gas hydrates are often important for models of the outer planets and their satellites and may have potential technological applications for carbon sequestration and gas transport. They are also models for the study of hydrophobic interactions which are important in the understanding of protein folding. This project aims to explore the structural systematics of gas hydrates at high pressure and to understand the factors determining hydrate stability. Experiments will be done on neutron and x-ray sources in Oxfordshire and in Grenoble, France.

Ice and Water

Dr. John Loveday (Edinburgh)

Neutron diffraction will be is used to investigate a proposed new form of ice at very high pressure and temperature, and what form of water it melts to under these extreme conditions. Experiments will be done on the UK neutron source in Oxfordshire, and possibly also on the European neutron facility in Grenoble, France. Results will be relevant both to understanding ice and water in a fundamental way and also to the physics of ice in planets and satellites.

Planetary Mineralogy

Dr. John Loveday (Edinburgh)

In the context of the outer solar system, the planet forming 'minerals' are hydrogen, helium, water, ammonia and methane. The high pressure properties of these systems and their mixtures is thus crucial for models of the evolution of planets such as Uranus and Neptune and large satellites such as Ganymede, Titan and Triton. This project will explore the high pressure structures of systems such as methane, ammonia-water, ammonia, etc using x-rays and neutrons. Experiments will be done on neutron and x-ray sources in Oxfordshire and in Grenoble, France.

Quantum Effects in Hydrogen

Dr. John Loveday (Edinburgh)

Hydrogen is the simplest of elements and one of the few systems where quantum behaviour has strong effects on the crystal structure. These quantum effects are of considerable interest to theoretical modellers since they provide a rigorous test of modelling techniques where both the electrons and nuclei are treated as quantum objects. However, the crystal structure of hydrogen remains very poorly characterised. We aim to use neutron diffraction (the only technique able to determine the crystal structure of hydrogen accurately) to explore the crytal structure of hydrogen at low temperatures and high pressure. Experiments will be done on the UK neutron source in Oxfordshire, and possibly also on the European neutron facility in Grenoble, France.

Mesoscopic unconventional superconductors and Fermi liquids

Prof. Andy Mackenzie (St. Andrews) and Prof. Amir Yacoby (Harvard)

In this project, we aim to bridge the gap between two fields in which huge progress has been made over the past twenty years. In mesoscopic physics, the aim is to work with samples that are specially fabricated so that their physical size becomes comparable with one or more of the fundamental length scales of the underlying physics. In a metal this might be the mean free path, and in a superconductor it might be the coherence length or the penetration depth. So far, the vast majority of research into mesoscopic physics has been performed on traditional materials in which the electron-electron interactions are relatively weak. In parallel with these developments, equally rapid progress has been made on research into new materials with very strong electron-electron interactions, which lead to high quasiparticle masses and an exciting variety of metallic, superconducting and magnetic ground states. For technical reasons the two fields have advanced in parallel, with little cross-fertilisation of ideas and techniques. The goal of this jointly supervised project is to combine the different expertise of our two groups to bring strongly interacting electrons into the mesoscopic regime. You will work both in St Andrews and at the spectacular new Harvard Nanoscience Center, performing pioneering experiments on the fabrication and measurement of correlated electron mesoscopic devices.

Quantum phase transitions in two dimensional electron gases

Prof. Andy Mackenzie (St. Andrews) and Prof. Amir Yacoby (Harvard)

In recent years there has been a resurgence of interest in strictly two-dimensional electron systems. The two-dimensional electron gas (2DEG) first came to prominence in semiconductor devices, on which famous discoveries such as the Integer and Fractional Quantum Hall Effects were made. Now, because of the discovery that 2DEGs exist in other material systems such as graphene and oxide multilayers, there is the promise of discovering rich new physics. Graphene is proving to be particularly interesting, with coupled bilayers showing a rich variety of quantum phases and phase transitions. It is possible that there are similarities with the behaviour seen in bulk materials such as Sr3Ru2O7 which consist of stacks of weakly coupled bilayers. This project is to study and understand the fascinating phase diagrams that can arise in such systems, and to assess the role that quantum fluctuations play in determining their fascinating properties. The work, which combines the expertise of two collaborating research groups, will be carried out both in St Andrews and at the new Harvard Nanoscience Center.

Superconductivity and Spin-Orbit Coupling in Sr2RuO4

Prof. Andy Mackenzie & Dr. Santiago Grigera (St. Andrews)

The superconductivity of Sr₂RuO₄ was discovered nearly fifteen years ago, but continues to be a major open topic. The symmetry of the superconducting state seems to be highly unusual, with pairing in the spin triplet channel, in analogy to that in the famous superfluid ³He [1]. The material also offers the intriguing possibility, long-term, of providing a platform for the implementation of exotic schemes for ‘non abelian quantum computing’ [2]. In order to tell whether that is an achievable goal, much more needs to be understood. Does the superconducting state contain the domains predicted by some theories and inferred from some experimental results? If so, can we find out how to control them? Can mesoscopic patterning be performed without destroying the fragile superconductivity? How big is spin-orbit coupling and what role does it play? As a first step to answering these questions, we have recently made what we believe to be the best single crystals ever grown of Sr₂RuO₄. These will enable us to instigate some ambitious experiments both in-house and with our collaborators in Bath, Cambridge, Harvard and Kyoto. The project will involve working on one or more of the topics listed above, according to unfolding priorities.

[1] A.P. Mackenzie and Y. Maeno, Rev. Mod. Phys. 75, 657 (2003)
[2] For a series of on-line talks on the issue see: online.itp.ucsb.edu/online/chiralsc_m07

Direct measurement of the entropic landscape in quantum critical systems.

Prof. Andy Mackenzie, Dr. Santiago Grigera, Dr. Andreas Rost (St. Andrews)

Quantum criticality is one of the most intriguing fields of research in modern condensed matter physics. A quantum critical point is a continuous phase transition for which the phase change is driven by quantum rather than thermal fluctuations, and the approach to quantum criticality has proven to be an effective ‘breeding ground’ for the formation of novel quantum order [1]. In a recent breakthrough during the PhD work of Andreas Rost, we have shown that precise measurement of the magneto-caloric effect can be used to deduce the full magnetic field and temperature dependence of the entropy of a system on the verge of quantum criticality, making far fewer assumptions than are necessary if deducing it purely from the specific heat. The entropy is arguably the most fundamental of all thermodynamic potentials, so this gives us access to a class of information not previously attainable experimentally. So far, we have only studied Sr₃Ru₂O₇ using our new technique. This project will involve work on other known quantum critical systems, and probably also the extension to entirely new ones.

[1] A.P. Mackenzie & S.A. Grigera, Science 309, 1330 (2005) and references therein.

Electrical Transport and Calorimetry in Sr3Ru2O7 in Vector Magnetic Fields

Prof. Andy Mackenzie, Dr. Santiago Grigera, Dr. Andreas Rost (St. Andrews)

The material at the heart of this project, Sr₃Ru₂O₇, is one of the most fascinating in condensed matter physics. Over a decade of study, our collaboration has succeeded in growing the world’s purest single crystals of it, and discovering that in the very best crystals, a new quantum phase forms at high magnetic fields [1]. This phase appears to have the characteristics of an electronic nematic liquid crystal of the sort predicted in the late 1990s [2], with the properties making a transition from four-fold to two-fold symmetric over a narrow range of applied field. The observations to date raise a number of intriguing questions about the behaviour of such systems, which can only be answered by study in rotating, or ‘vector’ magnetic fields. In a major project funded by the UK’s Engineering and Physical Sciences Research Council, we have commissioned the design and construction of the world’s largest three-axis vector magnet, which is scheduled for delivery in early summer 2009. This project will involve using the unique new capability to perform both transport and thermodynamic measurements as the field angle is rotated relative to the crystal axes of the sample.

[1] R.A. Borzi, S.A. Grigera, J. Farrell, R.S. Perry, S. Lister, S.L. Lee, D.A. Tennant, Y. Maeno & A.P. Mackenzie, Science 315, 214 (2007).
[2] S. A. Kivelson, E. Fradkin, V. J. Emery, Nature 393, 550 (1998).

Search for Novel Metamagnetic Quantum Criticality and Phase Formation

Prof. Andy Mackenzie, Dr. Andreas Rost (St. Andrews)

In recent years there has been a resurgence of interest in the phenomenon of itinerant metamagnetism, in which metallic systems undergo a strong, non-linear change in magnetic moment in an applied magnetic field. A number of interesting observations have been made, but arguably the most prominent discoveries are those of an electronic liquid-crystal like phase in Sr₃Ru₂O₇ [1] and re-entrant superconducitivity in URhGe [2]. Observations like these motivate the search for other materials displaying metamagnetism that might be driven quantum critical. This is essentially a chemical physics PhD project, involving decisions about material classes to study, chemical synthesis of appropriate materials, high purity crystal growth and, ultimately, low temperature measurement.

[1] R.A. Borzi, S.A. Grigera, J. Farrell, R.S. Perry, S. Lister, S.L. Lee, D.A. Tennant, Y. Maeno & A.P. Mackenzie, Science 315, 214 (2007)
[2] F. Lévy, I. Sheikin & A.D. Huxley, Science 309, 1343 (2005).
and references therein

Computational Physics of Liquid Crystal Composites

Dr. Davide Marenduzzo and Prof. Mike Cates (Edinburgh)

Liquid crystals are a fascinating example of soft materials. Like liquids, they flow and may be poured from one vessel to another. Like solids, they possess long range orientational order. Common examples are nematic liquid crystals (in which molecules align along a preferred axis) and cholesterics (in which this ordering axis acquires a spatial twist). Both are used in optical displays. The project is to to devleop simulation code to examine a new class of soft materials. Edinburgh physicists have developed lattice Boltzmann algorithms for large-scale numerical simulations of the hydrodynamics of liquid crystals, and used this to study permeation flows and the exotic ‘blue phase’ [1]. We have also studied binary mixtures of simple fluids, and colloids (including magnetic colloids) in single and binary solvents; this has led to the prediction by simulation of a completely new material [2] which was then found experimentally by our collaborators [3]. In progressing this leading edge work to the next stage, you will exploit our existing codes as well as develop new ones, aiming to investigate a new class of soft materials in which colloids (possibly magnetic) are dispersed in liquid crystals, and/or binary fluid mixtures are formed in which one of the two fluids is liquid crystalline. Such materials should allow new levels of control over properties and unusual responses to fields and flow. There is so far only a small experimental literature on these composite systems [4] and virtually no simulation work. The field is open for new discoveries: our in-house experimental collaborators [3,4] await our findings with interest!

[1] Rheology of Cholesteric Blue Phases. A Dupuis, D Marenduzzo, E Orlandi and J M Yeomans, Physical Review Letters, 95, 097801 (2005)

[2] Colloidal Jamming at Interfaces: A Route to Fluid-Bicontinuous Gels. K Straftord, R Adhikari, I Pagonabarraga, J-C Desplat and M E Cates, Science 309, 2198-2201 (2005); E Kim et al, Langmuir 24, 6549-6556 (2008)

[3] Bicontinuous Emulsions Stabilized by Colloidal Particles. E M Herzig, K A White, A B Schofield, W C K Poon and P S Clegg, Nature Materials 6, 966-971 (2007)

[4] Network Formation in Colloid-Liquid Crystal Mixtures, J Cleaver and W C K Poon, J. Phys. Condensed Matter 16, S1901-1909 (2004)

High-Pressure Alchemy: Turning Simple Metals into Complex Non-Metals

Prof. Malcolm McMahon (Edinburgh)

At ambient conditions, the group I elements (Li, Na, K, Rb Cs) are regarded as “simple metals” whose single valence electrons have only a weak interaction with the atomic core. Under pressure, however, the same simple metals are found to undergo transitions to very complex forms, which calculations suggest may be semi-metallic, or even semi-conducting. In this project, you will use nano-fabrication techniques to make "designer diamond" anvils, which will be used to measure the resistivity of alkali metals to extreme pressures. Changes in resistivity will be correlated with changes in crystal structure, determined using x-ray diffraction at the synchrotron radiation sources Diamond and the ESRF.

The Theory of Superconductivity on the Border of Charge Ordering

Dr Philippe Monthoux (Edinburgh)

Charge Ordering, a long range order of different metal oxidation states, is implicated in many interesting electronic phenomena, for example, the low temperature Verwey state in magnetite, Fe3O4, colossal magnetoresistances and phase separation phenomena in magnanese oxide perovskites, and superconductivity in doped BaBiO3 and the layered cuprates. Although charge order is an apparently simple phenomenon, there is little theoretical understanding in comparison to the descriptions that have been developed for phenomena such as magnetism and superconductivity. Recently, Monthoux and Attfield (manuscript in preparation) proposed a model Hamiltonian which at the Hartree-Fock level of approximation reproduces the salient features of both the observed charge disproportionated (e.g BaBiO3) and semivalent (e.g La0.5Ca0.5MnO3) charge order in oxides. These result from the interplay between electron-electron correlations and local electron-lattice softening. The model predicts competing magnetic, charge ordered, and magnetic charge ordered ground states.This project aims to see whether this model can also lead to superconducting instabilities, and whether it can describe the salient features of superconductivity on the border of charge ordering as experimentally observed in potassium doped BaBiO3 for example. The insights provided by this theoretical study could be used to guide the search for new materials with interesting electronic properties, in collaboration with the group of Prof. J.P. Attfield.

Novel condensed matter systems with cold atoms

Dr. Patrick Ohberg (Heriot-Watt)

At temperatures on the order of a nano Kelvin, strongly correlated systems of bosons and fermions are completely dominated by quantum effects. In this project we will theoretically investigate strongly correlated bosons and fermions. The system we are interested in is very peculiar and can be best made using interacting ultracold atoms. It is charge neutral, hence it will not react to a magnetic field the way an electron would do. We will, however, optically induce an effective gauge potential. With the optically prepared quantum state we can study a number of interesting scenarios. The most striking effects are seen if we prepare a spin system which is defined by an effective two-level system which couples to a matrix gauge potential. Now we have system which is spin-orbit coupled; the spin rotates depending on in which direction the atoms are moving. This is a non-Abelian effect, and truly unchartered territory. The spin-orbit coupled quantum system is for instance believed to give rise to a highly degenerate groundstate. This leads us to consider exotic many-body systems which are strongly correlated.

This project ties together a number of phenomena from a broad range of physical scenarios ranging from condensed matter physics, mathematical physics, and quantum optics. Our goal is to understand novel strongly correlated many-body quantum states emerging from the light-matter interaction and design experimentally viable schemes for testing the frontiers of our understanding of the foundations of quantum physics.

5d Transition Metal Oxides

Dr. Robin Perry (Edinburgh)

The project aims to extend our success in materials preparation of 4d metal oxides to look at 5d compounds, which potentially offer a richer interplay of electronic energy scales. The project will work on crystal growth with a new image furnace in tandem with a novel way to control the oxidation state of the 5d atoms to grow crystals of the compounds we expect to show the most interesting physics. The crystals will be investigated to look for new quantum ordered states in house, at central facilities and through international collaborations including with leading Japanese groups. Progress in producing the best quality crystals worldwide of 4d metal oxides such as Sr₃Ru₂O₇ has directly led to the discovery that mysterious quantum phases appear under magnetic field in only the cleanest crystals. The project will explore whether similar physics occurs for 5d systems or whether differences in band structure lead to new phenomena. More information is available on the SUPA Quantum Ordering Group website.

Bringing Order to a ‘Zoo’ of Colloidal Gels

Prof. Wilson Poon (Edinburgh)

Sticky colloidal particles aggregate. When conditions are right, they can form a stringy, space-spanning structure — a ‘gel’ — which behaves in many ways like a solid even though the sample may contain more than 90% liquid. Many personal care products and foods (e.g. yoghurt) are such gels. Recent theoretical advances have suggested that gels can form through a variety of ‘kinetic pathways’, the precise one being chosen being sensitively ‘tuneable’ by varying external conditions. Using a combination of experimental techniques, including microscopy and mechanical measurements, you will test these theoretical ideas in a very well characterized ‘model colloid’ developed in Edinburgh (and now adopted by many groups worldwide). There may be opportunities to work with various industrial partners.

The rheology of colloids dispersed in liquid crystals

Prof. Wilson Poon and Dr. Tiffany Wood (Edinburgh)

When colloids are dispersed in liquid crystals, they form materials with unusual characteristics that are qualitatively different to the behaviour found when the particles are dispersed in simple liquids. In this project rheological measurements will be performed to quantify the flow properties of these materials and identify novel (and perhaps applicable) properties.

Preliminary measurements show (see photograph) that composites made with large (> 1 micron) particles display tacky behaviour at particle volume fractions of around 55%. There are also indications that this tacky behaviour occurs over a broader region of volume fractions for smaller particles. The reasons for this behaviour are not yet understood. Making progress on this and other fundamental questions may lead to the development of new generations of optically-tuneable stretchy materials.

Category: Experimental Soft Condensed Matter

Exciton Diffusion in Organic Semiconductors

Prof. Ifor Samuel (St. Andrews)

The discovery of semiconducting properties in organic materials has opened major new directions in semiconductor physics. Organic semiconductors combine the simple fabrication and tuning of properties that is typical of plastics with novel optoelectronic properties useful for devices such as light-emitting diodes and solar cells. The low-dimensional nature of these materials means that excitons (electron-hole pairs) are strongly bound even at room temperature and play a very important role in their physics. Whilst charge transport has been widely studied, exciton transport has been largely overlooked. We have now developed techniques based on time-resolved spectroscopy that allow the measurement of exciton diffusion. We now wish to apply them to understand the physics of exciton diffusion and the factors controlling it. A breakthrough in this field could in turn lead to a breakthrough in the efficiency of organic solar cells.

Ultrafast Photophysics of Organic Semiconductors

Prof Ifor Samuel (St. Andrews)

This project will explore the physics of remarkable plastic-like semiconductors, such as light-emitting polymers. These materials are model one-dimensional systems and this strongly influences their physics – for example it means that excitons are strongly bound and that there is a substantial distortion of the material when it is excited. The purpose of this project is to study the nature of the excited states in these materials and how they evolve when the sample is excited by light. The initial rearrangement of the molecules occurs on a timescale of 100 femtoseconds. Remarkably we can make measurements on this timescale using advanced femtosecond lasers. We wish to explore how the excited states form and then decay, and how these processes relate to the structure of the material. The results will help understand light emission and amplification, and complementary theoretical work is underway at Heriot-Watt University by Prof. Ian Galbraith.

Quantum electronics with graphene

Dr. Misha Titov (Heriot-Watt)

Graphene is a two dimensional crystal of carbon that has a surprising chemical stability and an exceptionally small number of defects. Nice graphene flakes can be found among the traces left by your pencil on a piece of paper, but it is quite difficult to find them. That's why the first graphene samples have been singled out only recently in 2004 in the University of Manchester.

Graphene has unique physical and chemical properties. In fact, it has a great potential to ignite a new industry of graphene-based electronics. Some elements, such as ultra-fast graphene transistors and molecular sensors, have already been realized. Graphene is currently the focus of intense world-wide research, but many of its peculiar electronic properties are not yet understood.

Two theoretical PhD projects are offered with the emphasis on graphene electronics. One project concerns the quantum charge transport in graphene that is described by the Dirac rather than Schrodinger equation. Another project is devoted to electronic properties of graphene-based superstructures that can be created by the controlled deposition of molecules on the graphene surface. The theoretical questions addressed in the projects are of both fundamental and practical importance. The projects involve close collaboration with world-leading experimental groups in Europe.

Magnetic measurements to probe unconventional superconductors

Dr Ed Yelland and Prof. Andrew Huxley (St. Andrews)

Magnetism and superconductivity are intimately connected in many so-called heavy fermion metals. A particularly dramatic case is URhGe, where two distinct superconducting regions exist – one coexisting with ferromagnetism, and the other at extremely strong applied magnetic fields that are sufficient to destroy conventional forms of superconductivity. This project will involve developing sensitive magnetic measurement apparatus that will operate at extremes of low temperature, high magnetic field and high pressure, and apply them to study URhGe and other related materials. The aims are both to gain a deeper understanding of how magnetic pairing may lead to superconductivity and to drive the search for new superconducting materials. The project could be based in either St Andrews or Edinburgh.

The project is an integral part of a major research effort to study quantum criticality and unusual quantum ordered phases using a variety of magnetic, electrical and thermal measurement techniques. The apparatus in St Andrews includes a state-of-the-art dilution refrigerator (commissioned December 2007) with a base temperature 10 millikelvin and equipped with a 17 tesla magnet, that will allow coverage of a wide region of experimental parameter space, including applied pressures up to 100 kbar.

The focus for the project is on magnetic measurements including torque magnetometry, field gradient magnetometry and a.c. susceptibility. By combining torque and field-gradient results, the vector magnetic moment can be determined as a function of magnetic field and its angle to the crystallographic axes. This will allow a complete phenomenological (Ginzburg-Landau) description of the magnetism close to the superconducting phase to be constructed, and will provide detailed information about the nature of the magnetic interactions that are important for superconductivity. Another important component of the work will be to use quantum oscillations in various magnetic quantities to study the Fermi surface and how these change approaching and crossing quantum phase transitions.