Theory of Condensed Matter
TCM and CDT graduate admission web pageshttp://www.tcm.phy.cam.ac.uk/vacancies/postgrad.html
https://www.csc.cam.ac.uk/academic/cdtcompmat
Ultracold atomic gases
Matter doesn't have to be dense to condense. One of the frontiers ofmodern condensed matter physics is the study of gases of atoms amillion times thinner than air. At sufficiently low temperatures(microkelvin!), the wavelength of the atoms exceeds the interparticleseparation and the properties of the gas are determined by quantummechanics. This radical departure from classical behaviour is typified by a BoseEinstein condensate,which existed only as a textbook example for more than seventy years before its experimentaldiscovery launched this field in 1995.
Since then the list of phenomena observed some familiar from the solid state and the relativelybalmy world of low temperature physics, and others completely new hasgrown with the ingenuity of experimentalists. Changing scale by six ordersof magnitude is easier for theorists, of course. Researchers in TCM arestudying novel magnets, artificial gauge fields, and atomic analogues ofMott insulators and superconductors. There are close links to theexperimental groups in ultracold physics at the Cavendish and elsewhere inthe world.
Benjamin Beri, Gareth Conduit, Nigel Cooper, Austen Lamacraft, RichardNeeds, Andreas Nunnenkamp, and Ben Simons
Self assembly and physical complexity inbiology
The interface between statisticalphysics and biology is a rapidlygrowing area of research. An areaof particular interest is selfassembly, which is an ubiquitousphenomenon in biology. In thiscontext we study deterministicand non deterministic selfassembly of structures on alattice (top figure), the relationshipbetween assembly and structuralcomplexity, as well as theassembly and evolution of selfassembling structures in biology,such as protein complexes andviruses (lower figures).
Sebastian Ahnert and MikePayne
Self assembled lattice structures(top) and examples of selfassembly in biology: a virus(bottom left) and a proteincomplex (bottom right).
Biologicallyinspired computer modelling
Molecular Dynamics (MD) simulations are computationalexperiments that are used to investigate the relationshipbetween molecular structure, movement and function. Inclassical MD, interactions between atoms are approximationsbased on experimental data or more accurate, but also moretimeconsuming, quantum mechanical simulations. Thesesimplifications mean that we can model the behaviour ofsystems of many thousands of atoms, such as biomolecules,on nanosecond timescales.
One such example is the investigation of protein assembly onsolid surfaces, which is of great importance for the design ofmaterials for implantablebiosensors. The adsorptionbehaviour of the protein,collagen, on silicon devices isfound to depend strongly onthe hydrophobicity of thesolid surface.
Mike Payne
OverviewTheoretical condensed matter physics is aboutbuilding models of physical processes, often drivenby experimental data, generalising the solutions ofthose models to make experimental predictions,and transferring the concepts gained into otherareas of research. Starting at the first principlesmicroscopic level – with the Schrödinger equation –many properties of materials can now be calculatedwith a high degree of accuracy. We work on refiningand developing new calculational tools andapplying them to problems in physics, chemistry,materials science, and biology.
Solids also often show unusual collective behaviourwhich results from cooperative quantum orclassical phenomena. For this type of physics amore model based approach is appropriate, and weare using such methods to attack problems inmagnetism, superconductivity, nonlinear optics,atomic gases, polymers, and colloids.
Collective behaviour comes even more to the fore insystems on a larger scale. As examples, we workwith statistical mechanics on self organisingstructures in ‘soft’ condensed matter systems,nonlinear dynamics of interacting systems, andmodels of biophysical processes, from themolecular scale up to neural systems.
Professor Ben Simons
The life of cells
In adult organisms, many tissues aremaintained and repaired by stem cells, whichdivide and differentiate to generate morespecialised progeny. The mechanisms thatcontrol the balance between selfrenewal anddifferentiation of stem cells promisefundamental insights into the origin and designof multicellular organisms. However, stemcells are often difficult to distinguish from theirmore differentiated progeny, and resolving these mechanisms hasproved controversial and challenging.
The development of inducible genetic labelling methodologies hasprovided indirect access to cell fate characteristics of stem cells andtheir progeny in vivo. Drawing on a wide range of data, researchers inthe condensed matter theory group have employed methods of nonequilibrium statistical mechanics to address clonal evolution. Theseinvestigations demonstrated how scaling behaviour and spontaneouspatterning reveal stochastic stem andprogenitor cell fate. The results provideinsight into the molecular regulatorymechanisms controlling themaintenance and repair of adulttissues, and point at commonorganisational principles.
Ben Simons
Computational Simulation of Nanomaterials
Nanomaterials offer us exciting new ways to control material properties,by varying material attributes which are not available in bulk systems.For example, in nanocrystals, growth conditions can be tuned to varyparticle size, shape, surface terminations, composition and defectstructure, and in an aggregate of nanocrystals, alignment, mutualinteractions and interations with a solvent come into play.Nanomaterials are thus the key to making a success of many emergingtechnologies, in particular Photovoltaics and Photocatalysis, means ofturning light from the sun into other useful forms of energy. However,these many variable factors result in a vast phase space to explore inorder to design optimal materials for a given purpose. First principlescomputational simulation can be used to explore this space, enablingcomputational “experiments” to disaggregate competing factorsinfluencing a property, in a way which is impossible in real world tests.For example, by modelling TiO2 nanocrystals, an important componentin many photoactive devices, we can understand how to exposespecific surfaces to maximise their potential for photocatalysis.Possible projects include developing new simulation tools fortheoretical spectroscopy, which will greatly augment experimentalmethods, eg Electron Energy Loss Spectroscopy, by elucidating theorigin of spectral features.
Similarly, nanoscale thin films of ferroelectric and multiferroic materialsare very promising for nanodevices of different sorts, which can offermuch more efficient and energy efficient solutions to future electronicsand spintronics. These materials can be simulated and new materialscan be proposed from theory. Nanoconfined liquid water is alsosimulated with analogous techniques. It is of great importance forunderstanding the behaviour of water between hydrated objects inclose proximity, as encountered between organelles andmacromolecules in a living cell.
Emilio Artacho and Mike Payne
Nonequilibrium Physics
The notion of thermal equilibrium plays a crucial role in any attemptto understand the macroscopic properties of matter in terms of itsmicroscopic constituents. The fundamental reason that matter canbe characterised by certain variables (temperature, pressure,magnetisation, etc.) independent of its past history is that theequilibrium macrostate occurs with overwhelming probability in alarge system. Despite this, nonequilibrium states are an importantfeature of the macroscopic world. This may be because a systemhas not had time to forget its initial state: think of the growth of acrystal from a supersaturated solution, or the evolution of theuniverse after the Big Bang. Alternatively, a system may be sustained out of equilibrium by an externalsource of energy (as in a turbulent fluid) or low entropy (life on Earth!). Such behaviour is technologicallyimportant — a computer’s memory must not come to thermal equilibrium — and can occur in any system ofmany entities where collective behaviour can emerge — as in a traffic jam.
Researchers in TCM are exploring the nonequilibrium dynamics of defects in novel magnetic systems(Castelnovo), quantum systems of molecules, ultracold atoms and light (Cooper, Nunnenkamp), andclassical stochastic models that can mapped to quantum many body systems (Lamacraft).
Benjamin Beri, Claudio Castelnovo, Nigel Cooper, Austen Lamacraft, and Andreas Nunnenkamp
Frustrated magnetism
One of the most fascinating phenomena in condensed matter is the ability of strong correlations to give riseto phases that behave as vacua for new types of degrees of freedom not directly present in the microscopicconstituents of the system. These quasiparticles are not bound by the same laws of nature that constrainthe `real' elementary constituents. Examples include fractional electric charge in acetylene, spinchargeseparation in SrCuO2, emergent magnetic monopoles in spin ice (figure), and anyons with fractionalstatistics in topologically ordered phases of matter.
Frustration in magnetic systems has been fertile ground for these phenomena. The term "frustration"indicates the inability of a system to reach its lowest energy state where all interaction terms aresimultaneously minimised (e.g., ferromagnetic order). The variety of new phenomena that emerge infrustrated magnets, combined with the many experimental probes that have been developed for magneticsystems, continue to produce new and exciting physics both concerning thermodynamic as well as far fromequilibrium behaviours.
Spin ice materials are a notable recent example of this area of research,where frustration leads to an emergent gauge symmetry and magneticmonopole excitations at low temperatures. Several open questions remainto be addressed for instance, understanding how emergentquasiparticles behave out of equilibrium is key to investigate the intriguingpossibility of manipulating these exotic degrees of freedom into new kindsof currents and circuits for technological applications.
Claudio Castelnovo
A TiO2 nanocrystal,showing local orbitalsoptimised using theONETEP code. Use oflocal orbitals enablescalculations on verylarge systems (1000s ofatoms)
