A quantitative understanding of bonding in condensed matter systems demands a solution of the many electron problem. This course will show how the many electron problem can be mapped onto single electron problems in an approximate way (Hartree and Hartree Fock approximations) and a formally exact way (density functional theory and the Kohn Sham equations). Further, some of the methodology used to solve the Kohn Sham equations in complex systems will be described. In the last part of the lectures, some examples will be discussed, which show how electronic structure theory was able to explain some selected phenomena.
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Mesoscopic physics is the name given to electronic behaviour in solid state nanostructures that are so small that their size is similar to relevant characteristic length scales. Examples of such length scales include the elastic mean free path (which governs the scale for ballistic transport), the phase coherence length (quantum interference effects), and the electronic wavelength (quantum confinement). The aim of this course is to describe key experimental transport phenomena including weak localisation, universal conductance fluctuations, Aharonov-Bohm oscillations, and conductance quantisation whilst giving an overview of theoretical methods such as the tight binding model, the Landauer-Büttiker formulism, scattering theory, and scaling theory.
Ed McCann works in the condensed matter theory group at Lancaster University. Recently, his research has been focussed on the properties of chiral electrons in graphene and graphene multilayers, looking at their transport and spectroscopic properties.
Quantum Information Processing is one of the most exciting applications of modern quantum physics, and has become a flourishing interdisciplinary field in its own right. In this short course we will concentrate on some aspects of the subject most relevant to condensed matter systems. We will start by defining qubits and quantum gates, then introduce quantum operations as a model for the action of a quantum system in a noisy environment and the Kraus representation theorem which provides a composite way to represent them. Then we will move on to quantum error correction and its connection to classical codes, and briefly discuss the physics of two of the most important solid-sate qubits: impurity spins in semiconductors and superconducting circuits. Finally we will talk about two alternatives to the standard gate model of quantum computation that particularly lend themselves to solid-state systems: adiabatic quantum computation (and the related topic of quantum annealing), and the topological computation (and related topological codes).
Andrew is Professor of Physics in the UCL Department of Physics and Astronomy and directory of the London Centre for Nanotechnology; formerly Junior Research Fellow at St John’s College Oxford (1989-93), Postdoctoral Fellow at the IBM Zurich Research Laboratory (1991-92), and Lecturer in Physics at the University of Durham (1993-95). He is Director of the new EPSRC Centre for Doctoral Training in Delivering Quantum Technologies, starting in 2014.
This course deals with the physics of soft materials. As the name suggests these materials are soft to touch (e.g. jello, creams, pastes etc.) as opposed to hard ones (e.g. metals, alloys)which fall under the purview of “Solid State Physics”. The important distinction between soft materials as opposed to their hard counterparts is that entropy and not internal energy dictates their equilibrium properties. Further these materials mostly comprise of organic molecules that interact weakly and as a result their properties are strongly influenced by thermal fluctuations, external fields, and boundary effects. This strong ‘susceptibility’ of soft matter leads to many fascinating properties. We will review a few generic features of soft materials, e.g. dominance of entropy, interplay between broken-symmetry and dynamic mode structure and topological defects that are common to such systems. The outline is as follows i) Introduction to soft condensed matter physics, (ii) Liquid Crystals and Polymers (iii) Fluid Membranes, (iv) Fluctuations and response of non-equilibrium soft systems.
Buddhapriya (Buddho) is a senior lecturer in the biological physics group at the University of Sheffield. His main research interests include soft condensed matter physics and biological physics.Please replace this text with a short biography about the lecturer.
Statistical Mechanics aims to provide a macroscopic description of a physical system starting from knowledge of its microscopic properties. The methodology and techniques are widely used throughout condensed matter physics and are also today being applied to understand the dynamics of model ecologies, economies and societies. In these lectures, we will revisit the equilibrium properties of matter – such as phase transitions and universality – from the perspective of dynamics (as opposed to statics, as is typically done in undergraduate courses). Then we will examine successively further-from-equilibrium systems, ending with a discussion of fluctuations in driven systems, a subject currently generating considerable excitement in this field.
Richard Blythe is a Reader at the University of Edinburgh. Since his PhD days, he has been researching models and theories for nonequilibrium dynamical systems. Applications of these models include transport in biological systems, traffic flow, population dynamics and language change.
This course deals mainly with the influence of interactions on the electrons in materials. We begin with a review of second quantisation and the Fermi gas theory of metals, and then progress to Landau’s Fermi liquid theory and the notion of quasiparticles. The effect of impurities on the Fermi liquid (including the Kondo effect) is discussed, and we then move on to consider how the Fermi liquid gives way to other phases as the interactions are increased, concentrating on the Stoner instability and the Mott insulator. We analyse the magnetism in the Mott insulating phase, developing the concept of spin waves. Finally, we make a survey of some experimental data on strongly correlated crystalline solids, giving basic interpretations in terms of the concepts developed in the course.
Chris Hooley is a theoretical condensed matter physicist at the University of St Andrews, and is interested in many aspects of the quantum many-body problem.
Quantum fluids are those many-particle systems in whose behaviour the effects of both the quantum mechanics and quantum statistics are important, which occurs at cold temperatures. The most important two examples are superfluids, such as liquid Helium, and superconductors. This lecture course will begin with the phenomenon of Bose condensation in an ideal Bose gas with interactions; explore why this is not a true superfluid, and go on to look at the role of interactions. It then proceeds to explore what is different when the particles are charged, and finally look at the BCS theory of superconductivity where one begins with fermions rather than bosons.
Derek Lee is a Senior Lecturer at Imperial College London. He works on correlated quantum liquids, such as liquid helium and excitonic condensates, and also on topological states of matter.
The well-known Landau theory of phase transitions classifies phases of matter according to broken symmetries and local order parameters, such as solids that break translational symmetry, or magnets that break magnetic rotation symmetry. It has been long known that there are phases of matter that defy this classification — the quantum Hall state being the most obvious (but by no means only) example. With the discovery of topological insulators about 10 years ago, interest in this field has exploded, and we now know of many distinct phases of matter with no local order parameter, but instead characterised by a topological invariant. This short lecture course will focus mostly on non-interacting band theory, and introduce topological invariants, boundary states, and the bulk-boundary correspondence necessary to understand the modern topic of topological insulators. Other manifestations of topology in modern condensed matter physics will also be exposed, although not discussed in detail.
Sam works on the theory of strongly correlated systems, specialising in low-dimensional systems both in and out of equilibrium. He has worked in groups in the US, Italy and Germany, and since 2013 has been a lecturer at the University of Kent in Canterbury where he is a founding member of the quantum materials group.