Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

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Topological insulators and superconductors

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

The behaviour of strongly correlated materials, and in particular unconventional superconductors, has been studied extensively for decades, but is still not well understood. This lack of theoretical understanding has motivated the development of experimental techniques for studying such behaviour, such as using ultracold atom lattices to simulate quantum materials. Here we report the realization of intrinsic unconventional superconductivity-which cannot be explained by weak electron-phonon interactions-in a two-dimensional superlattice created by stacking two sheets of graphene that are twisted relative to each other by a small angle. For twist angles of about 1.1°-the first 'magic' angle-the electronic band structure of this 'twisted bilayer graphene' exhibits flat bands near zero Fermi energy, resulting in correlated insulating states at half-filling. Upon electrostatic doping of the material away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature of up to 1.7 kelvin. The temperature-carrier-density phase diagram of twisted bilayer graphene is similar to that of copper oxides (or cuprates), and includes dome-shaped regions that correspond to superconductivity. Moreover, quantum oscillations in the longitudinal resistance of the material indicate the presence of small Fermi surfaces near the correlated insulating states, in analogy with underdoped cuprates. The relatively high superconducting critical temperature of twisted bilayer graphene, given such a small Fermi surface (which corresponds to a carrier density of about 1011 per square centimetre), puts it among the superconductors with the strongest pairing strength between electrons. Twisted bilayer graphene is a precisely tunable, purely carbon-based, two-dimensional superconductor. It is therefore an ideal material for investigations of strongly correlated phenomena, which could lead to insights into the physics of high-critical-temperature superconductors and quantum spin liquids.

Unconventional superconductivity in magic-angle graphene superlattices

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.

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The density-matrix renormalization group in the age of matrix product states

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

A comprehensive treatment of the theory of superfluid helium-3 is presented in this book. This treatment also illustrates many of the principal themes of theoretical condensed matter physics over the past two decades. The generalized BCS (Barden-Cooper-Schrieffer) pairing theory and the experimental properties of superfluid helium-3 are treated in detail. Extensive treatment of broken symmetries and their relation to macroscopic order and of the closely related topics of superflow and texture, defects in the order parameter field, and the dynamics of the nuclear spins as probed by nuclear magnetic resonance is included. This book should serve as a valuable reference for anyone working on superfluid helium-3 or on the closely related topics of unconventional superconductivity in heavy-electron metals and superfluidity of neutron star interiors.

http://www.gbv.de/dms/ohb-opac/017344565.pdf

The Superfluid Phases Of Helium 3

Diagrammatic, self-consistent treatment of the Anderson localization problem in d<=2 dimensions

Within the jellium model the zero wave vector, frequency-dependent conductivity is expressed in terms of a regular memory function. This quantity is calculated in lowest order in the impurity concentration and the electron-phonon coupling, thus yielding a reasonable approximation for the conductivity valid in the complete frequency regime. The standard results for the static conductivity including vertex corrections are reproduced. Deviations from Drude's formula a because of spin-flip scattering in a magnetic field, because of resonance scattering, because of phonon creation at low temperatures, and because of breaking of the screening cloud attached to charged impurities are discussed.

Homogeneous Dynamical Conductivity of Simple Metals

We present a systematic discussion of the effect of resonant impurity scattering on anisotropic model states of heavy-fermion superconductors. The impurity scattering is treated in the self-consistent T-matrix approximation including a renormalization of the frequency \ensuremath{\omega} and the quasiparticle energy ${\ensuremath{\xi}}_{k}$. Model states considered include the axial and polar states familiar from superfluid $^{3}\mathrm{He}$ as well as two states, termed hexial and hybrid, occurring in the group-theoretical classification of singlet states in hexagonal symmetry. We calculate the density of states, the critical temperature and the order parameter, the specific heat, the thermal conductivity, and the spin-lattice relaxation rate. Vertex corrections are included in the calculations of two-particle quantities. The observed properties of the prototype Fermi-liquid material ${\mathrm{UPt}}_{3}$ show many qualitative features in common with our model. However, it turns out to be difficult to identify any given state with certainty. An experimental test of our predictions on the behavior as a function of impurity concentration, particularly in the gapless regime at low temperatures, would allow for a more definitive characterization of the superconducting state.

Peter Wölfle

Papers

Fermi-liquid instabilities at magnetic quantum phase transitions

The Superfluid Phases Of Helium 3

Diagrammatic, self-consistent treatment of the Anderson localization problem in d<=2 dimensions

Homogeneous Dynamical Conductivity of Simple Metals

Consequences of resonant impurity scattering in anisotropic superconductors: Thermal and spin relaxation properties.