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

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 rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $(1{\mathrm{f}\mathrm{s}=10}^{\mathrm{\ensuremath{-}}15}\mathrm{}\mathrm{s})$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Intense few-cycle laser fields: Frontiers of nonlinear optics

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.

http://www.physics.udel.edu/~bnikolic/QTTG/NOTES/DMRG/SCHOLLWOCK=RMP_dmrg.pdf

The density-matrix renormalization group

In this paper we review experimental and theoretical results on higher electronic multipoles in solids with strong correlations. Recent experiments and their theoretical interpretation have confirmed the ordering of octupoles and even higher multipoles in rare-earth and actinide compounds with f electrons. The concept of multipoles is critically examined in point groups where spherical tensors of different ranks mix. Using a phenomenological approach, we demonstrate how linear and nonlinear couplings of different multipoles lead to rich phase diagrams and anomalies in physical observables. As actual representative systems, we first consider Ce x La 1- x B 6 , for which resonant X-ray scattering probed the octupole order for the first time, and NpO 2 , where quadrupoles induced by the octupole order have been observed. We then consider a class of compounds called skutterudites as the most convenient system for systematic study. Particular emphasis is placed on the ordering of scalar components from fourth-...

Multipole Orders and Fluctuations in Strongly Correlated Electron Systems

The Gutzwiller wave function is shown to be the exact solution of a supersymmetric t-J-type model. The model realizes a Fermi-liquid state in one dimension with a discontinuity in the momentum distribution. Analytic results are obtained for spin and charge susceptibilities, and the specific-heat coefficient with the help of the Luttinger-liquid theory. In the high-density limit the model exhibits a Mott-Hubbard gap and reduces to an antiferromagnetic spin chain with long-range exchange solved by Haldane and Shastry.

Exactly soluble supersymmetric t-J-type model with long-range exchange and transfer.

A 1-kHz, 0.66-TW Ti:sapphire laser has been developed. We obtained 21-fs, 14-mJ pulses with an extraction efficiency of 32% in the final amplifier. The dispersion through the system was successfully compensated for by insertion of a pair of prisms in a regenerative amplifier. The pulses were characterized by frequency-resolved optical gating and were in good agreement with dispersion calculated by three-dimensional ray tracing.

Generation of 0.66-TW pulses at 1 kHz by a Ti:sapphire laser.

A quantum mechanical phenomenology for heavy-fermion systems is formulated. The effective Lagrangian for low-energy excitations contains a localized spin-fluctuation part which is coupled with an itinerant fermion part. Each part represents the dual nature of strongly correlated f electrons. The coupling parameter is fixed by comparison with the Fermi-liquid theory for the Anderson model. The comparison also fixes the localized spin-fluctuation spectrum. As an advantage over the Fermi-liquid description the present model takes into account the RKKY interaction and non-linear effects of spin polarization. A formula for the magnetic equation of state is derived which is applicable to the metamagnetism and weak antiferromagnetism in heavy-fermion systems.

Yoshio Kuramoto

Papers

Multipole Orders and Fluctuations in Strongly Correlated Electron Systems

Exactly soluble supersymmetric t-J-type model with long-range exchange and transfer.

Generation of 0.66-TW pulses at 1 kHz by a Ti:sapphire laser.

Quantum Phenomenology for Heavy-Fermion Systems. I. Formulation of the Duality Model

Application of the numerical renormalization group method to the hubbard model in infinite dimensions