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

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.

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Berry phase effects on electronic properties

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

A modified periodic boundary condition adequate for non-Hermitian topological systems is proposed. Under this boundary condition, a topological number characterizing the system is defined in the same way as in the corresponding Hermitian system, and hence, at the cost of introducing an additional parameter that characterizes the non-Hermitian skin effect, the idea of bulk-edge correspondence in the Hermitian limit can be applied almost as it is. We develop this framework through the analysis of a non-Hermitian Su-Schrieffer-Heeger model with chiral symmetry and prove the bulk-edge correspondence in a generalized parameter space. A finite region in this parameter space with a nontrivial pair of chiral winding numbers is identified as topologically nontrivial, indicating the existence of a topologically protected edge state under an open boundary.

Generalized bulk-edge correspondence for non-Hermitian topological systems

The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of a disordered Z2 topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel single parameter scaling, collapsing onto two branches of a universal scaling function, which correspond to the Dirac semimetal and the diffusive metal. The diverging length scale critical exponent ν and the dynamical critical exponent z are estimated, and found to differ significantly from those for the conventional Anderson transition. Critical behavior of experimentally observable quantities near and at the tricritical point is also discussed.

Density of states scaling at the semimetal to metal transition in three dimensional topological insulators.

A global phase diagram of disordered weak and strong topological insulators is established numerically. As expected, the location of the phase boundaries is renormalized by disorder, a feature recognized in the study of the so-called topological Anderson insulator. Here, we report unexpected quantization, i.e., robustness against disorder of the conductance peaks on these phase boundaries. Another highlight of the work is on the emergence of two subregions in the weak topological insulator phase under disorder. According to the size dependence of the conductance, the surface states are either robust or "defeated" in the two subregions. The nature of the two distinct types of behavior is further revealed by studying the Lyapunov exponents.

Disordered weak and strong topological insulators.

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

The electronic spectrum on the spherical surface of a topological insulator reflects an active property of the helical surface state that stems from a constraint on its spin on a curved surface The induced spin connection can be interpreted as an effective vector potential associated with a fictitious magnetic monopole induced at the center of the sphere The strength of the induced magnetic monopole is found to be $g=\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}$, being the smallest finite (absolute) value compatible with the Dirac quantization condition We have established an explicit correspondence between the bulk Hamiltonian and the effective Dirac operator on the curved spherical surface An explicit construction of the surface spinor wave functions implies a rich spin texture possibly realized on the surface of topological insulator nanoparticles The electronic spectrum inferred by the obtained effective surface Dirac theory, confirmed also by the bulk tight-binding calculation, suggests a specific photoabsorption/emission spectrum of such nanoparticles

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Ken-Ichiro Imura

Papers

Generalized bulk-edge correspondence for non-Hermitian topological systems

Density of states scaling at the semimetal to metal transition in three dimensional topological insulators.

Disordered weak and strong topological insulators.

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

Spherical topological insulator