Related papers: Topological insulators and geometry of vector bund…
We study spintronics and spincaloritronics in topological insulators. We show spintronics effects in 2D topological insulator junctions and 3D topological insulators coupled to ferromagnets. We also investigate spin polarization on the…
Topological insulators are new phases of matter whose properties are derived from a number of qualitative yet robust topological invariants rather than specific geometric features or constitutive parameters. Here, Kagome lattices are…
Recent advancements in the field of topological band theory have significantly contributed to our understanding of intriguing topological phenomena observed in various classical and quantum systems, encompassing both wave and dissipative…
Topological insulators are a recently discovered class of materials with fascinating properties: While the inside of the solid is insulating, fundamental symmetry considerations require the surfaces to be metallic. The metallic surface…
In this letter we investigate some aspects of the noncommutative differential geometry based on derivations of the algebra of endomorphisms of an oriented complex hermitian vector bundle. We relate it, in a natural way, to the geometry of…
Topological insulators in the Bi$_2$Se$_3$ family manifest helical Dirac surface states that span the topologically ordered bulk band gap. Recent scanning tunneling microscopy measurements have discovered additional states in the bulk band…
The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $\theta$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous…
The symmetry-based indicator [H. C. Po, A. Vishwanath, H. Watanabe, Nat. Commun. 8, 50 (2017)] is a practical tool to diagnose topological materials in the band theory. In this note, we present two directions to generalize the…
Some intensive observables of the electronic ground state in condensed matter have a geometrical or even topological nature. In this Review I present the geometrical observables whose expression is known in a full many-body framework,…
Topological insulators represent unique phases of matter with insulating bulk and conducting edge or surface states, immune to small perturbations such as backscattering due to disorder. This stems from their peculiar band structure, which…
Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant…
We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the…
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
In this chapter, we report the recent progress in the understanding of the rich mathematical structures of topological insulators in the framework of index theory and noncommutative geometry.
Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited from the quantum groups, and their sections…
Topological phases are characterised by a topological invariant that remains unchanged by deformations in the Hamiltonian. Materials exhibiting topological phases include topological insulators, superconductors exhibiting strong spin-orbit…
We give a canonical description of the formal moduli space of a vector bundle on a variety; as an application, we prove the closedness of certain differential forms on moduli corresponding to the trace form on the endomorphism algebra of…
The electronic structures of graphene systems and topological insulators have closely-related features, such as quantized Berry phase and zero-energy edge states. The reason for these analogies is that in both systems there are two relevant…
Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological…
Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the…