相关论文: 'Real' gerbes and Dirac cones of topological insul…

We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant,…

Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I review a recent construction of torsion topological invariants for condensed matter…

We analyze continuous partial differential models of topological insulators in the form of systems of Dirac equations. We describe the bulk and interface topological properties of the materials by means of indices of Fredholm operators…

The topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional…

We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct…

We give field theory descriptions of the time-reversal invariant quantum spin Hall insulator in 2+1 dimensions and the particle-hole symmetric insulator in 1+1 dimensions in terms of massive Dirac fermions. Integrating out the massive…

We study topological indices of Fermionic time-reversal invariant topological insulators in two dimensions, in the regime of strong Anderson localization. We devise a method to interpolate between certain Fredholm operators arising in the…

Three-dimensional topological insulators support gapless Dirac fermion surface states whose rich topological properties result from the interplay of symmetries and dimensionality. Their topological properties have been extensively studied…

This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…

The coupled-wires approach has been shown to be useful in describing two-dimensional strongly interacting topological phases. In this manuscript we extend this approach to three-dimensions, and construct a model for a fractional strong…

Short-ranged and line-gapped non-hermitian Hamiltonians have strong topological invariants given by an index of an associated Fredholm operator. It is shown how these invariants can be accessed via the signature of a suitable spectral…

The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…

Three dimensional (3D) topological insulators are novel states of quantum matter that feature spin-momentum locked helical Dirac fermions on their surfaces and hold promise to open new vistas in spintronics, quantum computing and…

Topological insulators are most frequently constructed using lattices with specific degeneracies in their linear spectra, such as Dirac points. For a broad class of lattices, such as honeycomb ones, these points and associated Dirac cones…

Dirac semimetal is a class of semi-metallic phase protected by certain types of crystalline symmetries, and its low-energy effective Hamiltonian is described by Dirac equations in three dimensions (3D). Despite of various theoretical…

Topological insulators are transformative quantum solids with immune-to-disorder metallic surface states having Dirac band structure. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to…

The first experimental evidence is presented of the topological insulator state in PbBi$_{2}$Te$_{4}$. A single surface Dirac cone is observed by angle-resolved photoemission spectroscopy (ARPES) with synchrotron radiation. Topological…

Topological insulators, featuring bulk-boundary correspondence, have been realized on a large number of noncrystalline materials, among which amorphous network, quasicrystals and fractal lattices are the most prominent ones. By contrast,…

Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking…

The recent discovered antiferromagnetic topological insulators in Mn-Bi-Te family with intrinsic magnetic ordering have rapidly drawn broad interest since its cleaved surface state is believed to be gapped, hosting the unprecedented axion…