Related papers: Local Chern Marker for Periodic Systems
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
We introduce the electronic polarization originally defined in one-dimensional lattice systems to characterize two-dimensional topological insulators. The main idea is to use spiral boundary conditions which sweep all lattice sites in…
The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. We use electric circuits to…
We present a technique for detecting topological invariants -- Chern numbers -- from time-of-flight images of ultra-cold atoms. We show that the Chern numbers of integer quantum Hall states of lattice fermions leave their fingerprints in…
The study of topological property of band insulators is an interesting branch of condensed matter physics. Two types of topologically nontrivial insulators have been extensively studied. The first type is characterized by a nonzero TKNN…
Topological insulator-based methods underpin the topological classification of gapped bands, including those surrounding semi-metallic nodal defects. However, multiple bands with gap-closing points can also possess non-trivial topology. We…
Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations. When the inversion and time reversal symmetries are broken by the substrate or by strong…
We derive the expression for the local Hall conductivity for systems that lack translation symmetry and use it to study the local fluctuations of the Hall signal around disordered patches in magnetic insulators. We find that the regime in…
We consider interacting fermions in a magnetic field on a two-dimensional lattice with the periodic boundary conditions. In order to measure the Hall current, we apply an electric potential with a compact support. Then, due to the Lorentz…
The topological classification of fermion systems in mixed states is a long standing quest. For Gaussian states, reminiscent of non-interacting unitary fermions, some progress has been made. While the topological quantization of certain…
Strong directional disorder in local magnetic moments coupled to a Chern insulator gives rise to topological phases that cannot be continuously connected to the clean limit and are therefore genuinely disorder-driven. We demonstrate this in…
Chern insulators arguably provide the simplest examples of topological phases. They are characterized by a topological invariant and can be identified by the presence of protected edge states. In this article, we show that a local impurity…
Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional…
The classification of bandstructures by topological invariants provides a powerful tool for understanding phenomena such as the quantum Hall effect. This classification was originally developed in the context of electrons, but can also be…
The topological invariants of gapped time reversal invariant lattice superconductors are studied by mapping the superconducting mean field Hamiltonian to a Bloch Hamiltonian. There is a single $Z_2 $ invariant in two dimensions and four…
We propose a Haldane-like model of dice lattice analogous to graphene and explore its topological properties within the tight-binding formalism. The topological phase boundary of the system is identical to that of Haldane model of graphene…
This paper is a survey of the $\mathbb{Z}_2$-valued invariant of topological insulators used in condensed matter physics. The $\mathbb{Z}$-valued topological invariant, which was originally called the TKNN invariant in physics, has now been…
Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low…
We demonstrate that a Chern insulator could be realized on a real two-dimensional lattice of an organic Dirac semimetal {\alpha}-(BEDT-TTF)2I3 by introducing potential and magnetic modulations in a unit cell. It is a…
We propose an alternative formulation of the $Z_2$ topological index for quantum spin Hall systems and band insulators when time reversal invariance is not broken. The index is expressed in terms of the Chern numbers of the bands of the…