Related papers: Bulk-Edge Correspondence for Finite Two-dimensiona…
An effective Chern-Simons theory for the Abelian quantum Hall states with edges is proposed to study the edge and bulk properties in a unified fashion. We impose a condition that the currents do not flow outside the sample. With this…
Guided by the many-particle quantum theory of interacting systems, we develop a uniform classification scheme for topological phases of disordered gapped free fermions, encompassing all symmetry classes of the Tenfold Way. We apply this…
For certain systems, the N-particle ground-state wavefunctions of the bulk happen to be exactly equal to the N-point space-time correlation functions at the edge, in the infrared limit. We show why this had to be so for a class of…
The bulk-edge correspondence in topological phases is extended to systems with the generalized chiral symmetry, where the conventional chiral symmetry is broken. In such systems, we find that the edge state exhibits an unconventional…
A description of a large system of particles is often sought in a derivation from the detailed behaviour of just a few of the particles. The present thesis deals with the connection between such microscopic features and the nature of a…
A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting…
We introduce a characterization of topological order based on bulk oscillations of the entanglement entropy and the definition of an `entanglement gap', showing that it is generally applicable to pure and disordered quantum systems. Using…
The localization is one of the active and fundamental research in topology physics. Based on a generalized Su-Schrieffer-Heeger model with the quasiperiodic non-Hermitian emerging at the off-diagonal location, we propose a novel systematic…
We present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase…
In this work, we study the disorder effect on topological metals that support a pair of helical edge modes deeply embedded inside the gapless bulk states. Strikingly, we predict that a quantum spin Hall (QSH) phase can be obtained from such…
We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of…
We present minimal toy models for topological skyrmion phases of matter, which generically realize type-II topological phase transitions in effectively non-interacting systems, those which occur without closing of the minimum direct bulk…
We provide a unified analysis of a posteriori and a priori error bounds for a broad class of discontinuous Galerkin and $C^0$-IP finite element approximations of fully nonlinear second-order elliptic Hamilton--Jacobi--Bellman and Isaacs…
We use the bulk Hamiltonian for a three-dimensional topological insulator such as $\rm Bi_2 Se_3$ to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the…
We provide an elementary proof and refinement of a well-known idea from physics: a chiral-symmetric local Hamiltonian on a half-space has the same signed number of edge-localized states with energies in the bulk band gap, as its bulk…
Most of our quantitative understanding of disorder-induced metal-insulator transitions comes from numerical studies of simple noninteracting tight-binding models, like the Anderson model in three dimensions. An important outstanding problem…
Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional…
Identifying entanglement-based order parameters characterizing topological systems, in particular topological superconductors and topological insulators, has remained a major challenge for the physics of quantum matter in the last two…
We study the suppression of the conductance quantization in quantum spin Hall systems by a combined effect of electronic interactions and edge disorder, that is ubiquitous in exfoliated and CVD grown 2D materials. We show that the interplay…
We show that topological waves at the interface between two magnetic domains in a graphene device are possible. First, we consider the case of a linear relation between the applied gate voltage and local density in the channel and,…