Related papers: Counting topological interface modes using simplic…
We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps…
Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system…
The bulk-edge correspondence is a fundamental principle of topological wave physics, which states that the difference in gap Chern numbers between the interfaced materials is equal to the net number of topological edge modes. Although this…
This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.
The search for candidate materials for fractional Chern insulators (FCIs) has mainly focused on the topological and geometrical structures of single-particle Chern bands. However, there are inherent limitations in approaches that neglect…
In this paper, we study a one-dimensional boson system in a superlattice potential.This system is experimentally feasible by using ultracold atomic gases,and attracts much attention these days. It is expected that the system has a…
An acoustic topological insulator (TI) is synthesized using topology optimization, a free material inverse design method. The TI appears spontaneously from the optimization process without imposing requirements on the existence of pseudo…
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…
Topological phases with large Chern numbers have important implications. They were previously predicted to exist by considering fabricated long-range interactions or multi-layered materials. Stimulated by recent wide interests in Floquet…
We rigorously yet concisely prove the bulk-edge correspondence for general $d$-dimensional ($d$D) topological insulators in complex Altland-Zirnbauer classes, which states that the bulk topological number equals to the edge-mode index.…
Realizing topological insulators is of great current interest because of their remarkable properties and possible future applications. There are recent proposals, based on Floquet analyses, that one can generate topologically nontrivial…
Commonly, a two-dimensional topological insulator is characterized by non-zero Chern numbers associated with its band structure. In our work, we present the experimental demonstration of an anomalous topological insulator, for which the…
We describe a family of phase transitions connecting phases of differing non-trivial topological order by explicitly constructing Hamiltonians of the Levin-Wen[PRB 71, 045110] type which can be tuned between two solvable points, each of…
If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an…
We consider the moduli space of flat connections on the Riemann surface with marked points. The new efficient parametrization is suggested and used to construct an integrable model on the moduli space. A family of commuting Hamiltonians is…
Topological invariants are fundamental characteristics reflecting global properties of quantum systems, yet their exploration has predominantly been limited to the static (DC) transport and transverse (Hall) channel. In this work, we extend…
The study of unconventional phases and elucidation of correspondences between topological invariants and their intriguing properties are pivotal in topological physics. Here, we investigate a complex exceptional ring (CER), composed of a…
Moir\'e systems made from stacked two-dimensional materials host novel correlated and topological states that can be electrically controlled via applied gate voltages. We have used this technique to manipulate Chern domains in an…
The interacting SSH model provides an ideal ground to study the interplay between topologically insulating phases and electron-electron interactions. We study the polarization density as a topological invariant and provide an analytic…
Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems…