Related papers: Higher-order topological band structures
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
By stacking PbTe layers there is a non-monotonic topological phase transition as a function of the number of monolayers. Based on first principles calculations we find that the proper stacked crystal symmetry determines the topological…
Using the topological membrane approach to string theory, we suggest a geometric origin for the heterotic string. We show how different membrane boundary conditions lead to different string theories. We discuss the construction of closed…
A hyperbolic lattice allows for any $p$-fold rotational symmetry, in stark contrast to a two-dimensional crystalline material, where only twofold, threefold, fourfold or sixfold rotational symmetry is permitted. This unique feature…
In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The basic concepts,…
Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band structure in a four- (or higher-)dimensional momentum space.…
Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While…
While tremendous research has revealed that symmetry enriches topological phases of matter, more general principles that protect topological phases have yet to be explored. In this Letter, we elucidate the roles of subspaces in…
A topological pump enables robust transport of quantized particles when the system parameters are varied in a cyclic process. In previous studies, topological pump was achieved inhomogeneous systems guaranteed by a topological invariant of…
Understanding crystal growth and morphology is a fundamental issue in condensed matter physics. While crystal morphology due to the distribution and dynamics of the diffusion field has been intensively studied, how the intrinsic material…
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…
We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the…
The high-order harmonic generation in finite topological nanoribbons is investigated using a tight-binding description. The ribbons consist of hexagons and are almost one-dimensional. Two edge states emerge at the short edges of the ribbon…
Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner…
In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave…
Motivated by the abundance of symmetry breaking states in magic-angle twisted bilayer graphene and other two-dimensional materials, we study superconducting (SC) and charge orders in two-dimensional topological flat bands in the strong…
The emergent higher-order topological insulators significantly deepen our understanding of topological physics. Recently, the study has been extended to topological semimetals featuring gapless bulk band nodes. To date, higherorder nodal…
We elaborate an algebraic framework for describing internal topological symmetries of gapped boundaries of (2+1)D topological orders. We present a categorical obstruction to the coherence of bulk group symmetry and boundary symmetries in…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…