Related papers: Time-reversal invariant topological skyrmion phase…
We introduce topological phases of matter defined by skyrmions in the ground state spin -- or pseudospin -- expectation value textures in the Brillouin zone, the chiral and helical topological skyrmion phases of matter. These phases are…
Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic,…
We classify topological phases of non-Hermitian systems in the Altland-Zirnbauer classes with an additional reflection symmetry in all dimensions. By mapping the non-Hermitian system into an enlarged Hermitian Hamiltonian with an enforced…
Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterised by topological invariants. In energy-conserving…
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…
We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions ($d=2,3$). We show that in both cases nontrivial topology is manifested by the presence of the $(d-2)$-dimensional edge…
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…
The discovery of topological phases has ushered in a new era of condensed matter physics and revealed a variety of natural and artificial materials. They obey the bulk-boundary correspondence (BBC), which guarantees the emergence of…
Topological insulators, along with Chern insulators and Quantum Hall insulator phases, are considered as paradigms for symmetry protected topological phases of matter. This article reports the experimental realization of the time-reversal…
The interplay between time-reversal symmetry (TRS) and band topology plays a crucial role in topological states of quantum matter. In time-reversal-invariant (TRI) systems, the inversion of spin-degenerate bands with opposite parity leads…
We report finite-size topology in the quintessential time-reversal (TR) invariant systems, the quantum spin Hall insulator (QSHI) and the three-dimensional, strong topological insulator (STI): previously-identified helical or Dirac cone…
The hallmark of symmetry-protected topological (SPT) phases is the existence of anomalous boundary states, which can only be realized with the corresponding bulk system. In this work, we show that for every Hermitian anomalous boundary mode…
A one dimensional time reversal symmetric topological superconductor (symmetry class DIII) features a single Kramers pair of Majorana bound states at each of its ends. These holographic quasiparticles are non-Abelian anyons that obey…
A higher-order topological superconductor can experience topological phase transitions driven by variations in a bulk parameter without closing the bulk gap. This presents a challenge in establishing a direct bulk-boundary correspondence,…
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…
The integration of artificial intelligence (AI) into fundamental science has opened new possibilities to address long-standing scientific challenges rooted in mathematical limitations. For example, topological invariants are used to…
For conventional topological phases, the boundary gapless modes are determined by bulk topological invariants. Based on developing an analytic method to solve higher-order boundary modes, we present $PT$-invariant $2$D topological…
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…
For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological…
Recently there has been much effort in understanding topological phases of matter with gapless bulk excitations, which are characterized by topological invariants and protected intrinsic boundary states. Here we show that topological…