Related papers: Higher-order topological band structures
States of matter with nontrivial topology have been classified by their bulk symmetry properties. However, by cutting the topological insulator into ribbons, the symmetry of the system is reduced. By constructing effective Hamiltonians…
Symmetry-protected topological phases protected by crystalline symmetries and internal symmetries are shown to enjoy a fascinating one-to-one correspondence in classification. Here we investigate the physics content behind the abstract…
Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, but protected modes at corners or hinges.…
The topological properties of the bulk band structure of a three-dimensional topological insulator (TI) manifest themselves in the form of metallic surface states. In this paper, we propose a probe which directly couples to an exotic…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
Topological order in strongly correlated systems, including quantum spin liquids, quantum Hall states in lattices and topological superconductivity is treated. Various metallic non-Fermi-liquid states are discussed, including fractionalized…
Strongly interacting topological states in multi-particle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in…
Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…
We discuss the relation between bulk topological invariants and the spectrum of surface states in three dimensional non-interacting topological insulators. By studying particular models, and considering general boundary conditions for the…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
We study topological states of matter in quasicrystals, which do not rely on crystalline orders. In the absence of a bandstructure description and spin-orbit coupling, we show that a three-dimensional quasicrystal can nevertheless form a…
Topological acoustic and elastic waves have recently emerged as an exciting interdisciplinary field which is still mainly focused on low-dimensional structures and model systems. Here we demonstrate numerically an elastic-wave analogue of…
We show that lattices with higher-order topology can support corner-localized bound states in the continuum (BICs). We propose a method for the direct identification of BICs in condensed matter settings and use it to demonstrate the…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
Recent realizations of exotic topological states in condensed matter and cold atoms have advanced the exploration for topological characteristics, such as invariant topological orders and band inversion. Here we construct a 1D optical…
Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider…
The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for…
Topological band theory provides a conceptual framework to predict or even engineer robust metallic states at the boundaries of topologically distinct phases. The bulk-boundary correspondence requires that a topological electronic phase…
Band insulators appear in a crystalline system only when the filling -- the number of electrons per unit cell and spin projection -- is an integer. At fractional filling, an insulating phase that preserves all symmetries is a Mott…