Related papers: Topological Insulators in Random Lattices
A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are 6 new electronic…
Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry protected topological orders exist. In this paper, we…
In higher-order topological insulators (HOTIs), topologically nontrivial phases are usually associated with the shift of Wannier centers to topologically nontrivial positions on the edges of the unit cells, and the emergence of fractional…
Hopf insulators represent a unique class of topological insulators that exist exclusively in two-band systems and are inherently unstable upon the inclusion of additional bands. Meanwhile, recent studies have shown that non-Hermiticity…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…
We introduce new three-dimensional topological phases of two-band models using the Pontryagin-Thom construction. In symmetry class A these are the infinitely many Hopf-Chern topological insulators, which are hybrids of layered Chern…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
We show that hybrid structures of topological insulators and materials without topological protection can be employed to create perfectly conducting channels hosted in the non-topological part. These states inherit the topological…
As the thickness of a three-dimensional (3D) topological insulator (TI) becomes comparable to the penetration depth of the surface states, quantum tunneling between surfaces turns their gapless Dirac electronic structure into a gapped…
We investigate the exact solvability and point-gap topological phase transitions in non-Hermitian lattice models. These models incorporate site-dependent nonreciprocal hoppings $J e^{\pm g_n}$, facilitated by a spatially fluctuating…
The discovery and realization of topological insulators, a phase of matter which hosts metallic boundary states when the $d$-dimension insulating bulk is confined to ($d-1$)-dimensions, led to several potential applications. Recently, it…
Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary correspondence then links the topological properties of the bulk…
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.…
Topological superconductivity is an exotic quantum phenomenon with coupled nontrivial topological order and superconductivity together. A direct idea for producing topological superconductors is to create superconductivity based on the well…
Topological insulators are studied via tight-binding approximations of longitudinally driven photonic lattices with three lattice sites per unit cell. Two cases are considered in detail: Lieb and Kagome lattices. The lattice is decomposed…
Establishing the fundamental relation between the homotopy invariants and the band topology of Hamiltonians has played a critical role in the recent development of topological phase research. In this work, we establish the homotopy…
Higher-order topological insulator, as a newly found non-trivial material and structure, possesses a topological phase beyond the bulk-boundary correspondence. Here, we present an experimental observation of photonic higher-order…
The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been…
Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However,…
In this lecture for the Nobel symposium, we review previous research on a class of translational-invariant insulators without spin-orbit coupling. These may be realized in intrinsically spinless systems such as photonic crystals and…