Related papers: Real Hopf Insulator
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…
A dynamical Hopf insulator is experimentally synthesized with a quenched two-dimensional quantum anomalous Hall system on a square Raman lattice. The quench dynamics for the quasimomentum-time-dependent Bloch vectors defines a Hopf map from…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
We introduce two dimensional fermionic band models with two orbitals per lattice site, or one spinful orbital, and which have a non-zero topological Chern number that can be changed by varying the ratio of hopping parameters. A…
We report the theoretical discovery of a large class of 2D tight-binding models containing nearly-flat bands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of…
This paper presents a complex band analysis of one-dimensional (1D) square and high-root topological insulators (HRTIs). We show that edge-state bands of HRTIs are sliced sections of impurity bands of a uniform tight-binding chain. A…
We generalize the Pfaffian formalism, which has been playing an important role in the study of time-reversal invariant topological insulators (TIs), to 3D chiral higher-order topological insulators (HOTIs) protected by the product of…
For spinful systems with spin 1/2, it is generally believed that P and T invariant strong and second-order topologies exist in four band and eight band system, respectively. Here, by using periodic driving, we find it is possible to have…
The non-interacting band structure of spinless fermions in a two-dimensional ($d=2$) $p$-band honeycomb lattice exhibits two quadratic band touching points (QBTPs), which lie at the Fermi levels of filling $\nu=1/4$ and its particle-hole…
Solitonic symmetry has been believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum. We uncover…
We study a non-Hermitian non-Abelian topological insulator preserving $PT$ symmetry, where the non-Hermitian term represents nonreciprocal hoppings. As it increases, a spontaneous $PT$ symmetry breaking transition occurs in the perfect-flat…
Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter in graphene and other two-dimensional…
Topologically gapless edge states, characterized by topological invariants and Berry's phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a…
Higher-order topological insulators (HOTI) are a novel topological phase beyond the framework of the conventional bulk-boundary correspondence. In these peculiar systems, the topologically nontrivial boundary modes are characterized by a…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…
We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…
Recent years have seen multiple high-throughput studies reveal an immense number of topological materials through use of symmetry indicators. Despite this success, three-dimensional topological insulators (TI) admitting a band-gap larger…
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…
The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or…
The topological invariants of a time-reversal-invariant band structure in two dimensions are multiple copies of the $\mathbb{Z}_2$ invariant found by Kane and Mele. Such invariants protect the topological insulator and give rise to a spin…