相关论文: A mathematical study of periodic band inversion
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials…
We examine several properties of the Berry curvature for the organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ consisting of four bands, which exhibits a zero-gap state with Dirac cones. By adding a small potential acting on two molecular…
The emergence of topologically non-trivial flat bands in moir\'e materials provides an opportunity to explore the interplay between topological physics and correlation effects, leading to the recent experimental realization of interacting…
We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations…
We show that excitons forming between moir\'e flat Chern bands possess a substantial electric dipole moment comparable to the moir\'e lattice parameter times the elementary charge ($\sim10^2$ Debye). At a hole filling factor of one in…
Several IV-VI semiconductor compounds made of heavy atoms, such as Pb$_{1-x}$Sn$_{x}$Te, may undergo band-inversion at the $L$ point of the Brillouin zone upon variation of their chemical composition. This inversion gives rise to…
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…
The geometry of electronic bands in a solid can drastically alter single-particle charge and spin transport. We show here that collective optical excitations arising from Coulomb interactions also exhibit unique signatures of Berry…
Topological invariants are crucial quantities for classifying materials with topological phases. Hence, their connections with experimentally measurable quantities are extremely important. In this context, circular dichroism (CD) provides a…
We develop a theory to compute and interpret the photonic band structure of a periodic array of metallic helices for the first time. Interesting features of band structure include the ingenuous longitudinal and circularly polarized…
Recent experiments on multilayer graphene systems have rekindled interest in electronic crystal phases in two dimensions -- but now for phases enriched by non-trivial quantum geometry. In this work, we introduce a simple continuum model…
We present a theoretical treatment of overdamped Brownian motion on a multidimensional tilted periodic potential that is analogous to the tight-binding model of quantum mechanics. In our approach we expand the continuous Smoluchowski…
It is commonly believed that nonuniform Berry curvature destroys the Girvin-MacDonald-Platzman algebra and as a consequence destabilizes fractional Chern insulators. In this work we disprove this common lore by presenting a theory for all…
A Chern band is characterized by a Wannier obstruction indicating the absence of a basis of complete, orthogonal, and exponentially-localized states. Here, we study the properties of real space bases of a Chern band obtained by relaxing…
We study a special class of topological phase transitions in two dimensions described by the inversion of bands with relative angular momentum higher than 1. A band inversion of this kind, which is protected by rotation symmetry, separates…
We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely…
Recently, it has been shown how topological phases of matter with crystalline symmetry and $U(1)$ charge conservation can be partially characterized by a set of many-body invariants, the discrete shift $\mathscr{S}_{\text{o}}$ and electric…
We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrodinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays,…
We investigate the possibility of exactly flat non-trivial Chern bands in tight binding models with local (strictly short-ranged) hopping parameters. We demonstrate that while any two of three criteria can be simultaneously realized…
We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the…