Conventional Bulk-boundary Correspondence Research Articles

Edge States and Topological Invariants of Non-Hermitian Systems.

The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.

Minimal models for Wannier-type higher-order topological insulators and phosphorene

A higher order topological insulator is an extended notion of the conventional topological insulator, which belongs to a special class of topological insulators where the conventional bulk-boundary correspondence is not applicable. The bulk topological index may be described by the Wannier center located at a high symmetry point of the crystal. In this paper we propose minimal models for the second-order topological insulator in two dimensions and the third-order topological insulator in three dimensions. They are anisotropic two-band models with two different hopping parameters. The two-dimensional model is known to capture the essential physics of phosphorene near the Fermi level. It has so far been recognized as a trivial insulator due to the absence of topological edge states in nanoribbons. However, we demonstrate the emergence of topological boundary states in zero dimension, i.e., in nanodisks. In particular, the diamond structure exhibits such topological states at two corners, each of which carries a 1/2 fractional charge. We predict that these corner states will be observed in the diamond structure of phosphorene.