Topological Semimetal Phase with Exceptional Points in One-dimensional Non-Hermitian Systems

Abstract

AbstractIn Chap. 4, we show that the energy bands of a non-Hermitian crystalline system are described in terms of the generalized Brillouin zone. Because of the modification of the Brillouin zone, such a non-Hermitian system has unique features which are absent in Hermitian systems. In this chapter, we show that in a one-dimensional non-Hermitian tight-binding system with a sublattice symmetry and a time-reversal symmetry, a topological semimetal phase with exceptional points is stabilized by the unique features of the generalized Brillouin zone. Namely, under a change of the system parameters, the generalized Brillouin zone is deformed so that the system remains gapless. It is also shown that each energy band is divided into three regions, depending on the symmetry of the eigenstates, and the regions are separated by the cusps and the exceptional points on the generalized Brillouin zone.KeywordsTopological semimetal phase with exceptional pointsGeneralized Brillouin zone