Appearance of a topological semimetal phase in 1D non-Hermitian systems

In our previous work, we establish a non-Bloch band theory in one-dimensional (1D) tight-binding non-Hermitian systems [1]. We show how to determine the generalized Brillouin zone C_β for the complex Bloch wave number β=e^ik, k∈C. In contrast to Hermitian cases, where C_β is always a unit circle, in non-Hermitian systems C_β is a closed curve, not necessarily a unit circle. Furthermore, we find that C_β can have cusps, and its shape depends on system parameters. A byproduct of our theory is that one can prove the bulk-edge correspondence between the winding number defined from C_β and existence of topological edge states.
From the non-Bloch band theory, we show that in 1D non-Hermitian systems with both sublattice symmetry and time-reversal symmetry, a topological semimetal phase with exceptional points is stabilized, and this phase extends over a finite region on the phase diagram. This stems from unique features of the generalized Brillouin zone C_β; as a system parameter changes, C_β also changes so as to keep the system gapless. Furthermore, we also find that the motion of the exceptional points within the topological semimetal phase is related to the change of the value of the winding number. [1] K. Yokomizo and S. Murakami, Phys. Rev. Lett. 123, 066404 (2019)