Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system

TL;DR

This paper demonstrates how to derive non-Hermitian models with tunable real band structures from Hermitian models with chiral symmetry, enabling wide-range control of Dirac-cone features in non-Hermitian systems.

Contribution

It establishes a method to connect Hermitian chiral-symmetric models with non-Hermitian chiral-time symmetric models, allowing for tunable real band structures via imaginary potentials.

Findings

Non-Hermitian Hamiltonians are pseudo-Hermitian.

Eigenvalues/eigenvectors can be derived from Hermitian counterparts.

Example of cone structure from a Hermitian square lattice.

Abstract

We establish a connection between an arbitrary Hermitian tight-binding model with chiral (C) symmetry and its non-Hermitian counterpart with chiral-time (CT ) symmetry.We show that such a non-Hermitian Hamiltonian is pseudo-Hermitian. The eigenvalues and eigenvectors of the non-Hermitian Hamiltonian can be easily obtained from those of its parent Hermitian Hamiltonian. It provides a way to generate a class of non-Hermitian models with a tunable full real band structure by means of additional imaginary potentials.We also present an illustrative example that could achieve a cone structure from the energy band of a two-layer Hermitian square lattice model.