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

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.