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