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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 non-Hermitian Hamiltonian is pseudo-Hermitian.The eigenvalues and eigenvectors of the non-Hermitian Hamiltonian can be easilyobtained from those of its parent Hermitian Hamiltonian. It provides a way togenerate a class of non-Hermitian models with a tunable full real bandstructure by means of additional imaginary potentials.We also present anillustrative example that could achieve a cone structure from the energy bandof a two-layer Hermitian square lattice model.

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