Practical band interpolation with a modified tight-binding method

We present a scheme that interpolates the energy bands of a crystal with a modified tight-binding Hamiltonian. We start from a pseudopotential plane-wave calculation of the eigenvalues in a three-dimensional coarse uniform grid of k-points in the Brillouin zone and from the evaluation of the single particle Hamiltonian and overlap matrix elements for a small localised basis set of atomic orbitals in the same k-point grid. A simple matrix manipulation procedure that replaces the eigenvalues obtained from the atomic orbital method by the eigenvalues of the plane-wave method generates the modified tight-binding Hamiltonian on the coarse grid. A subsequent three-dimensional Fourier interpolation of the modified tight-binding Hamiltonian and overlap matrices leads to a fast, yet accurate, determination of interpolated Hamiltonians and overlap matrices at an arbitrary k-point, or in a denser grid of k-points. We present examples of the application of the scheme to density functional calculations of germanium, graphite, graphene, copper and a SiGe superlattice.