Pseudopotential band calculations along a symmetry axis: Central potential

Abstract

A method for band-structure calculations along a symmetry axis is introduced. It entails a cylindrical-coordinate multipole expansion of the wavefunction and an exact reduction of the 3D Schrodinger equation into a set of 1D wave equations for the multipoles. Group-theoretic considerations and energy arguments imply good convergence, regardless of the unit-cell extension along the symmetry direction. Calculations of a test case, the band structure of PbSe along the (111) direction without spin-orbit coupling, demonstrate the method's good convergence. The method is expected to be particularly useful for structures highly anisotropic along a symmetry axis, e.g., superlattices.