A Fast Method for Electronic Band Structure Calculations

Abstract

Band structure calculation provides a basis for the study of thermal, optical and magnetic properties of crystals. The reduced Bloch mode expansion (RBME) method is a model reduction method in which a selected set of Bloch eigenvectors within the irreducible Brillouin zone at high symmetry points are used to expand the unit cell problem at hand. In this method, a major reduction in computational cost is achieved with minimum loss of accuracy. The method applies to both classical and ab inito band structure calculations of periodic media, and to any type of wave propagation problem: phononic, photonic, electronic, etc. In this work, the applicability of RBME in calculating the three-dimensional (3D) electronic band structure for crystal structures with different symmetries is demonstrated. Using the Kronig-Penney fixed potential, a high-symmetry cubic model and a low-symmetry triclinic model are considered. For both cases, the energy (eigenvalues) and wave functions (eigenvectors) demonstrate very good convergence performance with the number of expansion points.