Generalized Bloch Theorem for Complex Periodic Potentials – A Powerful Application to Quantum Transport Calculations

Abstract

Band-theoretic methods with periodically repeated supercells have been a powerful approach for ground-state electronic structure calculations, but have not so far been adapted for quantum transport problems with open boundary conditions. Here we introduce a generalized Bloch theorem for complex periodic potentials and use a transfer-matrix formulation to cast the transmission probability in a scattering problem with open boundary conditions in terms of the complex wave vectors of a periodic system with absorbing layers, allowing a band technique for quantum transport calculations. The accuracy and utility of the method is demonstrated by the model problems of the transmission of an electron over a square barrier and the scattering of a phonon in an inhomogeneous nanowire. Application to the resistance of a twin boundary in nanocrystalline copper yields excellent agreement with recent experimental data.