Efficient Algorithm for Extracting Transmission Spectrum From Band Structure in Low‐Dimensional Systems

Abstract

Aiming at an efficient method to determine the transport properties of a physical system, an effective and accurate band‐counting algorithm is presented to extract the transmission spectrum of a low‐dimensional system, directly from the band structure. This approach is more efficient than Hamiltonian‐dependent formalisms such as the standard Green's function (GF) or the transfer matrix methods. The only constraint of the approach is that the bands should not be mixed, i.e., for each band in the k‐path, there should be a set of eigenvalues. The efficiency of the approach is comparable to that of Green's function method, and it is applicable to any computational approach whose output is a band structure, whether for particles or quasiparticles such as electrons and phonons. Since the transport coefficient is calculated separately for each band, the occurrence of eigenvalues at the same k‐point can be captured by the algorithm. The proposed algorithm will be useful for studying transmission coefficient‐dependent quantities, such as thermoelectric‐related quantities, and also the electric current within the Landauer–Büttiker formalism.