Symmetries and General Principies in the Multiband Effective Mass Theory: A Transfer Matrix Study

TL;DR

This paper investigates symmetry properties of transfer matrices in multiband effective mass theory, focusing on time reversal and space inversion symmetries, and reveals new exchange properties in subspace quantities.

Contribution

It provides a detailed analysis of symmetry relations in transfer matrices and uncovers new exchange properties in subspace quantities within the Kohn-Luttinger model.

Findings

(4x4) model satisfies symmetry requirements

(2x2) subspaces generally do not, except at Gamma point

New exchange properties between subspace quantities

Abstract

We study the time reversal and space inversion symmetry properties of those transfer matrices mostly used in the calculation of energy spectra and transport-process. We study the time reversal and space inversion symmetry properties of those transfer matrices mostly used in the calculation of energy spectra and transport-process quantities. We determine the unitary transformation relating transfer matrices. We consider the Kohn-Luttinger model for a quasi-2D system and show that even though the system studied in the (4 x 4) scheme satisfies all the symmetry requirements, the (2 x 2)subspaces do not fulfill such constrains, except in the Gamma point of the Brillouin Zone. We find new exchange properties between the (2\times 2)subspace quantities.