Oscilações de Shubnikov-de Haas em isolantes topológicos

Abstract

Topological insulators (TIs) were introduced around the 1980s in the study of topological states in quantum systems, i.e., states protected by continuous deformations and impurities. It was only at the beginning of the 21st century that this class of materials was effectively implemented in the study of advanced materials in the field of condensed matter physics and spintronics when physicists Bernevig, Hughes, and Zhang (BHZ) studied the quantum spin Hall effect in HgTe quantum wells. This modeling of topological materials, which became known as the ``BHZ model'', describes topological edge states with impurity-protected conductivity, making it highly promising in the materials industry. Theoretical interpretations of this effect are provided by quantum oscillations, such as the Shubnikov-de Haas (SdH) effect, which corresponds to oscillations in magneto-resistance in two-dimensional systems subjected to an external magnetic field. The analytical description of this phenomenon is based on the Lifshitz-Kosevich (LK) equation; however, analytical solutions of this for the BHZ Hamiltonian do not produce accurate results in the presence of spin-orbit coupling (SOI) and Zeeman effect terms without significant approximations. Therefore, this research aims to study the effects of SOI and Zeeman on SdH oscillations in two-dimensional systems, particularly TIs. For this purpose, we consider the Drude model for electronic transport combined with the Born approximation for the scattering rate to rewrite the longitudinal resistance of the quantum Hall effect in terms of the density of states (DOS) at the Fermi level. As a result, using the Kwant package in Python to numerically calculate the DOS, the spectrum of SdH oscillation frequencies in TIs and two-dimensional electron gases, such as GaAs and InSb, is obtained. This quantum phenomenon is a fundamental tool for characterizing quantities related to electronic transport in materials, such as charge density, Hall resistivity, effective band mass, Berry phase, among other information that aids in the development of new materials for the spintronics industry, contributing to the advancement of more efficient and powerful electronic devices in the field of quantum computing.