Quantum Transport Properties of Two-Dimensional Quantum Lattices under Synthetic Magnetic Fields

Abstract

Motivated by recent experimental progress, we study the quantum transport properties of two-dimensional electron gases under high perpendicular magnetic fields. We use a simple tight-binding model to model the system and open-source software to simulate quantum electronic transport properties such as band structure variations and conductance-flux relationships in such systems. Dependence of quantum transport properties on two-dimensional square, triangular and kagome lattice shapes were studied adding a Gaussian noise to account for the impurities. Numerical simulations are presented to predict the emergence of physical effects related to quantum Hall effect, such as the existence of Landau levels and edge states. The kagome lattice exhibits a different band structure giving rise to a flat band, due to its trihexagonal geometry. The peak conductance value increases with decreasing lattice constant due to higher transmission probability. The transport properties vary significantly with lattice geometries, both with the lattice type and the lattice constant.