Hall Conductance of a Two-Dimensional Electron Gas in Periodic Lattice with Triangular Antidots

TL;DR

This paper investigates how the geometry of triangular antidots in a periodic lattice affects quantum states and the quantization of Hall conductance in a two-dimensional electron gas, revealing critical parameters and differences from square lattices.

Contribution

It introduces the impact of triangular antidot geometry on Hall conductance quantization and identifies critical lattice parameters affecting topological properties.

Findings

Hall conductance quantization depends on antidot geometry.

Critical lattice parameters cause drastic changes in Hall conductance.

Differences observed compared to square lattice with cylindrical antidots.

Abstract

The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidos located on the sites of the square lattice. In a such system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values of lattice parameters defining the shape of triangular antidots at which the Hall conductance is changed drastically are determined. We demonstrate that the quantum states and Hall conductance quantization law for the triangular antidot lattice differ from the case of the square lattice with cylindrical antidots. As an example, the Hall conductances of magnetic subbands for different antidot geometries are calculated for the case when the number of magnetic flux quanta per unit cell is equal to three.