Quantum Phase Transition in Hall Conductivity on an Anisotropic Kagome Lattice

TL;DR

This paper investigates a novel quantum Hall effect phase on an anisotropic Kagome lattice, revealing unique quantization rules and a sequential phase transition driven by hopping anisotropy, distinct from known Dirac fermion systems.

Contribution

It introduces a new quantum Hall phase with distinct quantization rules and describes a sequential phase transition caused by anisotropy in the Kagome lattice.

Findings

Discovery of a new QHE phase with $\sigma_{xy}=2ne^{2}/h$

Sequential phase transition from isotropic to anisotropic QHE

Difference from Dirac fermion systems like graphene

Abstract

We study the quantum Hall effect(QHE) on the Kagom\'{e} lattice with anisotropy in one of the hopping integrals. We find a new type of QHE characterized by the quantization rules for Hall conductivity $\sigma_{xy}=2ne^{2}/h$ and Landau Levels $E(n)=\pm v_{F}\sqrt{(n+1/2)\hbar Be}$ ($n$ is an integer), which is different from any known type. This phase evolves from the QHE phase with $\sigma_{xy}=4(n+1/2)e^{2}/h$ and $E(n)=\pm v_{F}\sqrt{2n\hbar Be}$ in the isotropic case, which is realized in a system with massless Dirac fermions (such as in graphene). The phase transition does not occur simultaneously in all Hall plateaus as usual but in sequence from low to high energies, with the increase of hopping anisotropy.