Quantum phase transition in Hall conductivity on an anisotropic kagome lattice

Abstract

We study theoretically the quantum Hall effect (QHE) on the kagome lattice with anisotropy in one of the hopping integrals. We find an interesting quantum phase, in which the QHE exhibits the energy spectrum given by $E(n)=\ifmmode\pm\else\textpm\fi{}{v}_{F}\sqrt{(n+1/2)\ensuremath{\hbar}Be}$ ($n$ is an integer) being different from the known types, though its quantization rule for Hall conductivity ${\ensuremath{\sigma}}_{xy}=2n{e}^{2}/h$ is conventional. This phase evolves from the QHE phase with ${\ensuremath{\sigma}}_{xy}=4(n+1/2){e}^{2}/h$ and $E(n)=\ifmmode\pm\else\textpm\fi{}{v}_{F}\sqrt{2n\ensuremath{\hbar}Be}$ 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 but occurs in a sequence from low to high energies, with the increase in hopping anisotropy.