Anisotropic ground states of the quantum Hall system with currents

TL;DR

This paper investigates how finite electric currents influence anisotropic quantum Hall states, revealing a transition from the anisotropic charge density wave to the striped Hall state at a critical current, with implications for experimental observations.

Contribution

It introduces a detailed analysis of current effects on anisotropic quantum Hall states using effective action and block diagonalization on a von Neumann lattice, identifying a critical current for phase transition.

Findings

ACDW state energy increases faster with current than striped Hall state

Striped Hall state becomes energetically favorable above a critical current

Critical current estimated at about 0.04 - 0.05 nA, smaller than experimental currents

Abstract

Anisotropic states at half-filled third and higher Landau levels are investigated in the system with a finite electric current. We study the response of the striped Hall state and the anisotropic charge density wave (ACDW) state against the injected current using the effective action. Current distributions and a current dependence of the total energy are determined for both states. With no injected current, the energy of the ACDW state is lower than that of the striped Hall state. We find that the energy of the ACDW state increases faster than that of the striped Hall state as the injected current increases. Hence, the striped Hall state becomes the lower energy state when the current exceeds the critical value. The critical value is estimated at about 0.04 - 0.05 nA which is much smaller than the current used in the experiments. Our calculations are performed using a block diagonalization technique on a von Neumann lattice. We review this technique in this thesis.