Tunneling between two-dimensional electron systems in a high magnetic field: role of interlayer interactions

TL;DR

This paper models tunneling in bilayer quantum Hall systems using coupled Wigner crystals to analyze how interlayer interactions and magnetophonon modes influence tunneling current, matching experimental observations.

Contribution

It extends previous models by including out-of-phase magnetophonon modes in a continuum Wigner crystal framework for bilayer systems.

Findings

Tunneling current peak scales with magnetic field as previously found.

Peak value's dependence on interlayer separation matches experimental data.

Different scaling behavior of peak with interlayer separation compared to earlier models.

Abstract

We calculate the tunneling current for a bilayer quantum Hall system in the interlayer incoherent regime. In order to capture the strong correlation effects we model the layers as two Wigner crystals coupled through interlayer Coulomb interactions, treated in the continuum limit. By generalizing previous work by Johansson and Kinaret (JK), we are able to study the effect of the low energy out-of-phase magnetophonon modes on the electron ``shake-up'' which occurs during a tunneling event. We find the tunneling current peak value to scale with the magnetic field as found by JK; however, we find a different scaling of the peak value with the interlayer separation, which agrees with the measurements by Eisenstein \it{et al.}