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

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 et al. [Phys. Rev. Lett. 74, 1419 (1995)].

Figure 1

Tunneling current curves for different magnetic field values using the moment expansion solution of Eq. (24). The legend shows the peak bias values calculated by Eq. (30).

Figure 2

Normalized tunneling current curves for different interlayer separation distances $d$ measured in Å.

Figure 3

Tunneling current curves for different magnetic field values produced by numerically integrating Eq. (24). The legend shows the peak bias values obtained with this approach. They are in close agreement with the analytic results.