Anomalous Hall resistance in bilayer quantum Hall systems

Abstract

We present a microscopic theory of the Hall current in the bilayer quantum Hall system on the basis of noncommutative geometry. By analyzing the Heisenberg equation of motion and the continuity equation of charge, we demonstrate the emergence of the phase current in a system where the interlayer phase coherence develops spontaneously. The phase current arranges itself to minimize the total energy of the system, as induces certain anomalous behaviors in the Hall current in the counterflow geometry and also in the drag experiment. They explain the recent experimental data for anomalous Hall resistances due to Kellogg et al. [M.

Spin supercurrent in the canted antiferromagnetic phase

“…This is precisely the same as in the ν = 1 bilayer QH system. Indeed, the supercurrent leads to the same formula [10] of the anomalous Hall resistivity for the counterflow and drag geometries as the one at ν = 1. What is remarkable is that the total current flowing the bilayer system is a supercurrent carrying solely spins and not charges in the counterflow geometry.…”

“…Other examples are the anomalous behavior of the Hall resistance reported in counterflow experiments [7,8] and in drag experiments [9]. They are triggered by the supercurrent within each layer [10]. Quite recently, careful experiments [11] were performed to explore the condition for the tunneling current to be dissipationless.…”

Nambu–Goldstone modes and the Josephson supercurrent in the bilayer quantum Hall system

“…A bilayer system consists of the two layers and the volume between them. The Coulomb energy in the volume is minimized [12] by the condition…”

“…Other examples are the anomalous behavior of the Hall resistance reported in counterflow experiments [8,9] and in drag experiments [10]. They are triggered by the Josephson supercurrent within each layer [12].…”

“…A related topic has been investigated in [20]. The supercurrent in the CAF phase leads to the same formula [12] for the anomalous Hall resistivity for the counterflow and drag geometries as the one at ν = 1. What is remarkable is that the total current flowing in the CAF phase is a Josephson supercurrent carrying solely spins in the counterflow geometry.…”