Eur. Phys. J. B (2012) 85: 270
https://doi.org/10.1140/epjb/e2012-30026-2

Regular Article

Interlayer phase coherence and Josephson effects in bilayer quantum Hall systems

¹ Nishina Center, RIKEN, 351-0198 Wako, Japan
² Department of Physics, Tbilisi State University, 0128 Tbilisi, Georgia
³ Research Center for Low Temperature and Materials Sciences, Kyoto University, 606-8501 Kyoto, Japan

^a e-mail: ezawa@riken.jp

Received: 10 January 2012
Received in final form: 10 May 2012
Published online: 6 August 2012

Abstract

When an electron is confined within the lowest Landau level, its position is described solely by the guiding center, whose X and Y coordinates do not commute with one another. The equations of motion do not follow from the kinetic Hamiltonian but from the noncommutative property of the space. Based on this microscopic theory, we analyze the bilayer QH system at the filling factor ν = 1, and show that there develops an interlayer phase coherence. It is interpreted that the phase coherence occurs due to the Bose-Einstein condensation of composite bosons, which are single electrons bound to magnetic flux quanta. The phase coherence can induce the Josephson inplane current as well as the Josephson tunneling current, which are dissipationless as in superconductor. We demonstrate that the Josephson inplane current provokes anomalous behaviors in the Hall resistance in counterflow and drag experiments. Furthermore, we investigate the condition on the input current for the tunneling current to be coherent and dissipationless. We predict also how the condition changes when the sample is tilted in the magnetic field.