Josephson tunneling in bilayer quantum Hall system

A Bose–Einstein condensation is formed by composite bosons in the quantum Hall state. A composite boson carries the fundamental charge (−e  ). We investigate Josephson tunneling of such charges in the bilayer quantum Hall system at the total filling ν=1$\nu =1$. We show the existence of the critical current for the tunneling current to be coherent and dissipationless. Our results explain recent experiments due to L. Tiemann, Y. Yoon, W. Dietsche, K. von Klitzing, W. Wegscheider, Phys. Rev. B 80 (2009) 165120] and due to Y. Yoon, L. Tiemann, S. Schmult, W. Dietsche, K. von Klitzing, Phys. Rev. Lett. 104 (2010) 116802]. We predict also how the critical current changes as the sample is tilted in the magnetic field.