Interlayer tunneling and the problem of superfluidity in bilayer quantum Hall systems

A possibility of nondissipative transmission of electrical current from the source to the load using superfluid electron-hole pairs in bilayers is studied. The problem is considered with reference to quantum Hall bilayers with the total filling factor νT=1. At nonzero interlayer tunneling the current pattern looks as a sum of uniform planar counterflow currents and Josephson vortices. The difference of electrochemical potentials of the layers (that is required to support the current in the load circuit) causes the motion of the Josephson vortices. In such situation, the second superfluid viscosity comes into play and results in dissipation of energy. It is found that the power of losses is proportional to the square of the matrix element of the interlayer tunnelling and depends nonlinearly on the load resistance