Superfluidity and Superconductivity in Double-Layered Quantum Hall state

We discuss and review the basic physics that leads to superfluidity/superconductivity in certain quantum Hall states, in particular the so-called double-layered (mmm) state. In the K-matrix description of the quantum correlation in quantum Hall states, those states with det(K) = 0 contain a special correlation that leads to superfluidity/superconductivity. We propose a four-terminal measurement to test the DC Josephson-like effect in interlayer tunneling, so that the superfluidity/superconductivity in the (mmm) states can be settled experimentally. Almost 10 years ago we predicted[1, 2, 3, 4] that under certain circumstances a double layered quantum Hall system would exhibit the physics of superfluidity/superconductivity. Recently, this apparently surprising and somewhat counter-intuitive prediction was verified dramatically by Eisenstein et al[5] in a form of (two-terminal) DC Josephson-like effect for interlayer tunneling. Historically, the gapless mode in the (111) double layered quantum Hall state was first discovered by Fertig[6]. Later, the effect of interlayer tunneling was included[7, 8]. However, superfluidity and superconductivity were not discussed in these earlier work. In Ref. [1, 2], we discovered and identified the spontaneously broken U(1) symmetry in the (mmm) states and emphasized the resulting superfluidity and superconductivity. The properties we discussed include the Kosterlitz-Thouless transition, the zero resistivity in the counter-current flow, the DC/AC Josephson-like effect in interlayer