Broken Symmetry and Josephson-Like Tunnelling in Quantum Hall Bilayers

Abstract

I review recent novel experimental and theoretical advances in the physics of quantum Hall effect bilayers. Of particular interest is a broken symmetry state which optimizes correlations by putting the electrons into a coherent superposition of the two different layers.The various quantum Hall effects are among the most remarkable many-body phenomena discovered in the second half of the twentieth century. 1, 2, 3, 4 The fractional effect has yielded fractional charge, spin and statistics, as well as unprecedented order parameters. 5 There are beautiful connections with a variety of different topological and conformal field theories of interest in nuclear and high energy physics.The quantum Hall effect (QHE) takes place in a two-dimensional electron gas formed in a quantum well in a semiconductor host material and subjected to a very high magnetic field. In essence it is a result of a commensuration between the number of electrons, N , and the number of flux quanta, N Φ , in the applied magnetic field. The electrons condense into distinct and highly non-trivial ground states ('vacua') formed at each rational fractional value of the filling factor ν ≡ N/N Φ .The essential feature of (most) of these exotic states is the existence of an excitation gap. The electron fluid is incompressible and flows rigidly past obstacles (impurities in the sample) with no dissipation. A weak external electric field will cause the fluid to move, but the excitation gap prevents the fluid from absorbing any energy from the electric field. Hence the current flow must be exactly at right angles to the field and the conductivity tensor takes the remarkable universal formIronically, this ideal behavior occurs because of imperfections and disorder in the samples which localize topological defects (vortices) whose motion would otherwise dissipate energy. In a two-dimensional superconductor, such vortices undergo a confinement phase transition at the Kosterlitz-Thouless temperature and dissipation ceases. In most cases in the QHE, an analog of the Anderson-Higgs mechanism causes the vortices to be deconfined 5 so that dissipation is strictly zero only at zero temperature. In practice, values of σ xx /σ xy as small as 10 −13 are not difficult to obtain at dilution refrigerator tempertures. Recent technological progress in molecular beam epitaxy techniques has led to the ability to produce pairs of closely spaced two-dimensional electron gases. Strong correlations between the electrons in different layers lead a great deal of completely new physics involving spontaneous interlayer phase coherence. 6,

Paired states on a torus

“…Further such an interaction could account for a current flow between the layers also in the absence of uniform tunneling. All that is in agreement with recent experimental observations [27]; other theoretical analysis in such a context have been already presented in [28]. Then a coherent superposition of interlayer interactions could drive the system to a more symmetric phase in which the two layers are indistinguishable, i.e.…”