Phase Relaxation and Counterflow Dissipation in Bilayer Quantum Hall Systems

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The incompressible quantum Hall state at total filling factor ʋT = 1 in a bilayer system can be understood as an excitonic superfluid with quantum coherence between the two individual layers. The most striking experimental manifestation of such excitonic superfluidity is a Josephson like enhancement of the interlayer tunnel conductance and almost dissipationless counterflow-currents. A large number of experimental results can be quantitatively explained under the assumption that the topological excitations of the superfluid, so-called merons, give rise to a relaxation rate for the superfluid phase, such that interlayer tunneling can be treated perturbatively in the regime of small tunnel couplings, similarly to the case of dissipative Josephson junctions. A quantitative theory of phase relaxation in ʋT = 1 bilayer systems is missing so far, and the development of such a theory is the main focus of this proposal. Similarly to dephasing in diffusive electronic systems, where voltage fluctuations give rise to a randomization of the quantum mechanical phase, in bilayer systems fluctuations in the interlayer voltage randomize the phase of the excitonic superfluid. As a first goal, we plan to relate the phase relaxation rate to the resistance of counter-flow currents by using a variant of the fluctuation-dissipation theorem. Such a relation would be experimentally testable. As a second goal, we aim at computing the temperature dependence of the counter-flow resistance and thus also of the phase relaxation rate. Since counter-flow resistance arises due to the presence of mobile merons, an understanding of the temperature dependent mobility of merons is needed to achieve this goal. We plan to compute the meron mobility by using analogies with the quantum motion of vortices in a gauge glass and by using results from the theory of interacting localized fermions.