Phase Relaxation and Counterflow Dissipation in Bilayer Quantum Hall Systems

双层系统中总填充因子ʋT=1的不可压缩量子霍尔态可以理解为两层之间具有量子相干的激子超流体。这种激子超流最显著的实验表现是层间隧道电导和几乎无耗散的逆流的约瑟夫森式的增强。大量的实验结果可以在这样的假设下得到定量的解释，即超流的拓扑激发引起超流相的驰豫速率，使得层间隧道效应可以在小隧道耦合的情况下微扰处理，类似于耗散约瑟夫森结的情况。到目前为止，ʋT=1双层体系中的相松弛还没有一个定量的理论，而这一理论的发展是这个提议的主要焦点。类似于扩散电子系统中的去相，在扩散电子系统中，电压波动引起量子力学相的随机化，在双层系统中，层间电压的波动使激子超流体的相随机化。作为第一个目标，我们计划利用涨落耗散定理的一种变体，将相位驰豫率与逆流电流的阻力联系起来。这种关系在实验上是可以检验的。作为第二个目标，我们的目标是计算逆流阻力的温度依赖性，从而也计算相松弛速率的温度依赖性。由于流动梅隆的存在会产生逆流阻力，因此需要了解梅隆的温度依赖的迁移率才能实现这一目标。我们计划通过与规范玻璃中涡旋的量子运动进行类比，并利用局域费米子相互作用理论的结果来计算Meron迁移率。

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.