Phase Relaxation and Counterflow Dissipation in Bilayer Quantum Hall Systems

双层体系中总填充因子为T = 1时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性的激子超流体。这种激子超流动性最显著的实验表现是层间隧道电导率和几乎无耗散逆流的约瑟夫森式增强。大量的实验结果可以定量解释的假设下，拓扑激励的超流体，所谓的介子，引起超流体相的弛豫率，使得层间隧道可以处理微扰在小隧道耦合的制度，类似于耗散约瑟夫森结的情况。迄今为止，还没有一个关于二元体系相松弛的定量理论，而这一理论的发展是本文的主要重点。类似于扩散电子系统中的失相，其中电压波动引起量子力学相位的随机化，在双层系统中，层间电压波动使激子超流体的相位随机化。作为第一个目标，我们计划使用波动耗散定理的一个变体来将相松弛率与逆流阻力联系起来。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。由于流动介子的存在会产生逆流阻力，因此需要了解介子的温度依赖迁移率才能实现这一目标。我们计划通过与量规玻璃中涡旋的量子运动的类比以及利用相互作用局域费米子理论的结果来计算介子的迁移率。

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.