Phase Relaxation and Counterflow Dissipation in Bilayer Quantum Hall Systems

在双层系统中，总填充因子T = 1的不可压缩量子霍尔态可以理解为两个单独层之间具有量子相干性的激子超流体。这种激子超流性最显著的实验表现是层间隧道电导的约瑟夫森增强和几乎无耗散的逆流电流。大量的实验结果可以定量地解释的假设下，拓扑激发的超流，所谓的merons，引起弛豫率的超流相，这样层间隧穿可以处理微扰的小隧道耦合的制度，类似的情况下耗散约瑟夫森结。一个定量的理论相弛豫在λ T = 1双层系统是失踪，到目前为止，这样一个理论的发展是本建议的主要焦点。类似于扩散电子系统中的退相，其中电压波动引起量子力学相位的随机化，在双层系统中，层间电压的波动使激子超流体的相位随机化。作为第一个目标，我们计划通过使用波动耗散定理的变体将相位弛豫速率与逆流电流的电阻相关联。这种关系是可以用实验来检验的。作为第二个目标，我们的目标是计算的温度依赖性的逆流阻力，从而也相弛豫速率。由于逆流阻力的出现是由于存在移动的merons，需要了解温度依赖的merons的流动性，以实现这一目标。我们计划通过使用与量杯中涡旋的量子运动的类比和使用相互作用局域费米子理论的结果来计算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.