Counterflow Superfluidity and Tunnelling in Quantum Hall Bilayers

电子是负责在日常材料中导电的带电粒子，如铜线和个人电脑中的硅芯片。在过去的十年里，研究人员发现，如果我们将电子挤压成只有百万分之一厘米厚的平板，它们的行为似乎与我们的预期截然不同。平地上最引人注目的电子例子是高温超导体，电子生活在铜氧化物平面上。电子似乎在没有遇到任何阻力的情况下流动。这意味着电流可以在这些材料中流动，而不会损失热量。如果我们能说服这些材料在室温下表现出这样的行为，就会有一系列令人兴奋的新技术的基础。这个项目着眼于另一个表现出同样奇怪效果的平原系统，贝尔实验室和普林斯顿大学的研究人员最近看到了这一点。在一系列实验技术中，他们成功地制造了两个非常接近的平行平板电子，每个平板上都独立地连接着导线。然后，他们将样本置于强磁场(地球磁场强度的一百万倍)中。在这个双层中，他们看到了看起来非常像超导的东西，当它们导致电流在两个电子薄片中以相反的方向流动时！换句话说，逆流电流可以在没有阻力的情况下流动。他们把这种效应称为逆流超流。理论家怀疑，这种现象与这样一个事实密切相关，即平地中的电子对存在于它们之间的排斥力特别敏感。在这种情况下，不同薄片中的电子之间的排斥力与同一薄片中的电子之间的排斥力一样强。因此，顶层的电子运动会导致底层的电子朝着相反的方向移动。这个项目旨在探索逆流超流的理论图景。虽然已经提出了许多理论，但它们都不能解释实验数据中的一些非常显著的特征。事实上，没有人能解释为什么整个样本都会出现逆流现象。为什么电子从样品的一边一直走到顶层的另一边，却在底层从另一个方向回来--它们可能已经跳到了一半！我们想提供一个微观理论，可以解释实验中的谜题。只有解决了这些难题，我们才能确信这种逆流超流现象的存在。从更广泛的角度来看，我们希望我们为这个问题开发的理论将为如何理解电子在平地上玩的有趣的游戏提供一些启示。

Electrons are the charged particles that are responsible for the conduction of electricity in everyday materials, such as copper wires and the silicon chips in a PC. In the last decade, researchers have discovered that, if we squeeze the electrons into flat sheets which are just a millionth of a centimetre in thickness, they appear to behave quite differently from what we expect.The most dramatic examples of electrons in flatland are the high-temperature superconductors where the electrons live on copper-oxide planes. The electrons appear to flow without experiencing any resistance. This means that electric currents can flow in these materials without losing energy as heat. If we can persuade these materials to behave like this at room temperature, there will be the basis for a whole variety of exciting new technologies.This project looks at another flatland system which displays equally bizarre effects, recently seen by researchers in Bell Labs and Princeton. In a tour de force of experimental techniques, they have managed to fabricate two parallel flat sheets of electrons very close together with leads attached independently to each sheet. They then placed their sample in a strong magnetic field (a million times the strength of the Earth's magnetic field). In this bilayer , they see something which looks very much like superconductivity, when they cause currents to flow in opposite directions in the two electron sheets! In other words, the counterflowing currents can flow without resistance. They have called this effect counterflow superfluidity .Theorists suspect that this phenomenon is intimately connected to the fact that electrons in flatland are particularly sensitive to the repulsive forces that exist between them. In this case, the repulsion between electrons in different sheets is as strong as the repulsion between electrons in the same sheet. So, the motion of electrons in the top layer causes electrons in the bottom layer to move away in the opposite direction.This project is designed to explore this theoretical picture of counterflow superfluidity. Many theories have been put forward, but they cannot explain some very prominent features in the experimental data. Indeed, no one can explain why the counterflow can occur over the whole sample. Why do the electrons go all the way from one side of the sample to the other on the top layer, only to come back in the other direction on the bottom layer -- they could have jumped over halfway along!We want to provide a microscopic theory that can explain the puzzles from the experiments. Only when these puzzles are resolved can we be confident that this phenomenon of counterflow superfluidity exists. From a wider perspective, we hope that the theory that we develop for this problem will shed some light on how to understand the intriguing games that electrons play in flatland .