Correlated states of electrons in two dimension

二维电子系统在某种意义上是理解三维物理学的范例。但在其他意义上，新的物理学可以出现，这是完全不同的，由于减少维度。这项工作将检查几个systems相关的电子系统在两个维度的实验和理论都留下了悬而未决的基本问题要解决。我们今后的主要研究方向是：（1）分数量子Hall态的Dirac对偶性和Chern-Simons费米子描述。nu=1/2费米液体的量子场论对半满朗道能级及其附近的分数量子霍尔态给出了非常成功的描述。然而，近年来，这一图像受到了来自狄拉克谱的不同图像的挑战。在许多方面，这两个理论给出了相同的实验预测。然而，这两种理论似乎预测了非常微妙的差异。这是一个重要的悬而未决的问题，这两种方法是否是等效的或没有。这是一个最近被发现的非平凡对偶的大家族中最简单的例子--理清这个问题具有巨大的根本重要性。(2)双层石墨烯中的输运。虽然这个系统已经研究了十多年，但新的、非常干净的实验已经显示出一些令人惊讶的结果，这些结果在任何现有理论中都无法完全理解。特别是，了解在整体中性的电荷和热传输仍然是一个开放的和令人兴奋的问题。这项工作福尔斯属于EPSRC的研究领域“凝聚态物理”和大挑战领域的出现和物理远离平衡，也量子物理的新量子技术。目前还没有公司参与这项工作（尽管我有时会与微软合作，这项工作可能会涉及与微软的合作）。我们设想与Dung Nguyen Xuan合作，他是牛津大学的博士后，由EPSRC EP/N 01930 X/1资助。与日内瓦的迪马·阿巴宁教授合作的可能性很大。

Electronic systems in two dimension are in some sense a paradigm for undersanding physics in three dimensions. But in other senses new physics can emerge which is completely different due to the reduced dimensionality. This work will examine several sysems of correlated electronic systems in two dimensions where both experiment and theory have left outstanding fundamental questions to be solved. The two main directions we will pursue in the immeidate future are:(1) Duality of Dirac and Chern-Simons fermion description of fractional quantum Hall states. The HLR theory of the nu=1/2 fermi liquid has given a remarkably successful description of the half-filled Landau level, and the fractional quantum Hall states nearby. In recent years, however, this picture has been challenged by a different picture which starts from a Dirac spectrum. In many ways these two theories give the same experimental predictions. However, it seems possible that the two theories predict very subtle differences. It is an important open question as to whether these two approaches are equivalent or not. This is the simplest example of a huge family of nontrivial dualities which have been conjectured recently - sorting out this issue is of enormous fundamental importance.(2) Transport in bilayer graphene. Although this system has been studied for a decade or more, new, extremely clean experiments have shown some surprsing results which cannot be fully understood within any existing theory. In particular, understanding the charge and heat transport at overall neutrality remains an open and exciting problem. This work falls into the EPSRC reseach area "condensed matter physics" and the Grand Challenge areas Emergence and Physics Far from Equilibrium and also Quantum Physics for New Quantum Technologies. Currently there are no companies involved in this work (although I sometimes colalborate with microsoft and it is possible that this work will involve collaboration with microsoft). We envision collaboration with Dung Nguyen Xuan, a postdoc at Oxford funded by EPSRC EP/N01930X/1 . There is some chance of collaboration with Dima Abanin a professor in Geneva.