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的范例。但在其他意义上，由于维度的降低，新的物理学可能会出现，这是完全不同的。这项工作将检查几个系统的相关电子系统在二维，其中实验和理论都留下了突出的基本问题有待解决。我们将在不久的将来追求的两个主要方向是：(1)Dirac的对偶性和分数量子霍尔态的chen - simons费米子描述。nu=1/2费米液体的HLR理论非常成功地描述了半填充的朗道能级和附近的分数量子霍尔态。然而，近年来，这一观点受到了来自狄拉克谱的不同观点的挑战。在许多方面，这两种理论给出了相同的实验预测。然而，这两种理论似乎有可能预测出非常微妙的差异。这两种方法是否等同，这是一个重要的悬而未决的问题。这是最近被推测出的一大堆非平凡对偶性中最简单的一个例子——理清这个问题具有极其重要的基础意义。(2)双层石墨烯的输运。尽管这个系统已经被研究了十多年，但新的、非常干净的实验显示了一些令人惊讶的结果，这些结果在任何现有的理论中都无法完全理解。特别是，理解电荷和热输运在整体中性仍然是一个开放的和令人兴奋的问题。这项工作属于EPSRC研究领域“凝聚态物理”和大挑战领域涌现和远离平衡的物理以及新量子技术的量子物理。目前还没有公司参与这项工作（尽管我有时会与微软合作，而且这项工作可能会与微软合作）。我们设想与由EPSRC EP/N01930X/1资助的牛津大学博士后阮璇（Dung Nguyen Xuan）合作。与日内瓦教授迪马·阿巴宁（Dima Abanin）有一些合作的机会。

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.