Correlated states of electrons in two dimension

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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.