Effects of disorder on transport properties of low-dimensional electronic systems with unconventional band structure

本文研究了二维无质量狄拉克费米子在石墨烯和某些有机金属中在磁场中的输运性质。我们发现，作为石墨烯量子霍尔效应的标志，n=0朗道能级对手性对称的失序具有惊人的鲁棒性。这种鲁棒性表现为n=0朗道能级的异常锐度，导致量子霍尔跃迁的非常规临界。我们也推广了手性对称以包含一般倾斜狄拉克费米子，并证明了广义手性对称确实保护了n=0朗道能级免受失序。这些发现表明，非常规量子霍尔跃迁可以在广泛的系统中实现，例如光学晶格中的冷原子。

Transport properties of two-dimensional massless Dirac fermions, which is realized in graphene and in certain organic metals, in a magnetic field has been investigated both numerically and analytically. We have found that the n=0 Landau level, which is a hallmark of the graphene quantum Hall effect, is surprisingly robust against disorder respecting the chiral symmetry. This robustness appears as a anomalous sharpness of the n=0 Landau level leading to the unconventional criticality of the quantum Hall transition. We have also generalized the chiral symmetry to encompass the generic tilted Dirac fermions and show that the generalized chiral symmetry indeed protects the n=0 Landau level against disorder. These findings suggest that the unconventional quantum Hall transition can be realized in a wide range of systems such as cold atoms in an optical lattice.