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

用数值方法和解析方法研究了石墨烯和某些有机金属中实现的二维无质量狄拉克费米子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之一的n=0朗道能级，对手征对称性的无序具有惊人的健壮性。这种稳健性表现为n=0朗道能级的反常锐化，导致量子霍尔跃迁的非传统临界性。我们还推广了手征对称性以涵盖一般的倾斜狄拉克费米子，并表明广义手征对称性确实保护了n=0朗道能级不受无序的影响。这些发现表明，非传统的量子霍尔跃迁可以在很多系统中实现，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.