Sbierski Björn, Dresselhaus Elizabeth J, Moore Joel E, Gruzberg Ilya A
Department of Physics, University of California, Berkeley, California 94720, USA.
Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
Phys Rev Lett. 2021 Feb 19;126(7):076801. doi: 10.1103/PhysRevLett.126.076801.
Two-dimensional (2D) Dirac fermions are a central paradigm of modern condensed matter physics, describing low-energy excitations in graphene, in certain classes of superconductors, and on surfaces of 3D topological insulators. At zero energy E=0, Dirac fermions with mass m are band insulators, with the Chern number jumping by unity at m=0. This observation lead Ludwig et al. [Phys. Rev. B 50, 7526 (1994)PRBMDO0163-182910.1103/PhysRevB.50.7526] to conjecture that the transition in 2D disordered Dirac fermions (DDF) and the integer quantum Hall transition (IQHT) are controlled by the same fixed point and possess the same universal critical properties. Given the far-reaching implications for the emerging field of the quantum anomalous Hall effect, modern condensed matter physics, and our general understanding of disordered critical points, it is surprising that this conjecture has never been tested numerically. Here, we report the results of extensive numerics on the phase diagram and criticality of 2D DDF in the unitary class. We find a critical line at m=0, with an energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results ν_{IQH}=2.56-2.62 from models of the IQHT. At E=0, however, we obtain ν_{0}=2.30-2.36 incompatible with ν_{IQH}. This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.
二维（2D）狄拉克费米子是现代凝聚态物理的核心范式，用于描述石墨烯、某些类型的超导体以及三维拓扑绝缘体表面的低能激发。在零能量E = 0时，质量为m的狄拉克费米子是带绝缘体，在m = 0时陈数跳跃1。这一观察结果促使路德维希等人[《物理评论B》50, 7526 (1994年)PRBMDO0163 - 182910.1103/PhysRevB.50.7526]推测，二维无序狄拉克费米子（DDF）中的转变和整数量子霍尔转变（IQHT）由同一个不动点控制，并具有相同的普适临界性质。鉴于这一推测对新兴的量子反常霍尔效应领域、现代凝聚态物理以及我们对无序临界点的一般理解具有深远影响，令人惊讶的是，这一推测从未通过数值方法进行检验。在此，我们报告关于酉类中二维DDF的相图和临界性的广泛数值计算结果。我们在m = 0处发现一条临界线，其局域长度指数与能量有关。在高能量下，我们关于DDF的结果与IQHT模型中最先进的数值结果ν_{IQH}=2.56 - 2.62一致。然而，在E = 0时，我们得到ν_{0}=2.30 - 2.36，与ν_{IQH}不兼容。这一结果挑战了IQHT不同模型之间的推测关系，并讨论了几种解释。
