无序三维Dirac和Weyl半金属的稀有区诱导避免量子临界

J. Pixley, D. Huse, S. Sarma
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引用次数: 52

摘要

我们数值研究了短程势无序对无质量非相互作用的三维Dirac和Weyl费米子的影响,重点讨论了分离半金属相和扩散金属相的量子临界点问题。我们利用$H^2$上的Lanczos和$H$上的核多项式相结合的方法,确定了无序狄拉克哈密顿量($H$)的特征态的性质,并精确计算了接近零能量的态密度(DOS)。我们建立了两种不同类型的低能本征态的存在,这些低能本征态导致了弱无序半金属态的无序密度。这些是(i)典型的特征态,可以很好地用线性色散摄动修饰的狄拉克态来描述,以及(ii)非摄动稀有特征态,它们在具有最大(和最稀有)局部随机势的实空间区域中具有弱色散和准局域化。利用扭曲边界条件,我们能够系统地找到并研究这两类本征态。我们发现狄拉克态在有限大小的DOS中贡献了低能峰,这些低能峰是由在无序存在下移位和变宽的干净特征态产生的。另一方面,我们建立了稀有的准局域本征态贡献了一个非零背景DOS,它仅在零能量附近弱能量依赖,并且在弱无序时呈指数小。我们发现预期的半金属到扩散金属的量子临界点被转换为一个被非扰动效应“舍入”的量子临界点,在Dirac能量附近的DOS中没有任何奇异行为的迹象。我们讨论了我们的结果对无序狄拉克和Weyl半金属的影响,并调和了大量现有的数值工作,显示量子临界与稀有区域效应的存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Rare region induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals
We numerically study the effect of short ranged potential disorder on massless noninteracting three-dimensional Dirac and Weyl fermions, with a focus on the question of the proposed quantum critical point separating the semimetal and diffusive metal phases. We determine the properties of the eigenstates of the disordered Dirac Hamiltonian ($H$) and exactly calculate the density of states (DOS) near zero energy, using a combination of Lanczos on $H^2$ and the kernel polynomial method on $H$. We establish the existence of two distinct types of low energy eigenstates contributing to the disordered density of states in the weak disorder semimetal regime. These are (i) typical eigenstates that are well described by linearly dispersing perturbatively dressed Dirac states, and (ii) nonperturbative rare eigenstates that are weakly-dispersive and quasi-localized in the real space regions with the largest (and rarest) local random potential. Using twisted boundary conditions, we are able to systematically find and study these two types of eigenstates. We find that the Dirac states contribute low energy peaks in the finite-size DOS that arise from the clean eigenstates which shift and broaden in the presence of disorder. On the other hand, we establish that the rare quasi-localized eigenstates contribute a nonzero background DOS which is only weakly energy-dependent near zero energy and is exponentially small at weak disorder. We find that the expected semimetal to diffusive metal quantum critical point is converted to an {\it avoided} quantum criticality that is "rounded out" by nonperturbative effects, with no signs of any singular behavior in the DOS near the Dirac energy. We discuss the implications of our results for disordered Dirac and Weyl semimetals, and reconcile the large body of existing numerical work showing quantum criticality with the existence of the rare region effects.
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