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The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of disordered Z2 topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel single parameter scaling, collapsing onto two branches of a universal scaling function, which correspond to the Dirac semimetal and the diffusive metal. The diverging length scale critical exponent ν and the dynamical critical exponent z are estimated, and found to differ significantly from those for the conventional Anderson transition. Critical behavior of experimentally observable quantities near and at the tricritical point is also discussed. Topological classification of different insulating phases [1,2] is an emerging new paradigm in condensed matter physics. Unlike in the Landau theory of phase transitions that is rooted in the idea of spontaneous breaking of symmetry [3], it is less clear how to describe different universality classes of the transitions between topologically different phases. This is because the usual notion of the local order parameter characterizing the different phases is often lacking. At the transition between topologically distinct phases, on the other hand, the gap closes, and the system becomes a semimetal. In three dimensions (3D) such a critical phase is stable in presence of weak disorder [4], but as disorder is increased it gives way to a diffusive metallic state [5]. This transition belongs to a distinct universality class that exhibits nontrivial dynamical and diverging length scale exponents z and ν, for example [5,6]. The 3D Dirac Hamiltonian in presence of disorder is ubiquitous: it applies to certain phases of superfluid 3 He [7], degenerate semiconductors [5], and to the Weyl semimetals [8][9][10][11]. Related theories of disordered critical points for two-dimensional interacting Dirac fermions and bosons were also advanced in the past [12,13].In this paper we discuss how this disorder-induced fermionic criticality is reflected in the scaling behavior of a readily available physical quantity, the single particle density of states (DOS), which can be understood as a proper order parameter that characterizes such a transition. We then express the critical behavior of Dirac electron velocity, diffusion coefficient, conductivity and anomalous diffusion exponent in terms of z and ν. Such a surprisingly simple description is contrasted with the conventional Anderson transition [14][15][16], where the DOS remains smooth through the transition. In order to produce and control the semimetallic phase, we focus on a 3D time-reversal symmetric topological insulator under disorder. The Z 2 topological insu...

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We report a finite size scaling study of the Anderson transition. Different scaling functions and different values for the critical exponent have been found, consistent with the existence of the orthogonal and unitary universality classes which occur in the field theory description of the transition. The critical conductance distribution at the Anderson transition has also been investigated and different distributions for the orthogonal and unitary classes obtained. [S0031-9007(97)

We report an estimate $\nu = 2.593$ $[ {2.587,2.598} ]$ of the critical exponent of the Chalker-Coddington model of the integer quantum Hall effect that is significantly larger than previous numerical estimates and in disagreement with experiment. We conclude that models of non-interacting electrons cannot explain the critical phenomena of the integer quantum Hall effect.Comment: 4 pages. Final version. Journal reference and DOI adde

We report a careful finite size scaling study of the metal-insulator transition in Anderson's model of localization. We focus on the estimation of the critical exponent ν that describes the divergence of the localization length. We verify the universality of this critical exponent for three different distributions of the random potential: box, normal and Cauchy. Our results for the critical exponent are consistent with the measured values obtained in experiments on the dynamical localization transition in the quantum kicked rotor realized in a cold atomic gas.

We studied effects of disorder in a three dimensional layered Chern insulator. By calculating the localization length and density of states numerically, we found two distict types of metallic phases between Anderson insulator and Chern insulator; one is diffusive metallic (DM) phase and the other is renormalized Weyl semimetal (WSM) phase. We show that longitudinal conductivity at the zero energy state remains finite in the renormalizd WSM phase as well as in the DM phase, while goes to zero at a semimetal-metal quantum phase transition point between these two. Based on the Einstein relation combined with the self-consistent Born analysis, we give a conductivity scaling near the quantum transition point.

We reconcile the phenomenon of mesoscopic conductance fluctuations with the single parameter scaling theory of the Anderson transition. We calculate three averages of the conductance distribution, exp(), , and 1/, where g is the conductance in units of e(2)/h and R = 1/g is the resistance, and demonstrate that these quantities obey single parameter scaling laws. We obtain consistent estimates of the critical exponent from the scaling of all these quantities.