Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node

Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced quantum phase transition between a semimetallic phase at weak disorder and a diffusive-metallic phase at strong disorder. Despite considerable effort, both numerically and analytically, the critical exponents $\nu$ and $z$ of this phase transition are not known precisely. Here we report a numerical calculation of the critical exponent $\nu=1.47\pm0.03$ using a minimal single-Weyl node model and a finite-size scaling analysis of conductance. Our high-precision numerical value for $\nu$ is incompatible with previous numerical studies on tight-binding models and with one- and two-loop calculations in an $\epsilon$-expansion scheme. We further obtain $z=1.49\pm0.02$ from the scaling of the conductivity with chemical potential

Quantum transport of disordered Weyl semimetals at the nodal point

Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder our results are consistent with a renormalization group flow towards an attractive pseudoballistic fixed point with zero conductivity and a scale-independent conductance; for stronger disorder diffusive behavior is reached. We identify the Fano factor as a signature that discriminates between these two regimes

Comparison of transport and density of states calculations

Double Weyl nodes are topologically protected band crossing points which carry chiral charge ±2. They are stabilized by C4 point-group symmetry and are predicted to occur in SrSi2 or HgCr2Se4. We study their stability and physical properties in the presence of a disorder potential. We investigate the density of states and the quantum transport properties at the nodal point. We find that, in contrast to their counterparts with unit chiral charge, double Weyl nodes are unstable to any finite amount of disorder and give rise to a diffusive phase, in agreement with the predictions of Goswami and Nevidomskyy [Phys. Rev. B 92, 214504 (2015)] and Bera, Sau, and Roy [Phys. Rev. B 93, 201302 (2016)]. However, for finite system sizes a crossover between pseudodiffusive and diffusive quantum transport can be observed

Proposed Rabi-Kondo Correlated State in a Laser-Driven Semiconductor Quantum Dot

Spin exchange between a single-electron charged quantum dot and itinerant electrons leads to an emergence of Kondo correlations. When the quantum dot is driven resonantly by weak laser light, the resulting emission spectrum allows for a direct probe of these correlations. In the opposite limit of vanishing exchange interaction and strong laser drive, the quantum dot exhibits coherent oscillations between the single-spin and optically excited states. Here, we show that the interplay between strong exchange and non-perturbative laser coupling leads to the formation of a new nonequilibrium quantum-correlated state, characterized by the emergence of a laser-induced secondary spin screening cloud, and examine the implications for the emission spectrum

Signatures of tilted and anisotropic Dirac and Weyl cones

We calculate conductance and noise for quantum transport at the nodal point for arbitrarily tilted and anisotropic Dirac or Weyl cones. Tilted and anisotropic dispersions are generic in the absence of certain discrete symmetries, such as particle-hole and lattice point group symmetries. Whereas anisotropy affects the conductance g, but leaves the Fano factor F (the ratio of shot noise power and current) unchanged, a tilt affects both g and F. Since F is a universal number in many other situations, this finding is remarkable. We apply our general considerations to specific lattice models of strained graphene and a pyrochlore Weyl semimetal

Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition

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)] 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 energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results \nu_IQH = 2.56 - 2.62 from models of the IQHT. At E=0 however, we obtain \nu_0 =2.30-2.36 incompatible with \nu_IQH. This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.Comment: close to published versio

Frustrated quantum spins at finite temperature Pseudo Majorana functional renormalization group approach

The pseudofermion functional renormalization group PFFRG method has proven to be a powerful numerical approach to treat frustrated quantum spin systems. In its usual implementation, however, the complex fermionic representation of spin operators introduces unphysical Hilbert space sectors which render an application at finite temperatures inaccurate. In this work we formulate a general functional renormalization group approach based on Majorana fermions to overcome these difficulties. We, particularly, implement spin operators via an SO 3 symmetric Majorana representation which does not introduce any unphysical states and, hence, remains applicable to quantum spin models at finite temperatures. We apply this scheme, dubbed pseudo Majorana functional renormalization group PMFRG method, to frustrated Heisenberg models on small spin clusters as well as square and triangular lattices. Computing the finite temperature behavior of spin correlations and thermodynamic quantities such as free energy and heat capacity, we find good agreement with exact diagonalization and the high temperature series expansion down to moderate temperatures. We observe a significantly enhanced accuracy of the PMFRG compared to the PFFRG at finite temperatures. More generally, we conclude that the development of functional renormalization group approaches with Majorana fermions considerably extends the scope of applicability of such method