Disorder correction to the minimal conductance of a nodal-point semimetal

Abstract

We consider the disorder-induced correction to the minimal conductance of an anisotropic two-dimensional Dirac node or a three-dimensional Weyl node. An analytical expression is derived for the correction $\delta G$ to the conductance of a finite-size sample by an arbitrary potential, without taking the disorder average, in second-order perturbation theory. Considering a generic model of a short-range disorder potential, this result is used to compute the probability distribution $P(\delta G)$, which is compared to the numerically exact distribution obtained using the scattering matrix approach. We show that $P(\delta G)$ is Gaussian when the sample has a large width-to-length ratio, and study how the expectation value, the standard deviation, and the probability of finding $\delta G<0$ depend on the anisotropy of the dispersion.

arXiv comment10+ pages, 6 figures

References in corpus (48)

• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Type-II Weyl Semimetals
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Topological nodal semimetals
• Bipolar supercurrent in graphene
• Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
• Strong suppression of weak (anti)localization in graphene
• Quantum-limited shot noise in graphene
• Electron transport in disordered graphene
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Demonstration of one-parameter scaling at the Dirac point in graphene
• Quantum criticality between topological and band insulators in $(3+1)$-dimensions
• Imaging electrostatically confined Dirac fermions in graphene quantum dots
• Quantum transport of disordered Weyl semimetals at the nodal point
• Disorder and metal-insulator transitions in Weyl semimetals
• Rare region effects dominate weakly disordered 3D Dirac points
• Anomalously large conductance fluctuations in weakly disordered graphene
• Dirty Weyl fermions: rare region effects near 3D Dirac points
• Quantum transport in Dirac materials: signatures of tilted and anisotropic Dirac and Weyl cones
• Critical transport in weakly disordered semiconductors and semimetals
• Effect of Disorder in a Three-Dimensional Layered Chern Insulator
• Phase diagrams of disordered Weyl semimetals
• Crossover from quantum to Boltzmann transport in graphene
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• Ballistic transport in disordered graphene
• Universal optical conductivity of a disordered Weyl semimetal
• Mesoscopic conductance fluctuations in graphene samples
• Quantum kinetic equation and universal conductance fluctuations in graphene
• Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node
• Universal conductance fluctuations in Dirac materials in the presence of long-range disorder
• Suppression of conductance fluctuation in weakly disordered mesoscopic graphene samples near the charge neutral point
• Critical exponents at the unconventional disorder-driven transition in a Weyl semimetal
• Universal scaling of current fluctuations in disordered graphene
• Conductance fluctuations and field asymmetry of rectification in graphene
• Quantum transport thermometry for electrons in graphene
• On the disorder-driven quantum transition in three-dimensional relativistic metals
• Quantum phase transitions of a disordered antiferromagnetic topological insulator
• Tilted disordered Weyl semimetals
• Vanishing density of states in weakly disordered Weyl semimetals
• Non-Ergodicity & Microscopic Symmetry Breaking of the Conductance Fluctuations in Disordered Mesoscopic Graphene
• Quantitative analytical theory for disordered nodal points [Article and Erratum]
• Numerical Study of Universal Conductance Fluctuation in Three-dimensional Topological Semimetals
• Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters
• Quantum transport at the Dirac point: Mapping out the minimum conductivity from pristine to disordered graphene
• Full counting statistics in disordered graphene at Dirac point: From ballistics to diffusion
• Relationship between conductance fluctuation and weak localization in graphene