Quantitative analytical theory for disordered nodal points [Article and Erratum]

Abstract

Disorder effects are especially pronounced around nodal points in linearly dispersing bandstructures as present in graphene or Weyl semimetals. Despite the enormous experimental and numerical progress, even a simple quantity like the average density of states cannot be assessed quantitatively by analytical means. We demonstrate how this important problem can be solved employing the functional renormalization group method and, for the two dimensional case, demonstrate excellent agreement with reference data from numerical simulations based on tight-binding models. In three dimensions our analytic results also improve drastically on existing approaches.

Erratum prepended (1 + 4 + 3 pages)

References in corpus (10)

• The Kernel Polynomial Method
• Electron transport in disordered graphene
• Modeling disorder in graphene
• Effect of Disorder on Transport in Graphene
• Rare region effects dominate weakly disordered 3D Dirac points
• Ballistic transport in disordered graphene
• Average Density of States in Disordered Graphene systems
• Tilted disordered Weyl semimetals
• Quantum transport in three-dimensional Weyl electron system -- in the presence of charged impurity scattering
• Local density of states in disordered graphene

Cited by in corpus (21)

• Weyl semimetal to metal phase transitions driven by quasiperiodic potentials
• Vanishing density of states in weakly disordered Weyl semimetals
• Nodal points of Weyl semimetals survive the presence of moderate disorder
• From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation
• Avoided quantum criticality in exact numerical simulations of a single disordered Weyl cone
• Disorder-driven quantum transition in relativistic semimetals: functional renormalization via the porous medium equation
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder
• Short note on the density of states in 3D Weyl semimetals
• Topological nodal line in superfluid ${}^3$He and the Anderson theorem
• Fermi arcs and surface criticality in dirty Dirac materials
• Viscosity Enhancement by Electron-Hole Collisions in Dirac Electron Fluid
• Interplay of disorder and interactions in subcritically tilted and anisotropic three-dimensional Weyl fermions
• Ballistic transport in disordered Dirac and Weyl semimetals
• Corrections to the self-consistent Born approximation for Weyl fermions
• Chiral anomaly without Landau levels: From the quantum to the classical regime
• Magnetic, charge, and transport properties of graphene nanoflakes
• Surface quantum critical phenomena in disordered Dirac semimetals
• Phases of translation-invariant systems out of equilibrium: Iterative Green's function techniques and renormalization group approaches
• Disorder correction to the minimal conductance of a nodal-point semimetal
• Boundary critical behavior of the Gross-Neveu-Yukawa model