Local density of states in disordered graphene

Abstract

We study two lattice models, the honeycomb lattice (HCL) and a special square lattice (SQL), both reducing to the Dirac equation in the continuum limit. In the presence of disorder (gaussian potential disorder and random vector potential), we investigate the behaviour of the density of states (DOS) numerically and analytically. While an upper bound can be derived for the DOS on the SQL at the Dirac point, which is also confirmed by numerical calculations, no such upper limit exists for the HCL in the presence of random vector potential. A careful investigation of the lowest eigenvalues indeed indicate, that the DOS can possibly be divergent at the Dirac point on the HCL. In spite of sharing a common continuum limit, these lattice models exhibit different behaviour.

12 pages, 10 figures

References in corpus (21)

• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor
• Electronic Properties of Disordered Two-Dimensional Carbon
• Strong suppression of weak (anti)localization in graphene
• Disorder Induced Localized States in Graphene
• Giant Phonon-induced Conductance in Scanning Tunneling Spectroscopy of Gate-tunable Graphene
• Transport in Bilayer Graphene: Calculations within a self-consistent Born approximation
• Gauge field induced by ripples in graphene
• Disorder Effects in Two-Dimensional d-wave Superconductors
• Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors
• Graphene via large N I: Renormalization
• Particle-hole symmetric localization in two dimensions
• Average Density of States in Disordered Graphene systems
• Disordered Dirac Fermions: the Marriage of Three Different Approaches
• Termination of Multifractal Behaviour for Critical Disordered Dirac Fermions
• Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model
• On the effect of weak disorder on the density of states in graphene
• Long-range correlations in disordered graphene
• Suppression of magnetotransport in strongly disordered graphene

Cited by in corpus (9)

• Fluctuation-induced quantum friction in nanoscale water flows
• Local density of states and Friedel oscillation in graphene
• Surface charge conductivity of topological insulator in a magnetic field: effect of hexagonal warping
• Quantitative analytical theory for disordered nodal points [Article and Erratum]
• Evidence for local spots of viscous electron flow in graphene at moderate mobility
• Gaps and tails in graphene and graphane
• The effects of disorder and interactions on the Anderson transition in doped Graphene
• Narrow depression in the density of states at the Dirac point in disordered graphene
• Universality, exponents and anomaly cancellation in disordered Dirac fermions