Two dimensional Dirac fermions in the presence of long-range correlated disorder

Abstract

We consider 2D Dirac fermions in the presence of three types of disorder: random scalar potential, random gauge potential and random mass with long-range correlations decaying as a power law. Using various methods such as the self-consistent Born approximation (SCBA), renormalization group (RG), the matrix Green function formalism and bosonisation we calculate the density of states and study the full counting statistics of fermionic transport at lower energy. The SCBA and RG show that the random correlated scalar potentials generate an algebraically small energy scale below which the density of states saturates to a constant value. For correlated random gauge potential, RG and bosonisation calculations provide consistent behavior of the density of states which diverges at zero energy in an integrable way. In the case of correlated random mass disorder the RG flow has a nontrivial infrared stable fixed point leading to a universal power-law behavior of the density of states and also to universal transport properties. In contrast to uncorrelated case the correlated scalar potential and random mass disorders give rise to deviation from the pseudodiffusive transport already to lowest order in disorder strength.

17 pages, 8 figures, revtex4

References in corpus (21)

• The electronic properties of graphene
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Weak localisation magnetoresistance and valley symmetry 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
• Gauge field induced by ripples in graphene
• Ordering of magnetic impurities and tunable electronic properties of topological insulators
• Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions
• Anomalous Orbital Magnetism and Hall Effect of Massless Fermions in Two Dimension
• Surface state charge dynamics of a high-mobility three dimensional topological insulator
• Ballistic transport in disordered graphene
• Mesoscopic conductance fluctuations in graphene samples
• Roughness of undoped graphene and its short-range induced gauge field
• Emergence of Dirac Electron Pair in Charge Ordered State of Organic Conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$
• Disorder effects at a nematic quantum critical point in d-wave cuprate superconductor
• Statics and dynamics of elastic manifolds in media with long-range correlated disorder
• Dirac fermions in a power-law-correlated random vector potential
• Full counting statistics in disordered graphene at Dirac point: From ballistics to diffusion
• Effects of disorder on the transmission of nodal fermions through a d-wave superconductor

Cited by in corpus (21)

• Space dependent Fermi velocity in strained graphene
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• On the disorder-driven quantum transition in three-dimensional relativistic metals
• New Quantum Transition in Weyl Semimetals with Correlated Disorder
• Anderson-Kitaev spin liquid
• Weyl node with random vector potential
• Critical behavior of the 2D Ising model with long-range correlated disorder
• Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator
• Sign change in the anomalous Hall effect and strong transport effects in a 2D massive Dirac metal due to spin-charge correlated disorder
• Condition for the emergence of a bulk Fermi arc in disordered Dirac-fermion systems
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder
• Random-mass disorder in the critical Gross-Neveu-Yukawa models
• Effect of disorder with long-range correlation on transport in graphene nanoribbon
• Surface quantum critical phenomena in disordered Dirac semimetals
• Transport of Dirac electrons in a random magnetic field in topological heterostructures
• Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas
• Two-loop Feynman integrals for ${\varphi }^4$ theory with long-range correlated disorder
• Quantum Fractality on the Surface of Topological Insulators
• Universality, exponents and anomaly cancellation in disordered Dirac fermions
• Emergent universal critical behavior of the 2D $N$-color Ashkin-Teller model in the presence of correlated disorder