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

Abstract

16 two-column pagesInternational audienceWe consider two dimensional 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's function formalism, and bosonization, 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 the correlated random gauge potential, RG and bosonization 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 the 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

Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator

“…For instance, for random gauge disorder one expects ρ(ε) = ε 2/z−1 with z = 1 + α D in weak disorder case (α D < 2) [23] and z = (8α D ) 1/2 − 1 in strong disorder case (α D > 2) [25]. Similarly, with random mass disorder, the DOS remains linear in ε up to logarithmic corrections [30]. Only for scalar potential disorder the DOS saturates at a finite value in the vicinity of the Dirac point [27].…”

“…Its effect crucially depends on properties of disorder such as preserved symmetries or the range of correlations. This has been intensively studied using different methods during last two decades [23][24][25][26][27][28][29][30]. On the contrary, much less is known on the disorder effects close to and at the topological semi-metal-insulator transition.…”

New quantum transition in Weyl semimetals with correlated disorder

“…This is indeed the case for the Anderson transition [24]. Moreover, the low energy properties of the Dirac phase in graphene are known to be sensitive to disorder correlations [25] . Such correlations may originate from the presence of linear dislocations, planar grain boundaries, unscreened charge impurities, etc.…”

“…1. First note that the case d = 2 (ε = 0), corresponding to graphene, is special since it corresponds to the lower critical dimension where no transition occurs: SR disorder is marginally relevant and drives the system to a strong disordered metallic phase, characterized by a finite zero-energy DOS [25]. For dimension d greater than 2 we must distinguish three regimes of disorder correlations :…”

“…The positive eigenvalues of the matrix (25) correspond to the unstable directions in the plane (∆ 1 , ∆ 2 ). The transition if it exists is controlled by a FP which has only one of two directions unstable, e.g.…”