Finite-size scaling in a 2D disordered electron gas with spectral nodes

Abstract

We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo-Greenwood conductivity formula. Disorder scattering is treated within the standard perturbation theory by summing up ladder and maximally crossed diagrams. The emergent gapless (diffusion) modes determine the behavior of the conductivity on large scales. We find a finite conductivity with an intermediate logarithmic finite-size scaling towards smaller conductivities but do not obtain the logarithmically divergence of the weak-localization approach. Our results agree with the experimentally observed logarithmic scaling of the conductivity in graphene with the formation of a plateau near e 2 /πh.

Conductivity of disordered 2d binodal Dirac electron gas: effect of internode scattering

“…In the past our approach [27] has been compared with experimental work, including the seminal article on graphene by Novoselov et al on graphene [6] and showed good agreement. More recently we also compared our theoretical results for finite-size scaling with experimental results [34], and found excellent agreement. Moreover, we have used two different approaches in this article, namely a functional integral approach based on symmetry considerations (Sect.…”

“…Technically, the evaluation of the conductivity contributions for each disorder type does not differ much from the single-cone model evaluation presented in our recent papers Ref. [33,34]. The number of massless modes is obtained by counting zero eigenvalues of the corresponding mass matrices given in Eqs.…”

“…This is the standard method in the weaklocalization approach, in which the Green's functions are expanded in terms of the random scattering elements and averaged afterwards [2][3][4][13][14][15][16][17][18][19][20][21][22]. As an extension of the analysis in our recent papers [33,34], where we were concerned with the conductivity behavior in the single-cone approximation, here we take both cones into account. The averaged two-particle Green's function…”

“…This paper aims at the understanding of the effects of different scattering types in systems with a nodal electronic spectrum at chemical neutrality. Previous studies are inconclusive on the role intra-and internode scattering processes may play in electronic transport, ranging from essentially no difference [13] to strong statements about a localization-antilocalization transition [14][15][16], while general symmetry arguments indicate that massless modes should survive in the presence of random internode scattering [33,34].…”

“…The inverse propagator of the effective action, obtained as Gaussian fluctuations around this vacuum, turns out to be identical, up to a unitary transformation, with the solutions of the Bethe-Salpeter equation. In the second part of the program we develop further the weak scattering formalism, formulated in our recent papers [33][34][35][36][37][38][39]. Besides the already mentioned comparison of two approaches, we calculate the conductivity for 16 different disorder types.…”