Metallic phases from disordered (2+1)-dimensional quantum electrodynamics

Abstract

Metallic phases have been observed in several disordered two dimensional (2d) systems, including thin films near superconductor-insulator transitions and quantum Hall systems near plateau transitions. The existence of 2d metallic phases at zero temperature generally requires an interplay of disorder and interaction effects. Consequently, experimental observations of 2d metallic behavior have largely defied explanation. We formulate a general stability criterion for strongly interacting, massless Dirac fermions against disorder, which describe metallic ground states with vanishing density of states. We show that (2+1)-dimensional quantum electrodynamics (QED3) with a large, even number of fermion flavors remains metallic in the presence of weak scalar potential disorder due to the dynamic screening of disorder by gauge fluctuations. We also show that QED3 with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.

Two-dimensional conductors with interactions and disorder from particle-vortex duality

“…The examples discussed above show that gauge fluctuations can stabilize metallic behavior in two dimensional systems, similar to the conclusions of a recent perturbative study [35]. The examples studied here all involve Dirac fermions with the chemical potential at neutrality, and hence are all somewhat special.…”

“…In this controlled limit, QED 3 flows to an interacting fixed point [34]. In a recent study [35] of the effects of disorder on this fixed point (see also Ref. [36]), it was found that (1) V U is strongly irrelevant at the clean interacting fixed point due to the screening of disorder by the longitudinal gauge field fluctuations and that (2) a P, T, and PH-invariant analogue of V M leads to a perturbatively accessible finite disorder fixed point corresponding to a dirty metallic phase with universal conductivity.…”

“…On the other hand, Ref. [35] showed that chemical potential disorder is irrelevant in an approximation where the number of fermion flavors is large. The reason is that at the clean large flavor fixed point, the electric part of the gauge fluctuations screen the disorder potential, making it short-range correlated.…”

Interplay of interactions and disorder at the superfluid-insulator transition: A dirty two-dimensional quantum critical point

“…This problem is particularly acute in bosonic systems undergoing SITs or superfluid-insulator transitions. While examples of quantum critical points and phases have been constructed in fermionic systems using perturbative and non-perturbative techniques [12][13][14][15] perature) disorder. This peculiar expansion, taken very far from the physical, quantum disordered situation of 2+1 spacetime dimensions, was introduced by Dorogovtsev [16] and by Boyanovsky and Cardy [17], who found a stable fixed point characterized by finite disorder and interactions (see also Ref.…”

Disordered fermionic quantum critical points

“…Limiting ourselves to 2D Dirac fermions, our prime concern, such studies have addressed the interplay of interactions and disorder on the integer quantum Hall plateau transition [28], the physics of graphene [29][30][31][32][33][34], and the surfaces of 3D topological insulators [35][36][37] and superconductors [38][39][40]. Recent work has also demonstrated the possibility of novel critical phases in massless (2+1)D relativistic quantum electrodynamics in the presence of quenched disorder [41][42][43], with possible applications to disordered spin liquids.…”