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

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 (${\mathrm{QED}}_3$) 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 ${\mathrm{QED}}_3$ with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.

Figure 1

The diagram which describes the screening of the random scalar potential by the fermion density-density polarization bubble at zero frequency. The dashed line represents the disorder interaction Eq. (9). The shading of the bubble denotes a geometric series of bubble diagrams.