Reduced QED with few planes and fermion gap generation

TL;DR

This paper generalizes reduced quantum electrodynamics to heterostructures with few layers, deriving effective theories, analyzing screened interactions, and studying fermion gap generation, revealing increased critical coupling due to additional screening.

Contribution

It introduces a formalism for reduced QED in few-layer heterostructures, deriving explicit interaction formulas and analyzing gap generation with enhanced screening effects.

Findings

Screened electromagnetic interactions are explicitly formulated for two and three layers.

Additional screening from a second layer raises the critical coupling for fermion gap generation.

Fermion gap generation is studied in a two-layer heterostructure with massless Dirac fermions.

Abstract

The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of few atomically thick layers and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced theory describes charged fermions confined to $N$ planes and contains $N$ vector fields with Maxwell`s action modified by non-local form factors whose explicit form is determined. Taking into account the polarization function, the explicit formulae for the screened electromagnetic interaction are presented in the case of two and three layers. For a heterostructure with two atomically thick layers and charged fermions described by the massless Dirac equation, the dynamical gap generation of the excitonic type is studied. It is found that additional screening due to the second layer increases the value of the critical coupling constant for the gap generation compared to that in graphene.