Monte Carlo Study of Strongly-Interacting Degenerate Fermions: a Model for Voltage-Biased Bilayer Graphene

TL;DR

This study models strongly-interacting relativistic fermions in 2+1 dimensions to simulate low-energy electronic excitations in voltage-biased bilayer graphene, revealing a novel strongly-correlated ground state with anomalous scaling behaviors.

Contribution

It introduces a lattice formulation of a relativistic fermion model for bilayer graphene under voltage bias, demonstrating new strongly-correlated phases near a quantum critical point.

Findings

Anomalous scaling of carrier density and excitonic condensate with chemical potential

Suppressed chiral condensate indicating a non-traditional ground state

Evidence of a superfluid excitonic condensate distorting the Fermi surface

Abstract

We formulate a model of N_f=4 flavors of relativistic fermion in 2+1d in the presence of a chemical potential mu coupled to two flavor doublets with opposite sign, akin to isopsin chemical potential in QCD. This is argued to be an effective theory for low energy electronic excitations in bilayer graphene, in which an applied voltage between the layers ensures equal populations of particles on one layer and holes on the other. The model is then reformulated on a spacetime lattice using staggered fermions, and in the absence of a sign problem, simulated using an orthodox hybrid Monte Carlo algorithm. With the coupling strength chosen to be close to a quantum critical point believed to exist for N_f<N_fc\approx4.8, it is found that there is a region below saturation where both the carrier density and a particle-hole "excitonic" condensate scale anomalously with increasing mu, much more rapidly that the corresponding quantities in free field theory, while the conventional chiral condensate is strongly suppressed. The corresponding ground state is speculated to be a strongly-correlated degenerate fermion system, with a remnant Fermi surface distorted by a superfluid excitonic condensate. The model thus shows qualitatively different behaviour to any model with mu=/=0 previously studied by lattice simulation.