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

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.

19 pages, 13 figures, figure 13 modified and discussion improved

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Cited by in corpus (3)

• Quantum Monte Carlo Calculations for Carbon Nanotubes
• Applications of lattice QCD techniques for condensed matter systems
• Strong Interaction Effects at a Fermi Surface in a Model for Voltage-Biased Bilayer Graphene