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arXiv:1509.03401 · Physical Review B

Strong interaction effects at a Fermi surface in a model for voltage-biased bilayer graphene

Wesley Armour, Simon Hands, Costas Strouthos

Published Dec 23, 2015• 1 citation
arXivHTMLPDF

Abstract

Monte Carlo simulation of a 2+1 dimensional model of voltage-biased bilayer graphene, consisting of relativistic fermions with chemical potential $\ensuremath{\mu}$ coupled to charged excitations with opposite sign on each layer, has exposed noncanonical scaling of bulk observables near a quantum critical point found at strong coupling. We present a calculation of the quasiparticle dispersion relation $E(k)$ as a function of exciton source $j$ in the same system, employing partially twisted boundary conditions to boost the number of available momentum modes. The Fermi momentum ${k}_{F}$ and superfluid gap $\mathrm{\ensuremath{\Delta}}$ are extracted in the $j\ensuremath{\rightarrow}0$ limit for three different values of $\ensuremath{\mu}$, and support a strongly interacting scenario at the Fermi surface with $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}O(\ensuremath{\mu})$. We propose an explanation for the observation $\ensuremath{\mu}<{k}_{F}$ in terms of a dynamical critical exponent $z<1$.

DOI
10.1103/physrevb.92.235143

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We revisit the effect of local interactions on the quadratic band touching (QBT) of Bernal stacked bilayer graphene models using renormalization group (RG) arguments and quantum Monte Carlo simulations of the Hubbard model. We present an RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased quantum Monte Carlo simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/tU/tU/t, despite the U=0U=0U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with a dynamical critical exponent z=1z=1z=1 as expected for 2+1 d Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.
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