Quantum multicriticality of bilayer graphene in the presence of a tunable energy gap
Abstract
We develop a theory for quantum phases and quantum multicriticality in bilayer graphene in the presence of an explicit energy gap in the noninteracting spectrum by extending previous renormalization group (RG) analyses of electronelectron interactions in gapless bilayer graphene at finite temperature to include the effect of an electric field applied perpendicular to the sample. We determine the possible outcomes of the resulting RG equations, represented by "fixed rays" along which ratios of the coupling constants remain constant and map out the leading instabilities of the system for an interaction of the form of a Coulomb interaction that is screened by two parallel conducting plates placed equidistant from the electron. We find that some of the fixed rays on the "target plane" found in the zerofield case are no longer valid fixed rays, but that all four of the isolated rays are still valid. We also find five additional fixed rays that are not present in the zerofield case. We then construct maps of the leading instability (or instabilities) of the system for the screened Coulomblike interaction as a function of the overall interaction strength and interaction range for four values of the applied electric field. We find that the pattern of leading instabilities is the same as that found in the zerofield case, namely that the system is unstable to a layer antiferromagnetic state for shortranged interactions, to a nematic state for longranged interactions, and to both for intermediateranged interactions. However, if the interaction becomes too longranged or too weak, then the system will exhibit no instabilities. The ranges at which the nematic instability first appears, the antiferromagnetic instability disappears, and the nematic instability disappears all decrease with increasing applied electric field.
 Publication:

arXiv eprints
 Pub Date:
 August 2014
 DOI:
 10.48550/arXiv.1408.4804
 arXiv:
 arXiv:1408.4804
 Bibcode:
 2014arXiv1408.4804T
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 17+\epsilon pages, 3 figures. Published in Phys. Rev. B