Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly

Details Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly

2010-06-06

arxiv.org/abs/1006.1136v2

Phys. Rev. B 82, 115431 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, 3 figures

Scientific paper

10.1103/PhysRevB.82.115431

We analyze the many-body properties of bilayer graphene (BLG) at charge neutrality, governed by long range interactions between electrons. Perturbation theory in a large number of flavors is used in which the interactions are described within a random phase approximation, taking account of dynamical screening effect. Crucially, the dynamically screened interaction retains some long range character, resulting in $\log^2$ renormalization of key quantities. We carry out the perturbative renormalization group calculations to one loop order, and find that BLG behaves to leading order as a marginal Fermi liquid. Interactions produce a log squared renormalization of the quasiparticle residue and the interaction vertex function, while all other quantities renormalize only logarithmically. We solve the RG flow equation for the Green function with logarithmic accuracy, and find that the quasiparticle residue flows to zero under RG. At the same time, the gauge invariant quantities, such as the compressibility, remain finite to $\log^2$ order, with subleading logarithmic corrections. The key experimental signature of this marginal Fermi liquid behavior is a strong suppression of the tunneling density of states, which manifests itself as a zero bias anomaly in tunneling experiments in a regime where the compressibility is essentially unchanged from the non-interacting value.

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