Many-body instability of Coulomb interacting bilayer graphene: Renormalization group approach

Abstract

Low-energy electronic structure of ͑unbiased and undoped͒ bilayer graphene consists of two Fermi points with quadratic dispersions if trigonal warping is ignored. We show that short-range ͑or screened Coulomb͒ interactions are marginally relevant and use renormalization group to study their effects on low-energy properties of the system. We find that the two quadratic Fermi points spontaneously split into four Dirac points. This results in a nematic state that spontaneously breaks the sixfold lattice rotation symmetry ͑combined with layer permutation͒ down to a twofold one, with a finite transition temperature. Critical properties of the transition and effects of trigonal warping are also discussed. This Rapid Communication is motivated by the observation that in noninteracting systems with susceptibilities diverging as the temperature approaches zero, the inclusion of arbitrarily small interaction leads to a finite but also arbitrarily small transition temperature into an ordered state. The analytical method of choice in this case is the renormalization group ͑RG͒, which has the virtue of unbiased determination of the leading instability. 1 Here we apply the RG method to the bilayer graphene with A-B stacking. 2-5 While in general, the motion of the noninteracting electrons in such potential does not lead to diverging susceptibilities due to trigonal warping, 3,4 if only nearest-neighbor ͑nn͒ hopping is considered each set of four Dirac points merges into a single degenerate point with parabolic dispersion ͑see Fig. 1͒. As the nearest-neighbor hopping amplitudes are the largest, the latter is the natural starting point of theoretical analysis. 6,7 The finite density of states associated with the parabolic dispersion leads to screening that renders Coulomb interaction short ranged and to diverging susceptibilities in several channels. We find that the leading instability triggered by the run-away RG flow is in the nematic channel, which effectively makes hopping amplitudes stronger along preferred direction ͓see Eqs. ͑17͒ and ͑18͔͒, and leads to spontaneous splittings of the Fermi points and breaking of the lattice rotation symmetry. Among other effects, this should lead to anisotropic transport in sufficiently clean samples, as well as suppression of the low-energy density of state: an effect, in principle, observable in STM.We start with the tight-binding Hamiltonian for electrons hopping on the bilayer honeycomb lattice with Bernal stackingwhere, in the nn approximation, the ͑real͒ hopping amplitudes t connect the in-plane nn sites belonging to different sublattices and, for one of the sublattices, also the sites vertically above it with amplitude t Ќ . Since there are four sites in the unit cell, there are four bands whose dispersion for the above model comes from the solution of the eigenvalue problem,K 0 K t 2t 3t 0 t 2t 3t K K' a 1 t b 1 a 2 t t 0.95K 1.05K K 0.4 0.2 0 0.2 0.4 FIG. 1. ͑Color online͒ ͑Upper left inset͒ Honeycomb bilayer unit cell. Atoms in the lower layer ͑2͒ are marked as smaller ͑black͒ c...

Landau level spectra and the quantum Hall effect of multilayer graphene

“…We considered a single-particle picture in order to provide a simple description of a broad range of features. Depending on sample quality, electron-electron interactions also contribute to symmetry breaking and Landau level splitting, [67][68][69][70][71][72][73][74][75][76][77][78][79] as does interlayer asymmetry due to the presence of an external gate or doping. 28,31,42,45,[80][81][82] Nevertheless, an experimental observation of features related to next-nearest layer couplings should be possible in high-mobility samples including suspended graphene 69,[83][84][85][86] or graphene on a boron nitride substrate.…”

Transport gap in suspended bilayer graphene at zero magnetic field

“…18,19 Detailed tight-binding-model studies showed that inclusion of next-neighbor interlayer coupling changes the band structure in the bilayer, producing a Lifshitz transition in which the isoenergetic line about each valley is broken into four pockets with linear dispersion. 2,23 At energies higher than 1 meV the four pockets merge into one pocket with the usual quadratic dispersion.…”

“…Moreover, electron-electron interactions might result in further energy spectrum transformation, where the number of low-energy cones can be reduced to 2 near each of the two K points. 18,19 In this case the minimum conductance of the bilayer graphene is supposed to be increased comparing to a bilayer with parabolic dispersion (8e 2 /h). This scenario was also supported by experimental results on suspended bilayer graphene in which strong spectrum reconstructions and electron topological transitions were observed.…”

“…There are two competing theories describing the ground state of BLG: a transition (i) to a gapped layer-polarized state [12][13][14][15][16][17] (excitonic instability) or (ii) to a gapless nematic phase. [18][19][20] Excitonic instability is a layer polarization in which the charge density contribution from each valley and spin spontaneously shifts to one of the two graphene layers. 16,17 This redistribution is caused by an arbitrarily weak interaction between charge from the conduction and valence band states.…”

Spontaneous Quantum Hall Effect via a Thermally Induced Quadratic Fermi Point

“…Explicit examples are tightbinding models on checkerboard and kagome lattices, respectively [9,13]. Topological quadratic Fermi points also appear in physical systems such as bilayer graphene [14][15][16][17][18][19], photonic crystals [20], oxide heterostructures [21], and surface state of topological insulators [22].…”