Competing nematic, antiferromagnetic, and spin-flux orders in the ground state of bilayer graphene

Abstract

We analyze the phase diagram of bilayer graphene (BLG) at zero temperature and zero doping. Assuming that at high energies the electronic system of BLG can be described within a weak-coupling theory (consistent with the experimental evidence), we systematically study the evolution of the couplings with going from high to low energies. The divergences of the couplings at some energies indicate the tendency towards certain symmetry breakings. Carrying out this program, we found that the phase diagram is determined by microscopic couplings defined on the short distances (initial conditions). We explored all plausible space of these initial conditions and found that the three states have the largest phase volume of the initial couplings: nematic, antiferromagnetic, and spin flux (a.k.a. quantum spin Hall). In addition, ferroelectric and two superconducting phases appear only near the very limits of the applicability of the weak-coupling approach. The paper also contains the derivation and analysis of the renormalization group equations and the group theory classification of all the possible phases which might arise from the symmetry breakings of the lattice, spin rotation, and gauge symmetries of graphene.

Wannier function approach to realistic Coulomb interactions in layered materials and heterostructures

“…Theoretical studies have predicted that charge-and spin-density waves (CDW or SDW), quantum spin hall states (QSH), nematic, superconducting and excitonic insulator states could emerge in the bilayer [34][35][36][37][38][39][40] . Different experiments have addressed the issue of symmetry broken ground states in bilayer graphene [41][42][43][44][45][46] but the issue remains controversial also from the experimental point of view and it is e.g.…”

Observation of Even Denominator Fractional Quantum Hall Effect in Suspended Bilayer Graphene

“…This theory takes into account the fact that the zero-energy Landau level in bilayer graphene has a unique eight-fold degeneracy which is lifted by the exchange interaction, so that spin and valley degeneracies are broken first, followed by the splitting of the orbital states, N=0 and N=1 (see the inset of Figure 4c). [34][35][36][37][38][39][40][41][42] As a consequence, in bilayer graphene, the Coulomb interaction can scatter electrons with the same spin/valley indices between these two levels, 23,[29][30][31][32][33] which is neither possible in conventional GaAs-based systems 2 nor in monolayer graphene (due to the large cyclotron gap). 6,7,[24][25][26][27]46 Numerical calculations based on this scenario show that the states between filling factors 2k <ν < 2k+1 (k = -2, -1, 0, and 1) correspond to a partially filled N=0 Landau level, while those between 2k+1 <ν < 2k+2 correspond to a partially filled N=1…”

“…[26][27][28] Comparing FQHE in mono-and bi-layer graphene -consisting of two Bernal-stacked monolayers-is particularly revealing, 23,[29][30][31][32][33] since in the absence of interactions the low-energy structure of Landau levels is very different in the two cases (despite the spin and valley degeneracy being identical). 34,35 Specifically, whereas only one N=0 Landau level is present at zero energy in monolayers, in bilayers N=0 and N=1 Landau level both have vanishing energy, leading to a unique additional degeneracy in the system [34][35][36][37][38][39][40][41][42] (conventional GaAsbased systems do not have this extra degeneracy). This difference is crucial as it leads to unexplored regimes of electronic interactions in 2DESs where mixing of two N=0 and N=1…”

Antiferromagnetic and topological states in silicene: A mean field study

“…Considering pseudospin (i.e., which layer), valley, and real electron spin degrees of freedom, various broken-symmetry phases have been predicted or considered. [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] Among these phases, the antiferromagnetic (AFM) state [31,[36][37][38][39] is considered to be the most possible one, due to its consistency with the later observations including their response to a perpendicular electric field [18,23] and tilted magnetic field. [22] Noticing the striking similarity between BLG and silicene, the electronelectron interaction might induce magnetism for silicene, and the competition between the magnetic state and topological state may lead to new physics, which is worthwhile to be carefully studied.…”