Competing many-body instabilities and unconventional superconductivity in graphene

Abstract

The band structure of graphene exhibits van Hove singularities (VHS) at doping x = ±1/8 away from the Dirac point. Near the VHS, interactions effects, enhanced due to the large density of states, can give rise to various many-body phases at experimentally accessible temperatures. We study the competition between different many-body instabilities in graphene using functional renormalization group (FRG). We predict a rich phase diagram, which, depending on long range hopping as well as screening strength and absolute scale of the Coulomb interaction, contains a d + id-wave superconducting (SC) phase, or a spin density wave phase at the VHS. The d + id state is expected to exhibit quantized charge and spin Hall response, as well as Majorana modes bound to vortices. In the vicinity of the VHS, we find singlet d + id-wave as well as triplet f -wave SC phases.

Superconductivity from repulsive interaction

“…The same result has been obtained in fRG approach [122]. Observe that α SC > 1/2, i.e., the divergence of the SC three legged vertex does indeed lads to a SC instability (which, we recall, leads to a d + id or d − id state, each breaks time-reversal symmetry).…”

“…A number of candidate ordered states has been considered, including superconductivity, SDW order, nematic order and so on. See [34,114,116,117,118,119,120,121,122]. Because the density of state diverges at the saddle points at Van Hove doping, each state can be can be self-consistently obtained at weak coupling.…”

“…The KL mechanism has been also applied to somewhat smaller dopings, when the FS still contains six disconnected pieces. In this doping range, KL-based analysis yields a novel spin-triplet f-wave superconductivity [115,116,46,122].…”

Chirald-wave superconductivity in doped graphene

“…They further argued, based on Ginzburg-Landau arguments, that the time-reversal symmetry breaking chiral d between the potential spin-density-wave and chiral d-wave superconducting states [103], and also embedding the special case of graphene into a broader picture for fermions on hexagonal lattices [38]. Kiesel et al [45] very recently analyzed the same situation using N -patch fRG. This approach is more flexible and also allows the study of doping levels away from the van Hove point, as well as a systematically investigation of how changes in the interaction profile affect the result.…”

Spontaneous Quantum Hall Effect via a Thermally Induced Quadratic Fermi Point

“…For the special case of Hubbard model, we have g = g ′ = U δ α,β /N , where U is the on-site Coulomb repulsion,β denotes the opposite spin, and N is the total number of sites. Although renormalization-group (RG) analysis indicated that superconductivity instability is asymptotically dominant [31], the SDW vertex is the largest at intermediate RG scale and becomes dominant by slightly doping away from the Van Hove singularity [32].…”