Annica M. Black-Schaffer

Chiral d-wave superconductivity in doped graphene

A highly unconventional superconducting state with a spin-singlet dx2-y2+/-idxy-wave, or chiral d-wave symmetry has recently been suggested to emerge from electron-electron interactions in doped graphene. It has been argued that graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverge, is particularly likely to be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss the multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review the means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.

Resonating valence bonds and mean-field d -wave superconductivity in graphite

We investigate the possibility of inducing superconductivity in a graphite layer by electronic correlation effects. We use a phenomenological microscopic Hamiltonian which includes nearest neighbor hopping and an interaction term which explicitly favors nearest neighbor spin-singlets through the well-known resonance valence bond (RVB) character of planar organic molecules. Treating this Hamiltonian in mean-field theory, allowing for bond-dependent variation of the RVB order parameter, we show that both s- and d-wave superconducting states are possible. The d-wave solution belongs to a two-dimensional representation and breaks time reversal symmetry. At zero doping there exists a quantum critical point at the dimensionless coupling J/t = 1.91 and the s- and d-wave solutions are degenerate for low temperatures. At finite doping the d-wave solution has a significantly higher T{sub c} than the s-wave solution. By using density functional theory we show that the doping induced from sulfur absorption on a graphite layer is enough to cause an electronically driven d-wave superconductivity at graphite-sulfur interfaces. We also discuss applying our results to the case of the intercalated graphites as well as the validity of a mean-field approach.

RKKY coupling in graphene

We study the carrier-mediated exchange interaction, the so-called RKKY coupling, between two magnetic moments in graphene using exact diagonalization on the honeycomb lattice. By using the tight-binding nearest neighbor band structure of graphene we avoid the use of a momentum cut-off which plagues results in the Dirac continuum model formulation. We extract both the short and long impurity-impurity distance behavior and show several corrections to earlier long distance results. In the bulk the RKKY coupling is proportional to

Importance of electron-electron interactions in the RKKY coupling in graphene

1/|{\bf R}|^3

Self-consistent solution for proximity effect and Josephson current in ballistic graphene SNS Josephson junctions

and displays

Josephson current in graphene: Role of unconventional pairing symmetries

(1+\cos(2{\bf k}_D\cdot {\bf R})

Strong potential impurities on the surface of a topological insulator

-type oscillations. A-A sublattice coupling is always ferromagnetic whereas A-B subattice coupling is always antiferromagnetic and three times as large. We also study the effect of edges in zigzag graphene nanoribbons (ZGNRs) and find that for impurities on the edge, the RKKY coupling decays exponentially because of the localized zero energy edge states. For impurities inside a ZGNR the bulk characteristics are quickly regained.

Magnon Dirac materials

We show that the carrier-mediated exchange interaction, the so-called Ruderman-Kittel-Kasuya-Yoshida (RKKY) coupling, between two magnetic impurity moments in graphene is significantly modified in the presence of electron-electron (el-el) interactions. Within the mean-field approximation of the Hubbard-

Odd-frequency superconducting pairing in multiband superconductors

U

Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism

model we show that for increasing el-el interactions the oscillations disappear and the power-law decay becomes more long ranged. In zigzag graphene nanoribbons the effects are even more striking with any finite