Chirald-wave superconductivity on the honeycomb lattice close to the Mott state

Abstract

We study superconductivity on the honeycomb lattice close to the Mott state at half filling. Due to the sixfold lattice symmetry and disjoint Fermi surfaces at opposite momenta, we show that several different fully gapped superconducting states naturally exist on the honeycomb lattice, of which the chiral d + id -wave state has previously been shown to appear when superconductivity appears close to the Mott state. Using renormalized mean-field theory to study the t-J model and quantum Monte Carlo calculations of the Hubbard-U model we show that the d + id -wave state is the favored superconducting state for a wide range of on-site repulsion U , from the intermediate to the strong coupling regime. We also investigate the possibility of a mixed chirality d-wave state, where the overall chirality cancels. We find that a state with d + id -wave symmetry in one valley but d − id -wave symmetry in the other valley is not possible in the t-J model without reducing the translational symmetry, due to the zero-momentum and spin-singlet nature of the superconducting order parameter. Moreover, any extended unit cells result either in disjoint Dirac points, which cannot harbor this mixed chirality state, or the two valleys are degenerate at the zone center, where valley hybridization prevents different superconducting condensates. We also investigate extended unit cells where the overall chirality cancels in real space. For supercells containing up to eight sites, including the Kekulé distortion, we find no energetically favorable d-wave solution with an overall zero chirality within the restriction of the t-J model.

Chirald-wave superconductivity in doped graphene

“…an effective t-J model, which explicitly gives zero-momentum spin-singlet pairing, cannot have such mixed chirality. Within the t-J model real space modulations of the chiral d-wave state was also investigated but a net zero sum chirality state was never found [88]. However, going beyond this model and allowing for spintriplet/spin-singlet mixing, while keeping the coupling between the two Fermi surfaces weak, could possibly still produce a mixed chirality state.…”

“…d x 2 −y 2 − id xy -wave symmetry, thus effectively canceling the overall chirality. However, assuming zero-momentum pairing, such that the electrons in a Cooper pair come from the K and K valleys, and a spinsinglet state this mixed chirality state has been shown to not be physically possible [88]. The argument boils down to the fact that the d xy -wave component, which changes signs between the two valleys, ends up with odd spatial parity in the Brillouin zone and must thus be a spin-triplet state, whereas the d x 2 −y 2 -wave component is still in a spin-singlet state, which is inconsistent with assuming only spin-singlet pairing.…”

Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions

“…In this paper, we investigate the possibility to utilize inhomogeneous perturbations, like those caused by impurity lattices, for this purpose. We point out that such perturbations are often naturally present in candidate materials for topological superconductors, since these are typically unconventional superconductors obtained by doping Mott insulators [8,[10][11][12][13][14]. Moreover, high quality topological insulators have recently been created by intentionally doping Si into InAs/GaSb heterostructures [15].…”

Topological states with broken translational and time-reversal symmetries in a honeycomb-triangular lattice

“…We describe tunneling and possible on-site energy modulations 063605-2 with the Hamiltonian (10) and choose˜ a ↓ = 0 in all subsequent calculations. The on-site and nearest neighbor interaction terms for the triangular and honeycomb-triangular lattices are the same.…”

“…On the other hand, chiral superconductors break time-reversal symmetry (TRS) because they feature gap parameters that wind in phase around the Fermi surface in multiples of 2π . Chiral superconductors also exhibit many other fascinating properties that are highly sought after for nanoscience applications [6][7][8][9][10], and broken TRS is a prerequisite for the quantum Hall effects (excluding the spin Hall effect) [11,12]. Moreover, in MgB 2 and iron pnictides [13][14][15][16] TRS may be broken due to interband couplings [17][18][19].…”