Kekule Superconductivity in the Kane-Mele Phase of Rhombohedral Graphene Systems.

In time-reversal- and inversion-symmetric systems, BCS pairing with zero center-of-mass momentum (Q=0) typically prevails. Here we show that band geometry can revert this trend and stabilize finite-momentum pairing at Q=2K_D in graphene-based platforms. We study superconductivity in the chiral bands of Z2 Kane–Mele phases with sublattice-dependent interactions. Projecting to valley bands decomposes the pairing into (i) intra-valley Cooper scattering/tunneling with Q=±2K_D and (ii) inter-valley scattering/exchange with Q=0.These interaction terms encode the effect of band geometry. Using mean-field theory and the linearized gap equation, we compute T_c versus carrier density n_{2D} and Kane–Mele mass λ. For sublattice-independent attraction (V_A=V_B=−|V|), the conventional Q=0 state holds across all densities. In contrast, sublattice-opposite interactions (V_A=−V_B=−|V|) drive a leading instability to an s-wave Kekulé superconductor at Q=2K_D once n_{2D} exceeds a λ-dependent threshold n_{crit,2D}(λ). We also evaluate the superfluid stiffness to assess the stability of the condensates. These results connect to observations of superconductivity in rhombohedral graphene and twisted transition-metal dichalcogenides.