Engineering kekule superconductivity from layer-selective interactions in rhombohedral graphene

Abstract

At weak coupling, finite-momentum superconductivity is typically associated with broken time-reversal or inversion symmetry of the Fermi surface. Here, we show that lattice-scale pair-density-wave order in rhombohedral multilayer graphene can arise from layer/orbital-dependent pairing interactions, band chirality, and Dirac-point-centered Fermi surface topology while preserving both symmetries. Using mean-field theory and comparing finite momentum sectors $Q = \pm 2 K_{D}$ with the $ Q = 0$ superconducting state, we find that layer-dependent interactions of opposite signs ($V_{1A}=-V_{JB}=-|V|$) favor an intra-valley Kekul\`e state with center-of-mass momentum ($ Q=\pm 2 K_D$). In the presence of a time-reversal and inversion symmetry-preserving Kane-Mele mass ($\lambda$), this state appears only above a critical carrier density ($n^{crit}_{K}(\lambda,J)$). The two superconducting condensates exhibit opposite chirality, $J(-J)$ for $K_D(-K_D) $ valleys, thereby preserving time-reversal and inversion symmetry. We map the phase diagram and analyze the dependence of $T_c$ on the chirality index $J$ and $\lambda$. We also evaluate the superfluid stiffness in the Kekul\`e superconducting state, thereby determining the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature. Our results show that orbital-dependent interactions in the presence of band chirality favor finite-momentum pairing in time-reversal and inversion symmetric Dirac materials.