Topological incommensurate Fulde-Ferrell-Larkin-Ovchinnikov superconductor and Bogoliubov Fermi surface in rhombohedral tetralayer graphene

Abstract

We performed a random-phase approximation calculation for a spin-valley-polarized model of the rhombohedral tetralayer graphene to study the possibility of a chiral superconductor from the Kohn-Luttinger mechanism. We included the realistic band structure and form factor in our calculation and solved the self-consistent equation numerically by sampling 20 000 points in the momentum space at a given temperature. Around the van Hove singularity, we find p−ip pairing with the Chern number switching from C=−1 to C=0 through a gap closing at k=(0,0) (defined relative to K). Although the superconductor is generically fully gapped at low temperature, we find the Bogoliubov Fermi surface at a temperature just below mean-field Tc. Besides, through calculation of the free energy, we conclude that the optimal Cooper pair momentum Q is generically finite and can be as large as 0.1kF. We dub the Q≠0 phase as an incommensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor to distinguish it from the Q=0 phase. Compared to the Q=0 phase, our incommensurate Q phase is a nematic superconductor if it is in the Fulde-Ferrell phase or exhibits a charge density wave if it is in the Larkin-Ovchinnikov phase. Our work demonstrates the rhombohedral tetralayer graphene as a wonderful platform to explore the Majorana zero-mode, FFLO physics, and the Bogoliubov Fermi surface within one single platform.

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