标题： 拓扑非共格 Fulde-Ferrell-Larkin-Ovchinnikov 超导体和菱方四层石墨烯中的 Bogoliubov 费米面 显示英文标题

标题： Topological incommensurate Fulde-Ferrell-Larkin-Ovchinnikov superconductor and Bogoliubov Fermi surface in rhombohedral tetra-layer graphene

摘要： 我们对菱方四层石墨烯的自旋-谷极化模型进行了随机相位近似（RPA）计算，以研究从Kohn-Luttinger机制中出现手性超导体的可能性。 我们在计算中包含了真实的能带结构和形式因子，并在给定温度下通过在动量空间中采样20,000个点数值求解自洽方程。 在范霍夫奇点（VHS）附近，我们发现p-ip配对，陈数从$C=-1$通过在$\mathbf k=(0,0)$处能隙关闭切换到$C=0$（相对于$\mathbf K$定义）。 尽管超导体在低温下通常是完全能隙的，但我们发现当温度略低于平均场时存在Bogoliubov费米面$T_c$。 此外，通过自由能的计算，我们得出最优库珀对动量$\mathbf Q$通常是有限的，可以达到$0.1 k_F$的大小。 我们将$\mathbf Q\neq 0$相称为非共格的 Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) 超导体，以区别于$\mathbf Q=0$相。与$\mathbf Q=0$相相比，我们的非共格$\mathbf Q$相如果处于 Fulde-Ferrell(FF) 相，则为向列超导体，如果处于 Larkin-Ovchinnikov (LO) 相，则表现出电荷密度波(CDW)。我们的工作展示了菱形四层石墨烯作为一个绝佳的平台，在单一平台上探索马约拉纳零模、FFLO 物理和 Bogoliubov 费米面。 显示英文摘要

摘要： We performed a random phase approximation (RPA) calculation for a spin-valley polarized model of the rhombohedral tetra-layer graphene to study the possibility of 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 (VHS), we find p-ip pairing with Chern number switching from $C=-1$ to $C=0$ through a gap closing at $\mathbf k=(0,0)$ (defined relative to $\mathbf K$). Although the superconductor is generically fully gapped at low temperature, we find Bogoliubov Fermi surface at temperature just below mean field $T_c$. Besides, through calculation of the free energy, we conclude that the optimal Cooper pair momentum $\mathbf Q$ is generically finite and can be as large as $0.1 k_F$. We dub the $\mathbf Q\neq 0$ phase as an incommensurate Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) superconductor to distinguish it from the $\mathbf Q=0$ phase. Compared to the $\mathbf Q=0$ phase, our incommensurate $\mathbf Q$ phase is a nematic superconductor if it is in the Fulde-Ferrell(FF) phase or exhibts charge density wave (CDW) if it is in the Larkin-Ovchinnikov (LO) phase. Our work demonstrates the rhombohedral tetra-layer graphene as a wonderful platform to explore Majorana zero-mode, FFLO physics and Bogoliubov fermi surface within one single platform.