We study superconductivity of twisted bilayer graphene with local and non-local attractive interactions. We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. We predict qualitative differences between local and non-local interaction schemes which could be distinguished experimentally. In the flat band limit where the pair potential exceeds the band width we show that the superfluid weight and BKT temperature are determined by multiband processes and quantum geometry of the band.Recent experimental discoveries of superconductivity in bilayer graphene twisted close to a "magic angle" θ * [1-3] call for a reconsideration of traditional theories of superconductivity [4, 5], in particular because the superconductivity occurs in a regime where the non-interacting electronic states form an asymptotically flat (dispersionless) band [6][7][8][9][10][11][12][13][14][15][16][17]. As the system is two-dimensional, the transition to superconductivity is bound to occur at the Berezinskii-Kosterlitz-Thouless (BKT) temperature T BKT [18][19][20] which can be determined from k B T BKT = π 8 arXiv:1906.06313v3 [cond-mat.mes-hall]

Recent experiments show how a bilayer graphene twisted around a certain magic angle becomes superconducting as it is doped into a region with approximate flat bands. We investigate the meanfield s-wave superconducting state in such a system and show how the state evolves as the twist angle is tuned, and as a function of the doping level. We argue that part of the experimental findings could well be understood to result from an attractive electron-electron interaction mediated by electronphonon coupling, but the flat-band nature of the excitation spectrum makes also superconductivity quite unusual. For example, as the flat-band states are highly localized around certain spots in the structure, also the superconducting order parameter becomes strongly inhomogeneous. arXiv:1805.01039v5 [cond-mat.supr-con]

In the search of high-temperature superconductivity one option is to focus on increasing the density of electronic states. Here we study both the normal and s-wave superconducting state properties of periodically strained graphene, which exhibits approximate flat bands with a high density of states, with the flatness tunable by the strain profile. We generalize earlier results regarding a one-dimensional harmonic strain to arbitrary periodic strain fields, and further extend the results by calculating the superfluid weight and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature TBKT to determine the true transition point. By numerically solving the self-consistency equation, we find a strongly inhomogeneous superconducting order parameter, similarly to twisted bilayer graphene. In the flat band regime the order parameter magnitude, critical chemical potential, critical temperature, superfluid weight, and BKT transition temperature are all approximately linear in the interaction strength, which suggests that high-temperature superconductivity might be feasible in this system. We especially show that by using realistic strain strengths TBKT can be made much larger than in twisted bilayer graphene, if using similar interaction strengths. We also calculate properties such as the local density of states that could serve as experimental fingerprints for the presented model. :1910.06671v2 [cond-mat.supr-con] arXiv