Spin-fluctuation-induced pairing in twisted bilayer graphene

We investigate the interplay of magnetic fluctuations and Cooper pairing in twisted bilayer graphene from a purely microscopic model within a large-scale tight-binding approach resolving the \AA ngstr\"om scale. For local onsite repulsive interactions and using the random-phase approximation for spin fluctuations, we derive a microscopic effective pairing interaction that we use for self-consistent solutions of the Bogoliubov-de-Gennes equations of superconductivity. We study the predominant pairing types as function of interaction strength, temperature and band filling. For large regions of this parameter space, we find chiral $d$-wave pairing regimes, spontaneously breaking time-reversal symmetry, separated by magnetic instabilities at integer band fillings. Interestingly, the $d$-wave pairing is strongly concentrated in the AA regions of the moir\'e unit cell and exhibits phase windings of integer multiples of $2\pi$ around these superconducting islands, i.e. pinned vortices. The spontaneous circulating current creates a distinctive magnetic field pattern. This signature of the chiral pairing should be measurable by state-of-the-art experimental techniques.Comment: 5 pages, 3 figure

Competition of Density Waves and Superconductivity in Twisted Tungsten Diselenide

Evidence for correlated insulating and superconducting phases around regions of high density of states was reported in the strongly spin-orbit coupled van-der Waals material twisted tungsten diselenide (tWSe$_2$). We investigate their origin and interplay by using a functional renormalization group approach that allows to describe superconducting and spin/charge instabilities in an unbiased way. We map out the phase diagram as function of filling and perpendicular electric field, and find that the moir\'e Hubbard model for tWSe$_2$ features mixed-parity superconducting order parameters with $s/f$-wave and topological $d/p$-wave symmetry next to (incommensurate) density wave states. Our work systematically characterizes competing interaction-driven phases in tWSe$_2$ beyond mean-field approximations and provides guidance for experimental measurements by outlining the fingerprint of correlated states in interacting susceptibilities.Comment: 7 pages, 3 figures, supplemental materia

Engineering Three-Dimensional Moire Flat Bands

Twisting two adjacent layers of van der Waals materials with respect to each other can lead to flat two-dimensional electronic bands which enables a wealth of physical phenomena. Here, we generalize this concept of so-called moire flat bands to engineer flat bands in all three spatial dimensions controlled by the twist angle. The basic concept is to stack the material such that the large spatial moire interference patterns are spatially shifted from one twisted layer to the next. We exemplify the general concept by considering graphitic systems, boron nitride, and WSe2, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride, we develop an ab initio fitted tight binding model that captures the corresponding three-dimensional low-energy electronic structure. We outline that interesting three-dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.This work is supported by the European Research Council (ERC-2015-AdG-694097), Grupos Consolidados (IT124919), and SFB925. A.R. is supported by the Flatiron Institute, a division of the Simons Foundation. We acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 1995 within the Priority Program SPP 2244 2DMP under Germany's Excellence Strategy -Cluster of Excellence and Advanced Imaging of Matter (AIM) EXC 2056-390715994 and RTG 2247. L.X. acknowledges the support from Distinguished Junior Fellowship program by the South Bay Interdisciplinary Science Center in the Songshan Lake Materials Laboratory. J.Z. acknowledges funding received from the European Union Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant Agreement 886291 (PeSD-NeSL)