Strong correlations and d+id superconductivity in twisted bilayer graphene

Abstract

We compute the phase diagram of twisted bilayer graphene near the magic angle where the occurrence of flat bands enhances the effects of electron-electron interactions and thus unleashes strongly-correlated phenomena. Most importantly, we find a crossover between d+id superconductivity and Mott insulating behavior near half-filling of the lowest electron band when the temperature is increased. This is consistent with recent experiments. Our results are obtained using unbiased many-body renormalization group techniques combined with a mean-field analysis of the effective couplings.Introduction-The discovery of correlated-insulator behaviour [1] and unconventional superconductivity (SC) in twisted bilayer graphene (TBG) by Cao et al. [2] has triggered an intense research effort to understand the phase diagram as well as other physical properties [3, 4] of this system. TBG is a van der Waals material consisting of two graphene layers which are rotated with respect to each other. At certain magic values of the rotation or twist angle, the Fermi velocity at the Dirac points of TBG vanishes resulting in flat bands in the vicinity of the Fermi energy [5,6]. For such a system, it is expected that electron-electron interactions play an important role and could potentially lead to the emergence of exotic correlated phases. The unveiling of this type of unconventional superconductivity and Mott physics in TBG is particularly exciting due to its resemblance to the physics of high-T c superconductors. In fact, the reported ratio [2] of the superconducting critical temperature to the Fermi temperature -a hallmark to decide whether superconductors are in the strong or weak coupling limit -puts experimentally realized TBG near the magic angle in the ballpark of those ratios obtained for high-T c cuprates (LSCO,YBCO,BSCCO), iron pnictides or monolayer iron selenide on a STO surface. These reside among the strongest coupling superconductors known today. Thus, TBG provides an intriguing route to study the largely unknown physics of such a superconductor in the extremely controllable framework offered by graphene where the ratio of the interaction to the kinetic energy can be tuned by approaching the magic twist angle and the filling can be modified by a bottom gate.To gain insight into the experimental results of Cao et al. [1,2], a wide range of models have been proposed in recent weeks [7]. Without assuming a specific microscoping pairing mechanism, Peltonen and coworkers [8] used mean-field theory to study SC in TBG and find a strongly inhomogeneous superconducting order parameter. Ray and Das [9] solve the Eliashberg equation for TBG and predict an extended s-wave as the leading pairing symmetry. In contast, Xu and Balents [10], Zhang

Valley Jahn-Teller Effect in Twisted Bilayer Graphene

“…There are already in literature several proposals about the superconducting states in tBLG. Most of them, however, invoke electron correlations as the element responsible, or strongly effecting the pairing [22,24,[55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. There are few exceptions [29,73,74] that instead propose, as we do, a purely phonon mediated attraction.…”

Possible nodeless s±-wave superconductivity in twisted bilayer graphene*

“…For small r 12 , the d-wave solutions dominate, indicating that the intraband interaction favors dwave superconductivity on both Fermi surfaces. Since d xy and d x 2 −y 2 are degenerate, the true gap function here is their linear combination, yielding a chiral d + id-wave pairing symmetry [47,48]. While for large r 12 1.2, the leading solution is nodeless s ± -wave, induced by a relatively strong interband interaction, as is in pnictide or some heavy fermion superconductors [79,91,92].…”

Competing phases of interacting electrons on triangular lattices in moiré heterostructures

“…Further, the fRG equations are well defined rooting in an exact flow equation 34 and include not only the leading ln 2 -diverging channels, but also subleading ln-divergent contributions. We extend previous fRG studies 19,20,30 by inclusion of other interaction types and a more comprehensive exploration of the induced ordering tendencies. The exploitation of SU(2)×SU(2) symmetry facilitates high Fermi-surface resolution, which is important near van-Hove singularities.…”

“…In this work, we consider a phenomenological model of electrons on a triangular lattice with two spin and two orbital states as well as onsite and nearest-neighbor interactions. We follow earlier arguments that the combined spin and orbital degrees of freedom form an approximate SU(4) flavor symmetry [16][17][18][19] and perturb it by Hund-like interactions down to SU(2)×SU (2). We assume that the experimental observations correspond to fillings close to a van-Hove singularity and a (near-)nested Fermi surface and determine potential ordered states induced by moderate interactions.…”