Chiral $p$-wave superconductivity in twisted bilayer graphene from dynamical mean field theory

B. Pahlevanzadeh,P. Sahebsara,David Sénéchal

doi:10.21468/scipostphys.11.1.017

Abstract

We apply cluster dynamical mean field theory with an exact-diagonalization impurity solver to a Hubbard model for magic-angle twisted bilayer graphene, built on the tight-binding model proposed by Kang and Vafek [1], which applies to the magic angle 1.30^\circ1.30∘. We find that triplet superconductivity with p+ip symmetry is stabilized by CDMFT, as well as a subdominant singlet d+id state. A minimum of the order parameter exists close to quarter-filling and three-quarter filling, as observed in experiments.

Highlights

Since the moiré pattern of TBG forms a triangular lattice, it was initially thought that the effective Hamiltonian would be defined on that lattice, and it was shown that the electron density associated with the low-energy bands is peaked around its sites
It was shown that no Wannier basis satisfying the minimal symmetry requirements could be constructed on a triangular lattice; on the contrary, the Wannier states have to be defined on the plaquettes of a triangular lattice, which form a graphene-like lattice
We find that a superconducting state exists around quarter filling and three-quarter filling and that it is a triplet state with p + i p symmetry, while a subdominant, singlet d + id solution exists

Summary

Low-energy model

There have been a few proposals for an effective tight-binding Hamiltonian describing the low-energy bands of TBG [1, 18,19,20]. To this tight-binding model we will add a local interaction term U. We define operators Si,r and Ti,r on the second layer, in terms of orbitals w2 and w3). A similar analysis could be carried out with longer-range pairing, with the same classification: This would add harmonics to the basic pairing functions This organization into representations of D3 is contingent on the importance of the interlayer hopping t13, which is an order of magnitude smaller than the intra-layer hopping. If t13 were zero, the two layers would be independent, the symmetry would be upgraded to C6v and the classification of pairing states would be the same as in Ref. Since t13 is small, we expect that the different pairing states of Table 2 (for a given total spin) will be nearly impossible to differentiate from an energetics point of view, except for the difference between s and d ± id (or between f and p ± i p)

Cluster dynamical mean field theory

General description

Cluster-bath system

Results and discussion