Superconductivity in the twisted bilayer graphene: emergent mystery in the magic angle, the topological bosons and the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover

ABSTRACT

Theory of superconductivity in twisted bilayer graphene (tBLG) is presented, based on the fact that Dirac fermions are pairing creating the topological bosons as consequence of topologically protected Lifshitz topological transition (TPLTT). We have shown that multiple TPLTTs are realised at low twisting angles in tBLG. At TPLTT the Berry phase changes from 2π in bilayer graphene to π in tBLG. It is favourable to form the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover (BCS-BEUC) when the attractive interaction for pairing dominates the repulsive screened Coulomb interaction. The theory yields a second-order phase transition for BCS-BEUC, and values of specific heat and the Ginzburg−Landau coherence length are calculated. The problem has been solved of emergent mystery in the magic angles at which there exists possibility for observation of BCS-BEUC. The solution is connected with the Umklapp processes when the quasiwave vector of the superconducting carriers is shifted from the Brillouin zone to other cell of the reciprocal space. The table is given of the allowed magic angles which include the corresponding effective masses of the pairing Dirac fermions.

KEYWORDS:

• Unconventional superconductivity
• moiré crystal
• twisted bilayer graphene
• magic angles
• moiré flat bands
• Lifshitz topological transition
• BCS-BEUC unconventional crossover

Acknowledgements

I thank Professor Peter Riseborough and the reviewers for helpful suggestions and comments. I appreciate the Production Editor Thaheer Hussain and his team for their excellent work with paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data accessibility

This work includes theoretical investigations.