Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene

By Yi-Zhuang You, Ashvin Vishwanath. npj Quantum Materials, 2018

185 citations recorded by the source corpus.

AbstarctThe recent discovery of the Mott insulating and superconducting phases in twisted bilayer graphene has generated tremendous research interest. Here, we develop a weak coupling approach to the superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral (d + id mixed with p−ip) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a near degeneracy of spin-singlet and triplet pairing. On increasing interactions, commensurate inter-valley coherence wave (IVCW) order can arise, with simultaneous condensation at the three M points in the Brillouin Zone, and a 2 × 2 pattern in real space. In simple treatments though, this leads to a full gap at fillings ± (1/2 + 1/8), slightly away from half-filling. The selection of spin-singlet or spin triplet orders, both for the IVCW and the superconductor, arise fcase corresponds to the Hundsrom SO(4) symmetry breaking terms. Mott insulators derived from phase fluctuating superconductors are also discussed, which exhibit both symmetry protected and intrinsic topological orders.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/bb87a62cb6521d09bec9cbe842b6ac0ef297d987

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Citations in the corpus

Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions (2018, background): “33, the coupling matrix is given by Tq1 = w(σ0 + σ1), but more generally one can take Tq1 = w0σ0 + w1σ1 without breaking any symmetries [6, 21, 25, 40].”