Abstract
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.
Highlights
There has been considerable interest in studying artificial lattices induced by a long wavelength Moiré potential in graphene and related materials
While Mott physics has been observed in a different Moiré superlattice system, induced by a boron nitride substrate on ABC trilayer graphene,[15] here we will focus on the twisted bilayer graphene (tBLG) system, which has already generated a significant amount of theoretical interest.[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]
Within a random phase approximation (RPA), we show that nesting-enhanced valley fluctuations give rise to an inter-valley pairing in the “d/p-wave” channel (d-wave and p-wave are generally mixed under C3 symmetry)
Summary
There has been considerable interest in studying artificial lattices induced by a long wavelength Moiré potential in graphene and related materials. These experiments have recently gathered momentum with the observation of superconductivity and correlated Mott insulators in bilayer graphene twisted to a particular “magic angle”. The Moiré superlattice induced in bilayer graphene twisted by a small angle leads to isolated bands near charge neutrality, whose bandwidth can be tuned by twist angle.[1,2,3,4,5,6,7,8,9,10,11,12] On approaching certain magic angles, the largest being ~1.1°, the bandwidth is significantly reduced allowing for correlation physics to take hold. While Mott physics has been observed in a different Moiré superlattice system, induced by a boron nitride substrate on ABC trilayer graphene,[15] here we will focus on the tBLG system, which has already generated a significant amount of theoretical interest.[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]
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