Abstract
It has long been speculated that quasi-two-dimensional superconductivity can reappear above its semiclassical upper critical field due to Landau quantization; yet this reentrant property has never been observed. Here, we argue that twisted bilayer graphene at a magic angle (MATBG) is an ideal system in which to search for this phenomenon because its Landau levels are doubly degenerate and its superconductivity appears already at carrier densities small enough to allow the quantum limit to be reached at relatively modest magnetic fields. We study this problem theoretically by combining a simplified continuum model for the electronic structure of MATBG with a phenomenological attractive pairing interaction and discuss obstacles to the observation of quantum Hall superconductivity presented by disorder, thermal fluctuations, and competing phases.
Highlights
Magnetic fields suppress superconductivity owing to either Pauli or orbital pair breaking, or a combination of the two
We focus on the carrier density that corresponds to the most robust superconducting dome observed in magic angle twisted bilayer graphene (MATBG) [23,28], employ a simplified continuum band structure model that is consistent with Shubnikov–de Haas data, and combine it with a phenomenological BCS interaction model that is consistent with the observed Tc and Hc2
We have employed a simplified model band structure that is motivated by the observation in experiment of a simple pattern of Shubnikov–de Haas oscillations indicative of two degenerate closed hole-like Fermi pockets
Summary
Magnetic fields suppress superconductivity owing to either Pauli or orbital pair breaking, or a combination of the two. Hartree-Fock band calculations [50,55,56] suggest that when C2T symmetry is broken, the valence band maximum and conduction band minimum near νs = ±2 filling occur at the moiré Brillouin zone centers, γ , γ This is further supported by an exact diagonalization study [57], the observed Landau level filling factors mentioned above, and the absence of a Berry phase associated with quantum oscillation data [48]. Reentrant superconductivity emerges in mean-field theory when an enhanced Fermi level density of states, produced by Landau quantization, trumps broken time-reversal symmetry It is captured only by a fully quantum treatment of the perpendicular magnetic field Bz. Using a Landau gauge for the vector potential A = (−By, 0, 0), the band Hamiltonian becomes h+(a, a†) =. √ − Y/ )/ Lx is a parabolic band nth LL wave function with φn being a one-dimensional (1D) harmonic oscillator wave function and Y being the LL guiding center
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