Superconductivity in twisted bilayer quasi-one-dimensional systems with flat bands

Abstract

Unconventional superconductivity recently observed in twisted bilayer graphene is associated with the presence of van-Hove singularities very close to the Fermi level reflecting the flattening of bands for a set of magic twist angles. In this paper, we address a stack of two identical quasi-one-dimensional layers, each one composed of a set of chains with p-wave orbitals at each site. When the layers are stacked with a 90∘ relative angle, the bilayer system resembles the Mielke lattice (which admits one exact flat band in the one-body tight-binding model for particular values of the hopping parameters). When a small rotation is applied to one of the layers, regions with different layer stacking appear that may be characterized as one-dimensional or two-dimensional regions according to the most relevant hopping integrals between layers. The system, for sizes smaller or of the order of the Moiré pattern unit cell, can be qualitatively described: (i) addressing individually each region, for example in what concerns the density of states, (ii) interpreting the full lattice as a coupled system of these regions. This generates a n-band model, where each band is associated to a particular region of the lattice. We address the role of these different regions on the upper critical field transition curve of a superconducting phase.

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