Charge-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>4</mml:mn><mml:mi>e</mml:mi></mml:math> Superconductivity from Multicomponent Nematic Pairing: Application to Twisted Bilayer Graphene
Rafael M. Fernandes, Liang Fu
Abstract
We show that unconventional nematic superconductors with multicomponent order parameter in lattices with three- and sixfold rotational symmetries support a charge-4e vestigial superconducting phase above T_{c}. The charge-4e state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is nonsuperconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities in the gauge sector and in the crystalline sector of the symmetry group. We argue that random strain generally favors the charge-4e state over the nematic phase, as it acts as a random mass to the former but as a random field to the latter. Thus, we propose that two-dimensional inhomogeneous systems displaying nematic superconductivity, such as twisted bilayer graphene, provide a promising platform to realize the elusive charge-4e superconducting phase.