  Recent mean-field calculations suggest that the superconducting state of
twisted bilayer graphene exhibits either a nematic order or a spontaneous
breakdown of the time-reversal symmetry. The two-dimensional character of the
material and the large critical temperature relative to the Fermi energy
dictate that the material should have significant fluctuations. We study the
effects of these fluctuations using Monte Carlo simulations. We show that in a
model proposed earlier for twisted bilayer graphene there is a
fluctuation-induced phase with quadrupling fermionic order for all considered
parameters. This four-electron condensate, instead of superconductivity, shows
a spontaneous breaking of time-reversal symmetry. Our results suggest that
twisted bilayer graphene is an especially promising platform to study different
types of condensates, beyond the pair-condensate paradigm.
