Effective Model and Magnetic Properties of the Resistive Electron Quadrupling State

Recent experiments [Grinenko et al. Nat. Phys. 17, 1254 (2021)] reported the observation of a condensate of four-fermion composites. This is a resistive state that spontaneously breaks the time-reversal symmetry, leading to unconventional magnetic properties, detected in muon spin rotation experiments and by the appearance of a spontaneous Nernst effect. In this Letter, we derive an effective model for the four-fermion order parameter that describes the observed spontaneous magnetic fields in this state. We show that this model, which is alike to the Faddeev-Skyrme model can host skyrmions: magnetic-flux-carrying topological excitations.