Quantum electronic fluids with spin and valley degrees of freedom have a correlation driven tendency to flavor polarization (generalized ferromagnetism). To first order in the long-range Coulomb interactions -- i.e. in the Hartree-Fock approximation -- spin and valley polarization exhibit a spurious degeneracy. We show that to second order -- or more generally in the random-phase approximation -- this degeneracy is lifted in a way that depends only on the underlying symmetry relating the two valleys. In two spatial dimensions, if the valleys are related by an n−fold rotation (n>2) or by mirror reflection and each valley is invariant under C2 or time reversal (as is the case in AlAs quantum wells) then valley polarization is preferred. If the valleys are related by time reversal or by C2 rotation symmetry (as in multilayer graphene systems) then spin order is selected.
@article{arxiv.2507.05344,
title = {Symmetry-determined generalized ferromagnetism in multi-valley electron fluids},
author = {Vladimir Calvera and Erez Berg and Steven A. Kivelson},
journal= {arXiv preprint arXiv:2507.05344},
year = {2025}
}