Unconventional discontinuous transitions in isospin systems

TL;DR

This paper reveals that two-dimensional fermion systems with specific dispersions experience first-order transitions to fully spin-polarized states, with a cascade of instabilities into fractional-metal phases, relevant for graphene and moiré materials.

Contribution

It demonstrates unconventional discontinuous transitions in isospin systems with various dispersions, extending understanding of phase behavior in 2D fermionic systems.

Findings

First-order spin polarization transition occurs despite diverging susceptibility.

Cascade of instabilities into fractional-metal states with band depletion.

Applicability to graphene and moiré heterostructures.

Abstract

We show that two-dimensional fermions with dispersion $k^2$ or $k^4$ undergo a first-order Stoner transition to a fully spin-polarized state despite that the spin susceptibility diverges at the critical point. We extend our analysis to systems with dispersion $k^{2\alpha}$ and spin and valley isospin and show that there is a cascade of instabilities into fractional-metal states with some electron bands fully depleted; narrow intermediate ranges of partially-depleted bands exist for $\alpha<1$ or $\alpha > 2$. The susceptibility becomes large near each transition. We discuss applications to biased bilayer and tri-layer graphene and moir\'e systems.