Unconventional discontinuous transitions in a 2D system with spin and valley degrees of freedom

TL;DR

This paper investigates unconventional phase transitions in 2D fermionic systems with spin and valley degrees of freedom, revealing discontinuous jumps into polarized states and complex cascades of metallic phases, with implications for graphene systems.

Contribution

It uncovers highly unconventional, discontinuous ordering transitions in 2D fermion systems with spin and valley degrees, including a cascade of metallic phases in SU(4) symmetric systems.

Findings

Susceptibility diverges or nearly diverges at the transition.

System jumps discontinuously into a fully polarized state.

Cascade of transitions into quarter-, half-, and three-quarter metals.

Abstract

We analyze the transition into the most favorable ordered state for a system of 2D fermions with spin and valley degrees of freedom. We show that for a range of rotationally invariant dispersions, the ordering transition is highly unconventional: the associated susceptibility diverges (or almost diverges) at the transition, yet immediately below it the system jumps discontinuously into a fully polarized state. We analyze the dispersion of the longitudinal and transverse collective modes in different parameter regimes above and below the transition. Additionally, we consider ordering in a system with full $\mathrm{SU(4)}$ symmetry and show that there is a cascade of discontinuous transitions into a set of states, which includes a quarter-metal, a half-metal and a three-quarter metal. We compare our results with the data for biased bilayer and tri-layer graphene.