Correlated phases in rhombohedral multilayer graphene

TL;DR

This paper studies how electron interactions lead to various correlated phases in rhombohedral multilayer graphene, revealing a complex phase diagram influenced by layer number, interaction symmetry, and chemical potential.

Contribution

It provides analytical expressions for susceptibilities, compares RPA and PA methods, and uncovers a rich set of phases and scaling laws for critical temperatures in multilayer graphene.

Findings

RPA supports only Stoner and IVC phases

PA reveals additional particle-particle instabilities

Critical temperature scales with layer number N and decreases non-monotonically with chemical potential

Abstract

We investigate the emergence of correlated electron phases in rhombohedral $N$-layer graphene due to two-valley Coulomb interactions within a low-energy $k \cdot p$ framework. Analytical expressions for Lindhard susceptibilities in intra- and intervalley channels are derived, and the critical temperatures for phase transitions are estimated using both the random phase approximation (RPA) and the parquet approximation (PA). Within RPA, only Stoner and intervalley coherent (IVC) phases are supported, while the PA reveals a richer phase structure including particle-particle (PP) channel instabilities. We establish a general scaling law for the critical temperature with respect to layer number $N$, highlighting an upper bound as $N \rightarrow \infty$, and demonstrate a non-monotonic decrease of the critical temperature with increasing chemical potential. The PA uncovers the role of interaction symmetry: $SU(4)$-symmetric interactions favor intervalley Stoner order in the density channel, whereas $SU(2) \times SU(2)$-symmetric interactions permit a broader set of phases. A crossover in the dominant instability occurs in the particle-hole channel at a critical layer number, suggesting the emergence of magnetic or IVC phases in thicker systems. We also identify conditions under which pair-density wave (PDW) order could form in the PP channel, though its physical realization may be constrained.