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Correlated phases in rhombohedral multilayer graphene

Arsen Herasymchuk1,*, Sergei G. Sharapov1,2,†, Oleg V. Yazyev3,‡, and Yaroslav Zhumagulov3,§

  • *Contact author: arsen.herasymchuk@epfl.ch
  • †Contact author: sharapov@bitp.kyiv.ua
  • ‡Contact author: oleg.yazyev@epfl.ch
  • §Contact author: iaroslav.zhumagulov@epfl.ch
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Phys. Rev. B 113, 035132 – Published 16 January, 2026

DOI: https://doi.org/10.1103/2q6v-4brs

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·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→∞, and demonstrate a nonmonotonic 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)×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.

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Phys. Rev. B 113, 035132– Published 16 January, 2026
  • Received 25 August 2025
  • Revised 1 December 2025
  • Accepted 16 December 2025
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