Correlated phases in rhombohedral multilayer graphene

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 $N\to \infty$, 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.

25 pages, 17 figures

References in corpus (40)

• The electronic properties of bilayer graphene
• Superconductivity in rhombohedral trilayer graphene
• Band Structure of ABC-Stacked Graphene Trilayers
• Isospin magnetism and spin-triplet superconductivity in Bernal bilayer graphene
• Spin-Orbit Enhanced Superconductivity in Bernal Bilayer Graphene
• Quantum cascade of new correlated phases in trigonally warped bilayer graphene
• Correlated Insulator and Chern Insulators in Pentalayer Rhombohedral Stacked Graphene
• Orbital Multiferroicity in Pentalayer Rhombohedral Graphene
• Pairing symmetry in a two-orbital Hubbard model on a square lattice
• Signatures of Chiral Superconductivity in Rhombohedral Graphene
• Large Quantum Anomalous Hall Effect in Spin-Orbit Proximitized Rhombohedral Graphene
• Electric transport and magnetic properties in multilayer graphene
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Spin and Orbital Metallic Magnetism in Rhombohedral Trilayer Graphene
• Metals, fractional metals, and superconductivity in rhombohedral trilayer graphene
• Spin-triplet superconductivity at the onset of isospin order in biased bilayer graphene
• Functional Renormalization Group Study of Superconductivity in Rhombohedral Trilayer Graphene
• Competing orders and cascade of degeneracy lifting in doped Bernal bilayer graphene
• Correlated metals and unconventional superconductivity in rhombohedral trilayer graphene: A renormalization group analysis
• Isospin and momentum polarized orders in bilayer graphene
• Ferroelectric and anomalous quantum Hall states in bare rhombohedral trilayer graphene
• Intravalley spin-polarized superconductivity in rhombohedral tetralayer graphene
• Surface ferromagnetism in rhombohedral heptalayer graphene moire superlattice
• Moiré disorder effect in twisted bilayer graphene
• Proximity spin-orbit and exchange coupling in ABA and ABC trilayer graphene van der Waals heterostructures
• Efficient fluctuation exchange approach to low-temperature spin fluctuations and superconductivity: from the Hubbard model to Na${}_x$CoO${}_2\cdot y$H${}_2$O
• Emergent correlated phases in rhombohedral trilayer graphene induced by proximity spin-orbit and exchange coupling
• SU(4) symmetry in twisted bilayer graphene - an itinerant perspective
• Inter-orbital singlet pairing in Sr${}_2$RuO${}_4$: a Hund's superconductor
• Superconductivity and magnetism in the surface states of ABC-stacked multilayer graphene
• Exchange interaction, disorder, and stacking faults in rhombohedral graphene multilayers
• Swapping exchange and spin-orbit induced correlated phases in proximitized Bernal bilayer graphene
• Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field
• Strain Disorder and Gapless Intervalley Coherent Phase in Twisted Bilayer Graphene
• Nodal pair density waves from a quarter-metal in crystalline graphene multilayers
• Layer-Dependent Quantum Anomalous Hall Effect in Rhombohedral Graphene
• Competing magnetic states on the surface of multilayer ABC-stacked graphene
• Supercell Wannier functions and a faithful low-energy model for Bernal bilayer graphene
• Chiral Stoner magnetism in Dirac bands
• Valley-dependent giant orbital moments and transport feature in rhombohedral graphene multilayers

Cited by in corpus (3)

• Pair density wave in quarter metals from a repulsive fermionic interaction in graphene heterostructures: A renormalization group study
• Various electronic crystal phases in rhombohedral graphene multilayers
• Charge density waves and stripes in quarter metals of graphene heterostructures