Half and quarter metals in rhombohedral trilayer graphene (2104.00653v3)

Abstract: Ferromagnetism is most common in transition metal compounds but may also arise in low-density two-dimensional electron systems, with signatures observed in silicon, III-V semiconductor systems, and graphene moir\'e heterostructures. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene drive the spontaneous ferromagnetic polarization of the electron system into one or more spin- and valley flavors. Using capacitance measurements on graphite-gated van der Waals heterostructures, we find a cascade of density- and electronic displacement field tuned phase transitions marked by negative electronic compressibility. The transitions define the boundaries between phases where quantum oscillations have either four-fold, two-fold, or one-fold degeneracy, associated with a spin and valley degenerate normal metal, spin-polarized half-metal', and spin and valley polarizedquarter metal', respectively. For electron doping, the salient features are well captured by a phenomenological Stoner model with a valley-anisotropic Hund's coupling, likely arising from interactions at the lattice scale. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, by rotational alignment of a hexagonal boron nitride substrate to induce a moir\'e superlattice, we find that the superlattice perturbs the preexisting isospin order only weakly, leaving the basic phase diagram intact while catalyzing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter metal states occur at half- or quarter superlattice band filling. Our results show that rhombohedral trilayer graphene is an ideal platform for well-controlled tests of many-body theory and reveal magnetism in moir\'e materials to be fundamentally itinerant in nature.

• The paper identifies a cascade of phase transitions leading to spin-polarized half-metal and fully polarized quarter-metal states in trilayer graphene.
• It combines capacitance measurements with a phenomenological Stoner model incorporating valley-anisotropic Hund's coupling to capture electron doping effects.
• The study reveals how hole doping and moiré superlattice engineering induce complex symmetry-breaking transitions, promising tunable quantum device applications.

Analysis of Half and Quarter Metals in Rhombohedral Trilayer Graphene

The paper by Zhou et al. discusses the emergence of unique electronic phases and magnetic properties in rhombohedral trilayer graphene, focusing on the interplay between the single-particle band structure and electron-electron interactions in the material. The research combines experimental observations with theoretical modelling to elucidate the electronic phenomena present in this system.

The paper begins by addressing the occurrence of ferromagnetic order in rhombohedral trilayer graphene. Ferromagnetism, usually associated with transition metal compounds, can also arise in low-density two-dimensional electron systems. The authors explore the electrical properties of rhombohedral trilayer graphene and observe ferromagnetic polarization induced by gate-tuned van Hove singularities. This polarization occurs in spin- and valley-flavored phases and is distinguished by a cascade of phase transitions, correlating with density and electronic displacement fields.

Key Findings:

• Phase Transitions and Compressibility: Through capacitance measurements, the paper identifies a sequence of phase transitions with negative electronic compressibility, marking transitions between different degeneracies of quantum oscillations. Specifically, these are associated with normal metallic, spin-polarized half-metal, and fully polarized quarter-metal phases.
• Stoner Model Application: To model these findings, a phenomenological Stoner model incorporating valley-anisotropic Hund's coupling is used. This model explains well the electron doping characteristics of the phase transitions observed experimentally, capturing the variations in phase boundaries with applied displacement fields.
• Complex Phase Diagram under Hole Doping: Hole doping introduces complexity via a finite-density van Hove singularity, giving rise to a richer phase diagram. This involves a complex interplay of broken symmetries and transitions in Fermi surface topology.
• Influence of Moiré Superlattice: On creating a moiré superlattice by aligning trilayer graphene with hexagonal boron nitride, the phase diagram remains largely unaffected. However, topologically nontrivial gapped states form at specific superlattice fillings, which emphasizes the moiré superlattice's role in tuning electronic properties without fundamentally altering the existing isospin orders.

The authors leverage these results to suggest that rhombohedral trilayer graphene is a potent platform for testing many-body theories, particularly due to its well-controlled environment for studying itinerant magnetism. The findings emphasize the intrinsic nature of the ferromagnetic order in graphene-based van der Waals heterostructures, providing insights into correlated electron physics.

Theoretical and Practical Implications:

Theoretically, this paper expands the understanding of isospin order and itinerant magnetism in graphene systems. The insights into the ferromagnetic behavior arising at low densities open pathways to further exploring other two-dimensional materials under similar theoretical frameworks. Practically, the stability of the phases and their tunability through external fields and moiré patterning offers novel methodology for device applications harnessing this tunable electronic and magnetic behavior. Such capabilities could enrich future quantum computing or sensing technologies, leveraging the controllable electronic properties of rhombohedral trilayer graphene.

The paper provides comprehensive empirical and theoretical insight into novel magnetic and electronic phenomena in trilayer graphene, illustrating the interplay of electronic interactions and external tunable parameters. Future research should continue to explore the role of symmetry breaking and interactions at finite densities to further unveil the fundamental properties inherent in graphene systems and their potential applications in emerging technologies.