Observation of Kondo Effect in Rhombohedral Graphene Superlattices

Technical Summary: Observation of Kondo Effect in Rhombohedral Graphene Superlattices

Problem and Context
The Kondo effect, arising from the antiferromagnetic coupling between itinerant conduction electrons and localized magnetic moments, is a fundamental mechanism in strongly correlated systems that leads to exotic quantum phenomena such as unconventional superconductivity and Kondo insulating states. While theoretical frameworks and experimental evidence have established the existence of Kondo lattices and heavy fermions in transition metal dichalcogenide (TMD) superlattices and magic-angle graphene systems, experimental verification in rhombohedral graphene (Rgr) moiré superlattices has remained elusive. In these 2D moiré systems, Wannier orbitals localized at high-symmetry stacking regions can theoretically serve as the localized $f$-electrons, while dispersive bands act as itinerant $c$-electrons, creating a tunable platform for Kondo physics. However, the specific signatures of Kondo interactions in Rgr-based moiré superlattices had not been conclusively demonstrated.

Methodology
The authors investigated hexalayer rhombohedral graphene (Rgr) encapsulated between hexagonal boron nitride (hBN) flakes, forming a dual-gated moiré superlattice device. The device features a moiré period of approximately 10.93 nm (twist angle $\theta \approx 0.87^\circ$). By independently controlling the carrier density ($n$) and the displacement electric field ($D$) via top and bottom gates, the researchers mapped the longitudinal resistance ($R_{xx}$) and Hall resistance ($R_{xy}$) across a wide range of filling factors ($\nu$), magnetic fields ($B$), and temperatures ($T$).

Key experimental approaches included:

• Magneto-transport measurements: Analyzing $R_{xx}$ and $R_{xy}$ as functions of perpendicular magnetic field to identify non-monotonic behaviors and sign reversals.
• Temperature-dependent transport: Examining $R_{xx}$ from cryogenic temperatures up to 180 K to distinguish between Kondo scattering, heavy fermion liquid behavior, and insulating states.
• Field orientation studies: Comparing the effects of perpendicular ($B_\perp$) and in-plane ($B_\parallel$) magnetic fields to probe the role of orbital degrees of freedom.
• Data fitting: Utilizing empirical models to fit Hall coefficient data and extracting coefficients (such as the Kadowaki-Woods coefficient $A$) to characterize quasiparticle effective mass.

Key Contributions and Results
The study provides experimental evidence for Kondo interactions in Rgr/hBN moiré superlattices, specifically in the moiré-proximal regime near filling factor $\nu \approx 2$. The primary findings include:

1. Kondo Breakdown Signatures: In the range $2 < \nu < 2.3$ under a displacement field of $D = -0.4275$ V/nm, the system exhibits a non-monotonic magnetoresistance. As the magnetic field increases, $R_{xx}$ rises to a peak at a critical field ($B_c$) and then decreases. Simultaneously, $R_{xy}$ undergoes a sign reversal near $B_c$. These features are attributed to the breakdown of Kondo singlets by the Zeeman field, which liberates carriers previously bound to localized moments and reconstructs the Fermi surface.
2. Heavy Fermion Liquid and Kondo Scattering: Temperature-dependent measurements of $R_{xx}$ reveal a characteristic insulator-to-metal transition at a Kondo temperature ($T_K \approx 8$ K).
   • Above $T_K$, $R_{xx}$ follows a logarithmic dependence ($-\log T$), indicative of spin-flip scattering mediated by the Kondo effect.
   • Below $T_K$, $R_{xx}$ exhibits a $T^2$ dependence, characteristic of a heavy fermion liquid. The extracted Kadowaki-Woods coefficient $A$ is orders of magnitude larger than in non-correlated regions, confirming a substantial enhancement of quasiparticle effective mass.
3. Tunability and Phase Transitions: The strength of the Kondo interaction is shown to be continuously tunable by both carrier density ($n$) and displacement field ($D$).
   • Varying $D$ allows the system to transition from a Kondo-screened metallic state to an insulating state (potentially a Mott or Kondo insulator) as the ratio of on-site Coulomb repulsion to bandwidth ($U/W$) increases.
   • The critical field $B_c$ decreases linearly with increasing $|D|$, vanishing near $D \approx -0.45$ V/nm, where the system enters an insulating regime.
4. Orbital Degrees of Freedom: The critical field required to break Kondo singlets is significantly larger for in-plane fields ($B_{c\parallel}$) than for perpendicular fields ($B_{c\perp}$), suggesting a dominant role for the orbital (valley) degree of freedom in the Kondo coupling, consistent with a large valley $g$-factor.
5. Low-Temperature Topological Features: At very low temperatures, $R_{xx}$ saturates to a quantized plateau of $h/2e^2$, suggesting the possible emergence of a topological insulating state with helical edge states, although the authors note that the small energy gap makes direct confirmation via quantum oscillations challenging.

Significance
The paper claims to provide deep insight into the Kondo effect within moiré-engineered flat-band systems. By demonstrating that Rgr/hBN superlattices host a tunable Kondo lattice, the work establishes a new platform for exploring strongly correlated quantum phases. The ability to continuously tune the interaction strength via electric fields and carrier density, and the observation of a transition from heavy fermion liquids to potential Kondo insulating states, suggests that these systems are versatile for studying exotic phenomena such as unconventional superconductivity and topological Kondo insulators. The findings bridge the gap between theoretical predictions of Kondo physics in moiré systems and experimental reality, paving the way for further exploration of correlated quantum phases in graphene-based heterostructures.