Heavy fermion phase diagram in magic-angle twisted trilayer graphene

Technical Summary: Heavy Fermion Phase Diagram in Magic-angle Twisted Trilayer Graphene

Problem and Context
Two-dimensional moiré superlattices with flat bands have emerged as a versatile platform for exploring strongly correlated electron systems, including unconventional superconductivity and correlated insulators. While magic-angle twisted bilayer graphene (MATBG) has demonstrated the formation of topological flat bands through the hybridization of localized $f$-like electrons and itinerant $c$-electrons, it lacks the additional tunability required to fully emulate the heavy-fermion phase diagram. Conventional rare-earth Kondo lattices exhibit a ground state that evolves via the competition between the Kondo effect (screening localized moments) and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction (mediating magnetic order). Magic-angle twisted trilayer graphene (MATTG) offers a unique opportunity to simulate this physics more comprehensively. Unlike MATBG, MATTG hosts both flat bands and a set of Dirac bands. The presence of these Dirac bands provides extra itinerant $c$-electrons and, crucially, allows for unprecedented in-situ tunability via a perpendicular displacement field ($D$). This study addresses the challenge of experimentally mapping the full heavy-fermion phase diagram in a 2D system, specifically investigating the continuous crossover between magnetic and heavy-fermion metallic states and the associated quantum critical phenomena.

Methodology
The researchers fabricated high-quality, dual-graphite-gated MATTG devices using the dry transfer method. The devices feature three adjacent graphene layers twisted in an alternating sequence with angles of approximately 1.52° (Device D1) and 1.45° (Device D2). The vertical mirror symmetry of the structure yields a unique band structure comprising MATBG-like flat bands and Dirac bands from the additional monolayer.

The experimental approach involved:

1. Transport Characterization: Systematic measurement of longitudinal resistance ($R_{xx}$) and Hall resistance ($R_{xy}$) as a function of filling factor ($\nu$), displacement field ($D$), and temperature ($T$).
2. Magnetic Field Dependence: Analysis of Shubnikov-de Haas (SdH) oscillations and quantum Hall states to determine effective mass ($m^*$), carrier density, and Fermi surface topology.
3. Field Tuning: Utilizing the displacement field to continuously tune the hybridization between localized flat-band electrons and itinerant Dirac electrons, effectively controlling the Kondo coupling strength.
4. Data Analysis: Extraction of characteristic temperatures (Néel temperature $T_N$, Kondo screening temperature $T^*$, and heavy Fermi liquid onset $T_{HFL}$) from the temperature dependence of resistance and its derivatives. Fast Fourier Transform (FFT) analysis of SdH oscillations was used to track Fermi surface evolution.

Key Results
The study successfully demonstrates an electrically tunable heavy fermion phase diagram in MATTG at a filling factor of $\nu = 3$:

• Heavy Fermion State Identification: At a high displacement field ($D = 0.9$ V nm$^{-1}$), the system exhibits a logarithmic temperature dependence of resistance ($R_{xx} \propto \ln T$) at high temperatures, indicative of spin-flip scattering via the Kondo effect. At low temperatures ($T < 10$ K), the system enters a Fermi liquid regime ($R_{xx} = R_0 + AT^2$). The coefficient $A$ is enhanced by a factor of ~33 compared to the non-flat-band regime, corresponding to an effective mass enhancement to $m^* \sim 2m_0$.
• Antiferromagnetic Semimetal Phase: At low displacement fields ($D \approx 0$ V nm$^{-1}$), the system displays semimetallic behavior with a resistance drop at low temperatures, attributed to the suppression of spin-disorder scattering. Magnetic susceptibility measurements follow the Curie-Weiss law with a negative Weiss temperature ($\theta_C = -115$ K), indicating predominant antiferromagnetic interactions. A Néel temperature of $T_N \approx 15$ K is identified.
• Quantum Critical Point (QCP): As the displacement field increases, the antiferromagnetic order is suppressed ($T_N \to 0$), and a new characteristic temperature $T^*$ (onset of Kondo screening) emerges. Near a critical displacement field $D_c \approx 0.5$ V nm$^{-1}$, the $A$ coefficient and effective mass exhibit divergent behavior, signaling a continuous quantum phase transition.
• Fermi Surface Reconstruction: The transition is accompanied by a reconstruction of the Fermi surface. In the low-$D$ antiferromagnetic semimetal phase, the Fermi surface is "small," comprising only itinerant Dirac electrons. In the high-$D$ heavy fermion liquid phase, the Fermi surface becomes "large," incorporating the localized moments into the Fermi volume via Kondo singlet formation. This is evidenced by the emergence of new SdH oscillation frequencies (shifting from ~1.1 T to 11.5 T) and a sign reversal in the Hall coefficient.
• Phase Diagram: The authors construct a gate-tunable Doniach phase diagram featuring an antiferromagnetic semimetal phase at low $D$ and a paramagnetic heavy fermion metal phase at high $D$, separated by a quantum critical region.

Significance and Claims
The paper claims to establish MATTG as a highly tunable platform for exploring correlated quantum phases in the two-dimensional limit. Key claims include:

• Realization of a Tunable Kondo Lattice: The work demonstrates the ability to continuously tune the interplay between localized moments and itinerant electrons via an electric field, a feat not possible in conventional bulk Kondo lattices or MATBG alone.
• Observation of a 2D Quantum Critical Point: The study provides direct experimental evidence of a continuous quantum phase transition from an antiferromagnetic semimetal to a paramagnetic heavy fermion metal, characterized by effective mass divergence and Fermi surface reconstruction.
• Versatility of Moiré Heterostructures: The findings suggest that moiré heterostructures can serve as a versatile arena for exploring emergent phenomena beyond bulk materials, including potential unconventional superconductivity in the heavy fermion regime.
• Mechanism for Unconventional Superconductivity: By mapping the generalized Doniach phase diagram, the work aims to illuminate the mechanisms behind unconventional superconductivity, which often arises near quantum critical points in heavy fermion systems.

The authors maintain a modest tone regarding future implications, noting that while similar phase diagrams (including heavy fermion superconductivity) are expected in other 2D moiré systems with coexisting flat and dispersive bands, the current work focuses on establishing the fundamental heavy fermion phase diagram in MATTG.