Contrasting $\Gamma$- and K-Valley Moiré Physics in Twisted Monolayer/Bilayer WSe$_2$

Technical Summary: Contrasting $\Gamma$ and $K$ Valley Moiré Physics in Twisted Monolayer/Bilayer WSe$_2$

Problem and Motivation
Electronic orbital degrees of freedom are fundamental in determining quantum phases in strongly correlated systems, ranging from Mott insulators in transition metal oxides to the distinctions between nickelate and cuprate superconductors. While two-dimensional (2D) moiré materials have emerged as highly tunable platforms for exploring correlated phenomena (e.g., fractional anomalous Hall states and superconductivity), the role of orbital degrees of freedom within these systems remains largely unexplored. In conventional correlated materials, orbital tuning typically requires chemical composition changes, high pressure, or strain, which often introduce disorder or structural effects. In contrast, 2D transition metal dichalcogenides (TMDs) offer a unique mechanism where the orbital character is intrinsically tied to the valley degree of freedom. Specifically, near the valence-band edge, the $K/K'$ valleys are dominated by transition metal $d_{x^2-y^2} \pm id_{xy}$ orbitals, while the $\Gamma$ valley contains substantial $d_{z^2}$ and chalcogen $p_z$ orbitals. These distinct orbital characters lead to different effective masses, spin-orbit coupling strengths (Ising-like in $K$ vs. Heisenberg-like in $\Gamma$), and interlayer hybridization properties. However, previous studies of moiré physics in TMDs have focused almost exclusively on the $K$ valley. This work addresses the gap in understanding how the distinct orbital characters of the $\Gamma$ valley influence correlated phases in moiré systems.

Methodology
The authors investigate a twisted monolayer/bilayer WSe$_2$ heterostructure, where an exfoliated 2H-stacked bilayer is rotated by approximately $3.4^\circ$ and stacked onto a monolayer. This configuration creates an ABB' structure with a triangular moiré superlattice between the bilayer layers. The device is encapsulated in hexagonal boron nitride (hBN) with top and bottom gates to apply a vertical displacement field ($D$).

The study utilizes transport measurements (resistance $R_{xx}$) as a function of:

• Moiré filling factor ($\nu = n/n_M$)
• Displacement field ($D$)
• Temperature ($T$)
• Perpendicular magnetic field ($B$)

The displacement field serves as a critical tuning knob to selectively populate the $K$ or $\Gamma$ valley bands. Due to the asymmetry of the monolayer/bilayer stack and the different layer-polarization responses of the valleys, varying $D$ shifts the relative energy of the $K$ and $\Gamma$ bands, allowing the researchers to isolate and compare correlated states in each valley within the same device.

Key Results
The study identifies contrasting correlated phases at integer ($\nu=1$) and fractional ($\nu=1/3$) fillings for the $K$ and $\Gamma$ valleys:

1. At $\nu = 1$ (Integer Filling):

   • $K$ Valley: Exhibits a weak insulating state at low temperatures ($T < 10$ K), consistent with an antiferromagnetic state near a van Hove singularity in the intermediate-coupling regime, similar to observations in twisted bilayer WSe$_2$. The insulating state is suppressed by a magnetic field ($B \approx 4$ T), giving way to quantum oscillations.
   • $\Gamma$ Valley: Displays a pronounced Pomeranchuk effect. While the state is insulating over a broad temperature range, the resistance drops sharply below $\sim 7$ K. This behavior is attributed to the system being close to a Mott transition. The localized state possesses higher entropy (due to free magnetic moments and SU(2) spin symmetry) than the metallic state; thus, increasing temperature stabilizes the localized phase. The system is estimated to have a large interaction parameter ($U/t \approx 8$) and significant next-nearest-neighbor hopping, placing it near the onset of a Mott transition and potentially a quantum spin liquid phase.

2. At $\nu = 1/3$ (Fractional Filling):

   • $K$ Valley: Hosts a robust generalized Wigner crystal (GWC), evidenced by strong resistive states.
   • $\Gamma$ Valley: The state lies near the crystallization boundary. It exhibits a weaker resistive peak at $\nu=1/3$ and also shows a Pomeranchuk effect, where the resistance peak develops below $\sim 7$ K and decreases at lower temperatures. The localization is enhanced by increasing temperature or magnetic field, suggesting the system is on the verge of a quantum melting transition from the GWC to a liquid phase.

Significance and Claims
The paper claims that the orbital/valley degree of freedom acts as an effective tuning knob for defining quantum phases in moiré systems. By utilizing the twisted monolayer/bilayer WSe$_2$ platform, the authors demonstrate that the $\Gamma$ valley offers a distinct physical regime compared to the well-studied $K$ valley.

Key claims regarding the significance of the work include:

• Orbital Control: The study highlights how the distinct orbital characters ($d_{z^2}/p_z$ in $\Gamma$ vs. $d_{x^2-y^2}/d_{xy}$ in $K$) lead to different interaction parameters ($U/t$), spin symmetries (Heisenberg vs. Ising), and hybridization strengths, resulting in contrasting correlated phases.
• Proximity to Quantum Phase Transitions: The $\Gamma$ valley states at both $\nu=1$ and $\nu=1/3$ are identified as lying near their respective phase boundaries (Mott transition and GWC crystallization boundary). This makes the $\Gamma$ valley a promising platform for exploring correlated phenomena where competing phases and enhanced fluctuations may give rise to unconventional phases, such as quantum spin liquids.
• Pomeranchuk Effect: The observation of the Pomeranchuk effect in both integer and fractional fillings in the $\Gamma$ valley underscores the importance of spin entropy in stabilizing localized states near quantum phase transitions.

The authors conclude that their work opens new routes for exploring correlated states in the $\Gamma$ valley, emphasizing the importance of orbital character in the design and understanding of moiré quantum materials.