[Paper Review] Probing the fractional quantum Hall phases in valley-layer locked bilayer MoS$_{2}$

S.G. Zhao, Jinqiang Huang+17 more|arXiv (Cornell University)|Aug 5, 2023

Graphene research and applications51 references4 citations

TL;DR

This study reports the first observation of fractional quantum Hall (FQH) states at filling fractions 4/5 and 2/5 in bilayer MoS₂, enabled by high-mobility, valley-layer locked 2D electron gas and tunable Coulomb screening via gate and dielectric engineering. The FQH states manifest as quantized Hall plateaus and resistance minima under high magnetic fields (up to 34 T) and low temperatures (300 mK), establishing bilayer MoS₂ as a tunable platform for topological quantum phenomena.

ABSTRACT

Semiconducting transition-metal dichalcogenides (TMDs) exhibit high mobility, strong spin-orbit coupling, and large effective masses, which simultaneously leads to a rich wealth of Landau quantizations and inherently strong electronic interactions. However, in spite of their extensively explored Landau levels (LL) structure, probing electron correlations in the fractionally filled LL regime has not been possible due to the difficulty of reaching the quantum limit. Here, we report evidence for fractional quantum Hall (FQH) states at filling fractions 4/5 and 2/5 in the lowest LL of bilayer MoS$_{2}$, manifested in fractionally quantized transverse conductance plateaus accompanied by longitudinal resistance minima. We further show that the observed FQH states sensitively depend on the dielectric and gate screening of the Coulomb interactions. Our findings establish a new FQH experimental platform which are a scarce resource: an intrinsic semiconducting high mobility electron gas, whose electronic interactions in the FQH regime are in principle tunable by Coulomb-screening engineering, and as such, could be the missing link between atomically thin graphene and semiconducting quantum wells.

Motivation & Objective

• To probe fractional quantum Hall (FQH) states in the lowest Landau level of bilayer MoS₂, a system with strong electron correlations and high mobility.
• To overcome the challenge of accessing the quantum limit in semiconducting TMDs due to difficulties in achieving low carrier density and proper dielectric screening.
• To establish bilayer MoS₂ as a tunable platform for FQH physics by engineering Coulomb interactions via gate and dielectric environment.
• To provide experimental evidence for FQH states in a high-mobility, intrinsic 2D semiconductor with strong spin-orbit coupling and valley-layer locking.

Proposed method

• Fabricated high-quality bilayer MoS₂ devices with 2D-widowed bismuth contacts to enable low-temperature, high-magnetic-field transport measurements down to 300 mK.
• Employed high magnetic fields up to 34 T and measured transverse conductance and longitudinal resistance to identify FQH plateaus and minima.
• Engineered Coulomb screening using hexagonal boron nitride (h-BN) dielectrics and top/bottom gates to tune the effective interaction potential.
• Modelled the effective Coulomb interaction using a dielectric-regularized Rytova-Keldysh potential that accounts for both long-range (gate screening) and short-range (layered structure) screening.
• Projected the Coulomb potential to the lowest Landau level using Haldane’s pseudopotentials, focusing on the first three odd-moment pseudopotentials (V₁, V₃, V₅) relevant for fermions.
• Performed exact diagonalization on a torus with up to 13 particles to simulate the many-body ground state and confirm the stability of FQH states at ν = 4/5 and 2/5.

Fig. 1 : Electrical transport in bilayer MoS 2 in the single-particle regime. (a) Schematic illustration of the fabricated device. (b) Optical image of a typical dual-gated bilayer MoS 2 device. One of the 2D contact windows is highlighted by black dashed lines. Scale is 5 $\mu$ m. (c) Art view of t

Experimental results

Research questions

• RQ1 Can fractional quantum Hall states be realized and detected in the lowest Landau level of bilayer MoS₂, a semiconducting transition-metal dichalcogenide with strong spin-orbit coupling and valley-layer locking?
• RQ2 How does the dielectric environment and gate screening influence the stability of FQH states in bilayer MoS₂?
• RQ3 To what extent can the Coulomb interaction in bilayer MoS₂ be tuned to stabilize FQH states at specific filling fractions such as 4/5 and 2/5?
• RQ4 What is the role of the magnetic length and interlayer spacing in determining the effective interaction and FQH state formation in this system?
• RQ5 Can the observed FQH states be theoretically confirmed via exact diagonalization of the many-body Hamiltonian with realistic pseudopotential parameters?

Key findings

• Fractional quantum Hall states at filling fractions 4/5 and 2/5 were observed in bilayer MoS₂, evidenced by quantized transverse conductance plateaus and minima in longitudinal resistance at magnetic fields between 22 T and 34 T.
• The FQH states were stable at a magnetic length range of ℓ_B ≈ 4.5–6 nm, corresponding to a carrier density near the quantum limit.
• The observed FQH states are highly sensitive to dielectric and gate screening, with the Coulomb interaction tuned via the dielectric constant ε ≈ 5 and interlayer spacing δ = 0.65 nm.
• Theoretical modeling using Haldane’s pseudopotentials and exact diagonalization confirmed the stability of FQH states at ν = 4/5 and ν = 2/5, with the ground state energy splitting consistent with incompressible FQH states.
• The system exhibits a tunable interaction strength through gate and dielectric engineering, making it a promising platform for studying topological quantum phases.
• The data and exact diagonalization code are publicly available via Zenodo and DiagHam, enabling reproducibility and further theoretical exploration.

Fig. 2 : Electrical transport in bilayer MoS 2 in the single-particle regime. (a) Landau fan of sample-BS1 measured at $T$ = 300 mK and $V_{\textrm{bg}}$ = 4.72 V, in the magnetic field range from 0 to 12 T. White dashed lines are guides to eyes, and their crossing point indicates the band edge. (b)