Phase coherent transport in bilayer and trilayer $\mathrm{Mo}{\mathrm{S}}_{2}$

Phase coherent transport in bilayer and trilayer $Mo S_{2}$

Leiqiang Chu, Indra Yudhistira, Hennrik Schmidt, Tsz Chun Wu, Shaffique Adam, and Goki Eda

Phys. Rev. B 100, 125410 – Published 9 September 2019

Abstract

Bilayer $Mo S_{2}$ is a centrosymmetric semiconductor with degenerate spin states in the six valleys at the corners of the Brillouin zone. It has been proposed that breaking of this inversion symmetry by an out-of-plane electric field breaks this degeneracy, allowing for spin and valley lifetimes to be manipulated electrically in bilayer $Mo S_{2}$ with an electric field. In this work, we report phase coherent transport properties of double-gated mono-, bi-, and trilayer $Mo S_{2}$ . We observe a similar crossover from weak localization to weak antilocalization, from which we extract the spin relaxation time as a function of both electric field and temperature. We find that the spin relaxation time is inversely proportional to momentum relaxation time, indicating that the D’yakonov-Perel mechanism is dominant in all devices despite the centrosymmetry of the bilayer device. Further, we found no evidence of electric-field-induced changes in spin-orbit coupling strength. This suggests that the interlayer coupling is sufficiently weak and that electron-doped dichalcogenide multilayers behave electrically as decoupled monolayers.

Received 10 April 2019
Revised 22 August 2019

DOI:https://doi.org/10.1103/PhysRevB.100.125410

Physics Subject Headings (PhySH)

Quantum interference effects Quantum transport Spin dynamics Spin-orbit coupling Valleytronics

2-dimensional systems Devices Field-effect transistors Thin films Transistors Transition metal dichalcogenides Two-dimensional electron system

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Leiqiang Chu^1,2,*, Indra Yudhistira^1,3,*, Hennrik Schmidt^1,3, Tsz Chun Wu⁵, Shaffique Adam^1,3,6,†, and Goki Eda^1,3,4,‡

¹Department of Physics, National University of Singapore, 3 Science Drive 3, Singapore 117543
²Department of Physics, Shaoxing University, Shaoxing, 312000, China
³Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, 6 Science Drive 2, Singapore 117546
⁴Department of Chemistry, National University of Singapore, 2 Science Drive 3, Singapore 117551
⁵Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
⁶Yale-NUS College, 6 College Ave West, Singapore 138614

^*L.C. and I.Y. contributed equally to this work.
^†shaffique.adam@yale-nus.edu.sg
^‡g.eda@nus.edu.sg

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Vol. 100, Iss. 12 — 15 September 2019

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Figure 1
Theoretical expectation of electric field tunability of spin splitting energy. (a) Theoretical calculation for the effect of conduction band interlayer coupling strength $t_{⊥}^{c}$ on the tunability of bilayer D’yakonov-Perel spin splitting $λ_{int}$ with an interlayer electric field $E_{m}$ . At a zero electric field, the spin splitting vanishes due to the presence of inversion symmetry and time-reversal symmetry. However, at a large electric field, the inversion symmetry is broken, and the spin splitting approaches the single-layer value irrespective of coupling. Insets show a schematic illustration of the vertical electric field through bilayer $Mo S_{2}$ (up) and the K-point band structure at $E_{m} = 0$ and finite $E_{m}$ (down). (b) Theoretical calculation for the effect of Bychkov-Rashba spin-orbit coupling strength $λ_{B R}$ on the tunability of bilayer $λ_{int}$ with an interlayer coupling strength $t_{⊥}^{c} = 1$ meV. $λ_{int}$ increases with electric field when $λ_{B R}$ is nonzero, increasing more rapidly with larger $λ_{B R}$ .
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Figure 2
(a) $Mo S_{2}$ transfer characteristics for different layer thickness at various combinations of top gate and back-gate voltages. The transfer curves are shifted horizontally according to their conductivity with an indicated effective back-gate voltage bias. Inset shows the schematic illustration of the dual-gated device structure. The dashed lines are fitting curves. (b) Electrical displacement field strength at different combination of the dual gate voltages for a simple model which ignores interlayer charge density imbalance.
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Figure 3
(a–c) Top panel: Magneto-conductivity of monolayer, bilayer and trilayer $Mo S_{2}$ at different back-gate voltages of 40, 50, and 80 V and fixed top gate voltage of $V_{t g} = 1$ V(monolayer), $V_{t g} = 0$ V(bilayer and trilayer), and fixed temperature of $T = 10 K$ . Bottom panel: Magneto-conductivity of monolayer, bilayer, and trilayer $Mo S_{2}$ at different temperatures of 10, 20, and 40 K and fixed dual gate voltage of $V_{t g} = 1.7 V$ , $V_{b g} = 0 V$ . The left shaded curves are theoretically fits according to Eq. (1), and right curves in each panel are experimental results. To calculate $Δ σ$ , the measured magnetoresistance was symmetrized by $ρ (B) = [ρ (+ B) + ρ (- B)] / 2$ , and that classical quadratic contribution has been subtracted.
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Figure 4
D’yakonov-Perel spin relaxation in multilayer $Mo S_{2}$ is electric field independent. To show all the data in just one figure, we divide spin relaxation time $τ_{S O}$ by number of layers $g_{l}$ . The ratios of $τ_{S O}$ with $g_{l}$ as a function of inversed momentum relaxation time $τ_{p}^{- 1}$ correspond to monolayer, bilayer, and trilayer $Mo S_{2}$ , respectively. The dashed lines are fits using $2 ℏ^{2} / τ_{p} τ_{S O} = λ_{int}^{2}$ . The strength of spin-orbit interaction $λ_{int}$ is found to be 7.2 meV, 6 meV, and 4.1 meV, respectively. Inset shows a zoom in of the low spin relaxation time regime.
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Figure 5
Schematic of bilayer $Mo S_{2}$ in the presence of back and top gates.
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Physical Review B

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Phase coherent transport in bilayer and trilayer $Mo S_{2}$

Leiqiang Chu, Indra Yudhistira, Hennrik Schmidt, Tsz Chun Wu, Shaffique Adam, and Goki Eda

Phys. Rev. B 100, 125410 – Published 9 September 2019

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Physical Review B

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Phase coherent transport in bilayer and trilayer MoS2

Leiqiang Chu, Indra Yudhistira, Hennrik Schmidt, Tsz Chun Wu, Shaffique Adam, and Goki Eda

Phys. Rev. B 100, 125410 – Published 9 September 2019

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Phase coherent transport in bilayer and trilayer $Mo S_{2}$