Research ArticlePHYSICS

Direct observation of valley-coupled topological current in MoS2

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Science Advances  19 Apr 2019:
Vol. 5, no. 4, eaau6478
DOI: 10.1126/sciadv.aau6478
  • Fig. 1 Valley-coupled topological current.

    (A) Schematic of valley-coupled topological current due to VHE and iVHE in monolayer MoS2 and the device geometry (bottom), where W1 = 1 μm, W = W2 = 2 μm, L1 = 4.5 μm, and L = 0.5 μm. (B) Schematics of two measurement setups: type I and type II. (C) Patterned MoS2 flake (green) and lithographically defined metal electrodes (yellow).

  • Fig. 2 Comparison of nonlocal voltages obtained in monolayer and multilayer MoS2 devices.

    (A) Measured nonlocal voltage with respect to global back-gate voltage Vg in monolayer MoS2 using type I setup. Inset: Full range of Vg. Note that data points in the range of Vg < 40 V are not included in analysis because these large device resistances become comparable to the input impedance of the nanovoltmeter. (B) Ohmic contribution calculated from the measured sheet resistance: Vohmic=IDCρshWW1eπLW as a function of Vg, plotted with the same y-axis range as in (A). Inset: Zoom-in data. (C and D) Nonlocal voltage response in a multilayer MoS2 device for the same measurements performed in (A) and (B). Note that the y axis in both plots has a unit of millivolts.

  • Fig. 3 Electric potential mapping from a SPICE-based resistor network simulation.

    (A) SPICE simulation of a resistor grid with ~4 × 106 uniform resistors, where each resistor corresponds to ~3-nm channel length, with (x = 1500, y = 1400) points. Vds values applied at the two ends of the injector are V1 = 1.8 V and V2 = 0 V, respectively. Values greater than 0.94 V and less than 0.86 V are denoted with the same colors to resolve the nonlocal voltage distribution. (B) Voltage profiles along the y direction for four different positions denoted by arrows (1 to 4) in (A). Nonlocal voltage difference under open circuit condition is calculated to be ~29 mV.

  • Fig. 4 Temperature dependence and extraction of intervalley scattering length.

    (A) Measured Vnl as a function of temperature at different Vg for monolayer MoS2. (B) Temperature dependence of multilayer MoS2 at different Vg (dots) and the calculated trends (lines) using the modified ohmic equation, Vohmic=Vds(2RC+ρshL1W1)ρshWW1eπLW, with the consideration of the contact resistance contribution (see section S1). Note that the trends of Vnl with respect to temperature in (A) and (B) are completely opposite. (C) Device geometry and corresponding valley-circuit model that define the geometric parameters in Eq. 1. Details are given in section S3. (D) Temperature dependence of Rnlnorm (normalized to the maximum point) measured at Vg = 58 V [orange dots in (A)]. The empirical fittings use λ(T)=5.5T0.470.16 (dashed blue line) and λ=15T0.73 at T > 100 K (green line). Inset: Calculated temperature dependence of valley Hall angle, θ. (E) λ (T) extracted from Rnl and the power-law dependence described in (D). Inset: Theoretically calculated intervalley scattering length (solid line) and λT0.6 to guide the eye (dashed line).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/4/eaau6478/DC1

    Section S1. Optical and electrical characterizations

    Section S2. Details of resistor network for ohmic contribution

    Section S3. Derivation of nonlocal resistance, Rnl

    Section S4. Additional nonlocal measurements for multilayer MoS2 devices

    Section S5. Additional nonlocal measurements from other monolayer MoS2 devices

    Section S6. Channel length and width dependence in monolayer MoS2 device

    Section S7. Detailed θ calculation and its temperature trend

    Section S8. Detailed λ calculation and its temperature trend

    Section S9. Nonlocal internal resistance measurements

    Section S10. Applied in-plane magnetic field

    Fig. S1. Device layer number confirmations.

    Fig. S2. Device electrical characterizations.

    Fig. S3. SPICE-based resistor network.

    Fig. S4. The lumped valley-circuit model that is used to derive Eq. 1.

    Fig. S5. Comparison of analytical equations for Rnl with the full SPICE simulation of the circuit shown in fig. S4.

    Fig. S6. Long-channel multilayer MoS2 devices and additional monolayer MoS2 device measurements.

    Fig. S7. Length dependence in monolayer MoS2.

    Fig. S8. Valley Hall angle and intervalley scattering length.

    Fig. S9. Extraction of internal resistance in the nonlocal electrode.

    Fig. S10. Vnl measurements with in-plane magnetic field applied.

    References (3641)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Optical and electrical characterizations
    • Section S2. Details of resistor network for ohmic contribution
    • Section S3. Derivation of nonlocal resistance, Rnl
    • Section S4. Additional nonlocal measurements for multilayer MoS2 devices
    • Section S5. Additional nonlocal measurements from other monolayer MoS2 devices
    • Section S6. Channel length and width dependence in monolayer MoS2 device
    • Section S7. Detailed θ calculation and its temperature trend
    • Section S8. Detailed λ calculation and its temperature trend
    • Section S9. Nonlocal internal resistance measurements
    • Section S10. Applied in-plane magnetic field
    • Fig. S1. Device layer number confirmations.
    • Fig. S2. Device electrical characterizations.
    • Fig. S3. SPICE-based resistor network.
    • Fig. S4. The lumped valley-circuit model that is used to derive Eq. 1.
    • Fig. S5. Comparison of analytical equations for Rnl with the full SPICE simulation of the circuit shown in fig. S4.
    • Fig. S6. Long-channel multilayer MoS2 devices and additional monolayer MoS2 device measurements.
    • Fig. S7. Length dependence in monolayer MoS2.
    • Fig. S8. Valley Hall angle and intervalley scattering length.
    • Fig. S9. Extraction of internal resistance in the nonlocal electrode.
    • Fig. S10. Vnl measurements with in-plane magnetic field applied.
    • References (3641)

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