Surface transport and quantum Hall effect in ambipolar black phosphorus double quantum wells

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Science Advances  02 Jun 2017:
Vol. 3, no. 6, e1603179
DOI: 10.1126/sciadv.1603179


  • Fig. 1 Device schematics and image.

    (A) Side view of device schematics. (B) Optical microscope image of an hBN/BP/hBN stack and a finished device without top gate (inset).

  • Fig. 2 Transport data.

    (A and B) R(Vbg, Vtg) and line traces R(Vbg) at different Vtg at T = 1.7 K and B = 0. Note the logarithmic color scale (in Ω). (C) Right: R(Vbg, Vtg) at T = 0.5 K and B = 18 T, featuring a complicated quantum oscillations pattern. The color scale is in kΩ. Left: Schematics of the charge distributions that correspond to bipolar double-layer, single-layer, and unipolar double-layer regimes, respectively. Inset: Charge types for top and bottom surfaces at different combinations of gate voltages. p, hole-doped; n, electron-doped; i, intrinsic insulating state. (D) Band diagrams that correspond to the three regimes in (C), with dots illustrating mid-gap impurity states.

  • Fig. 3 Quantum oscillations at B = 18 T.

    (A) Background-subtracted resistance ΔR at Vtg = −6 V and T = 0.6, 1, 1.8, 4, 6, and 9 K, respectively. Arrows indicate nonmonotonic amplitude dependence on density. (B) Similar data set at Vtg = −4.4 V. (C) Oscillation amplitude as a function of temperature at Vtg = −3 V and different Vbg values (squares), fitted to Lifshitz-Kosevich formula (solid lines). The fits yield an effective mass m* ~ 0.43 ± 0.1 me. (D) ΔR(Vbg) at Vtg = 0 V and T = 1 K (solid lines) and fitted curve using Eq. 1 (dashed line), TD = 2 K and gm* = 1.15.

  • Fig. 4 QH states at high magnetic field.

    (A) R(Vbg, B) with the top gate disconnected for 18 < B < 31 T. Quantized plateaus at filling factors ν = 1, 2, 3, 4, 5, and 6 are observed. (B) Line traces of (A) at B = 24 T (blue) and B = 31 T (red), respectively. The dashed lines mark expected values of resistance plateaus. (C) Differentiated dR/dB(Vbg, B) at Vtg = −8 V. (D) Line traces of (D) at B = 20.3 T (blue) and B = 27.7 T (red). The dashed lines correspond to raw data, and solid lines are obtained by subtracting parallel conductance contributed by top surface states. Inset: Calculated conductance of the top surface states at Vtg as a function of B.

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