Phys. Rev. B 96, 195427 (2017) - Interaction between counter-propagating quantum Hall edge channels in the 3D topological insulator ${\mathrm{BiSbTeSe}}

Interaction between counter-propagating quantum Hall edge channels in the 3D topological insulator ${BiSbTeSe}_{2}$

Chuan Li, Bob de Ronde, Artem Nikitin, Yingkai Huang, Mark S. Golden, Anne de Visser, and Alexander Brinkman

Phys. Rev. B 96, 195427 – Published 20 November 2017

Abstract

The quantum Hall effect is studied in the topological insulator ${BiSbTeSe}_{2}$ . By employing top- and back-gate electric fields at high magnetic field, the Landau levels of the Dirac cones in the top and bottom topological surface states can be tuned independently. When one surface is tuned to the electron-doped side of the Dirac cone and the other surface to the hole-doped side, the quantum Hall edge channels are counter-propagating. The opposite edge mode direction, combined with the opposite helicities of top and bottom surfaces, allows for scattering between these counter-propagating edge modes. The total Hall conductance is expected to be integer valued only when the scattering is strong. For weaker interaction, a noninteger quantum Hall effect is expected and indications for this effect are measured.

Received 29 March 2017
Revised 21 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.195427

Physics Subject Headings (PhySH)

Edge states Quantum Hall effect Semiconductors

Topological insulators

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chuan Li¹, Bob de Ronde¹, Artem Nikitin², Yingkai Huang², Mark S. Golden², Anne de Visser², and Alexander Brinkman¹

¹MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
²Van der Waals–Zeeman Institute, Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands

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Vol. 96, Iss. 19 — 15 November 2017

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Figure 1
(a) Schematic drawing of a dual-gated quantum Hall device with either parallel propagation or counter-propagation in the edge states of the topological bottom and top surfaces of a 3D topological insulator. In the case of parallel propagation (upper panel), the charge carriers move in the same direction and the edges of the surfaces form equipotential lines $(μ_{\pm})$ [12]. For counter-propagation (lower panel), the electrons and holes come from different potential reservoirs (electrodes) and move in opposite directions. In this case, a nonzero probability exists for backscattering between the top and bottom surfaces, given by $(1 - τ)$ . (b) Two-dimensional gate map of the longitudinal resistance, $R_{x x}$ , as a function of the top and back gate voltages at zero magnetic field. The maximum resistance indicates the chemical potential lying at the Dirac point. The color-coded line cuts showing $R_{x x}$ versus gate voltages are also shown, as is an inset showing an optical microscopy image of the device, in which the top gate and the ${BiSbTeSe}_{2}$ flake are clearly visible. The black arrows indicate the sweep direction of the measurements.
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Figure 2
(a) Antisymmetrized $R_{x y}$ Hall data as a function of top-gate voltage and magnetic field for a fixed back-gate voltage $(V_{b g} = - 40 V)$ . Hall resistance traces as a function of field for different top-gate voltages are shown to the right of the 2D map. The sign of the slope of $R_{x y}$ versus $B$ changes when the top surface is tuned from electron doped (blue) to hole doped (red). At the threshold top-gate voltage (green), the $R_{x y}$ signal is almost flat due to a cancellation of the $R_{x y}^{t}$ and $R_{x y}^{b}$ signals. In the bottom figure, a plot of $R_{x y}$ versus $V_{t g}$ is plotted for a field of 2.3 T, and shows a sharp change when $R_{x y}$ crosses zero. (b) Carrier density, $N_{b}$ , and mobility, $μ_{b}$ , of the bottom surface as a function of back-gate voltage as the result of a multiband fit to the Hall data. The charge carrier density changes sign as the Fermi level is tuned through the Dirac point. Around the Dirac point (yellow shading), charge puddles give rise to a third conductance contribution. (c) Carrier density, $N_{t}$ , and mobility, $μ_{t}$ , of the top surface as a function of top-gate voltage.
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Figure 3
(a),(b) Unsymmetrized Hall conductance $G_{x y}$ as a function of top-gate voltage $(V_{t g})$ and back-gate voltage $(V_{b g})$ at +15 and $- 15$ T. (c) $G_{x y}$ gate map after (anti)symmetrization analysis. The dashed lines indicate the borders between plateaus corresponding to different filling factors, noted as $(ν_{t}, ν_{b})$ . The voltage indicators on the outside of the frame mark the positions of the cross sections in the subsequent panels. (d) Back-gate voltage dependence of $G_{x y}$ at the three values of $ν_{t}$ shown in (f). The vertical, dashed lines indicate different $ν_{b}$ . (e) Top-gate voltage dependence of $G_{x y}$ at the four different $ν_{b}$ 's given in (f). The vertical, dashed lines now indicate different $ν_{t}$ . (f) Expected values of the Hall conductance for different filling factors in units of $\frac{e^{2}}{h}$ . The measured values are shown between brackets. (g) Measured and calculated values for the change in $G_{x y}$ for successive bottom surface Landau levels, as indicated by the steps in (d) when going from one $ν_{b}$ value to the next. Error bars are extracted from the averaging carried out of the gating map data. Left: $ν_{t} = - \frac{1}{2}$ (counter-propagating modes). Right: $ν_{t} = \frac{1}{2}$ (parallel propagation). The calculated step sizes are shown both for perfect transmission $(τ = 1)$ and for $τ = 0.8$ . (h) Longitudinal resistance, $R_{x x}$ , at $B = 15$ T versus $V_{t g}$ and $V_{b g}$ . Blue solid lines indicate the borders of the Landau level plateaus. The hatched areas indicate regions with counter-propagating modes.
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Physical Review B

covering condensed matter and materials physics

Interaction between counter-propagating quantum Hall edge channels in the 3D topological insulator ${BiSbTeSe}_{2}$

Chuan Li, Bob de Ronde, Artem Nikitin, Yingkai Huang, Mark S. Golden, Anne de Visser, and Alexander Brinkman

Phys. Rev. B 96, 195427 – Published 20 November 2017

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Physical Review B

covering condensed matter and materials physics

Interaction between counter-propagating quantum Hall edge channels in the 3D topological insulator BiSbTeSe2

Chuan Li, Bob de Ronde, Artem Nikitin, Yingkai Huang, Mark S. Golden, Anne de Visser, and Alexander Brinkman

Phys. Rev. B 96, 195427 – Published 20 November 2017

Abstract

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Interaction between counter-propagating quantum Hall edge channels in the 3D topological insulator ${BiSbTeSe}_{2}$