Observation of the Spin-Orbit Gap in Bilayer Graphene by One-Dimensional Ballistic Transport

L. Banszerus, B. Frohn, T. Fabian, S. Somanchi, A. Epping, M. Müller, D. Neumaier, K. Watanabe, T. Taniguchi, F. Libisch, B. Beschoten, F. Hassler, and C. Stampfer

Phys. Rev. Lett. 124, 177701 – Published 1 May 2020

Abstract

We report on measurements of quantized conductance in gate-defined quantum point contacts in bilayer graphene that allow the observation of subband splittings due to spin-orbit coupling. The size of this splitting can be tuned from 40 to $80 μ eV$ by the displacement field. We assign this gate-tunable subband splitting to a gap induced by spin-orbit coupling of Kane-Mele type, enhanced by proximity effects due to the substrate. We show that this spin-orbit coupling gives rise to a complex pattern in low perpendicular magnetic fields, increasing the Zeeman splitting in one valley and suppressing it in the other one. In addition, we observe a spin polarized channel of $6 e^{2} / h$ at high in-plane magnetic field and signatures of interaction effects at the crossings of spin-split subbands of opposite spins at finite magnetic field.

Received 2 December 2019
Accepted 13 April 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.177701

Physics Subject Headings (PhySH)

Spin polarization Spin-orbit coupling Zeeman effect

Graphene Point contacts

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

L. Banszerus ^1,2, B. Frohn¹, T. Fabian ³, S. Somanchi¹, A. Epping^1,2, M. Müller ^1,2, D. Neumaier⁴, K. Watanabe⁵, T. Taniguchi⁵, F. Libisch ³, B. Beschoten ¹, F. Hassler ⁶, and C. Stampfer ^1,2,*

¹JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU
²Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany, EU
³Institute for Theoretical Physics, TU Wien, 1040 Vienna, Austria, EU
⁴AMO GmbH, 52074 Aachen, Germany, EU
⁵National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
⁶JARA-Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany, EU

^*Corresponding author. stampfer@physik.rwth-aachen.de

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Issue

Vol. 124, Iss. 17 — 1 May 2020

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Images

Figure 1
(a) Schematic illustration of the device highlighting the hBN/BLG/hBN heterostructure and the various gates. The inset shows an AFM image of the sample. The scale bar is 500 nm (details in Supplemental Material [27]). (b) Four-terminal conductance as function of $V_{F 1}$ for different displacement fields showing steps at multiples of $4 e^{2} / h$ . (c) Finite bias spectroscopy measurements. Different traces correspond to different values of $V_{F 1}$ , ranging from $- 9.4$ to $- 10.6 V$ . A clustering of traces at multiples of $4 e^{2} / h$ is visible at low bias voltages, vanishing at high bias. (d) Conductance through two QPCs in series separated by 260 nm. The conductance is quantized in multiples of $4 e^{2} / h$ and depends solely on the QPC with the lowest number of occupied modes.
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Figure 2
(a) Conductance as a function of $V_{F 1}$ for in-plane magnetic fields, $B_{∥}$ between $- 2$ and 6 T at $D = 0.28 V / nm$ . Plateaus at $2 e^{2} / h$ , $6 e^{2} / h$ , and $10 e^{2} / h$ appear. (b) Schematic illustration of the spin splitting of the first three subbands as a function of in-plane magnetic field. (c) Transconductance $d G / d V_{F 1}$ as a function of $V_{F 1}$ and $B_{∥}$ at $D = 0.28 V / nm$ . At the points marked by the black dots, the Zeeman energy matches the subband spacing. The rotated square indicates the point where the spin-up states of the first subband cross the spin-down states of the third one, see schematics in panel (b). The numbers indicate the conductance values in units of $e^{2} / h$ . (d) Energy difference $Δ E_{1, n}$ between the first and the $n$ th subband ( $n \leq 5$ ), for different displacement fields. The squared data points originate from finite bias spectroscopy and the round data points from the analysis of the Zeeman splitting, taking $Δ E_{1, n} = \sum_{i = 1}^{n - 1} Δ E_{i, i + 1}$ . The purple data points are extracted from the data of panel (c). The rotated square represents the energy difference $Δ E_{1, 3}$ as extracted from the position of the rotated square in panel (c).
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Figure 3
(a) Zoom of Fig. 2 around the first conductance step and low $B_{∥}$ , showing the presence of a shoulder at $2 e^{2} / h$ even at $B_{∥} = 0$ . (b) Transconductance as a function of $V_{F 1}$ and $B_{∥}$ . The dashed lines mark the evolution of the spin up (white) and spin down bands (black) of the first subband. (c) Extracted energy gap $Δ$ as a function of the displacement field.
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Figure 4
(a),(b) Transconductance $d G / d V_{F 1}$ as a function of $V_{F 1}$ and $B_{⊥}$ for two different values of the displacement field. (c),(d) Single-particle model calculations of $d G / d V_{F 1}$ . The $K$ -valley states are highlighted by dashed blue lines, and the $K^{'}$ -valley states by solid red lines. The gray-scale background shows an approximation for the differential conductance obtained by Gaussian smearing.
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