Large spin relaxation anisotropy and valley-Zeeman spin-orbit coupling in ${\mathrm{WSe}}_{2}$/graphene/$h$-BN heterostructures

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Large spin relaxation anisotropy and valley-Zeeman spin-orbit coupling in ${WSe}_{2}$ /graphene/ $h$ -BN heterostructures

Simon Zihlmann, Aron W. Cummings, Jose H. Garcia, Máté Kedves, Kenji Watanabe, Takashi Taniguchi, Christian Schönenberger, and Péter Makk

Phys. Rev. B 97, 075434 – Published 22 February 2018

Abstract

Large spin-orbital proximity effects have been predicted in graphene interfaced with a transition-metal dichalcogenide layer. Whereas clear evidence for an enhanced spin-orbit coupling has been found at large carrier densities, the type of spin-orbit coupling and its relaxation mechanism remained unknown. We show an increased spin-orbit coupling close to the charge neutrality point in graphene, where topological states are expected to appear. Single-layer graphene encapsulated between the transition-metal dichalcogenide ${WSe}_{2}$ and $h$ -BN is found to exhibit exceptional quality with mobilities as high as $1 \times 10^{5}$ ${cm}^{2}$ $V^{- 1}$ $s^{- 1}$ . At the same time clear weak antilocalization indicates strong spin-orbit coupling, and a large spin relaxation anisotropy due to the presence of a dominating symmetric spin-orbit coupling is found. Doping-dependent measurements show that the spin relaxation of the in-plane spins is largely dominated by a valley-Zeeman spin-orbit coupling and that the intrinsic spin-orbit coupling plays a minor role in spin relaxation. The strong spin-valley coupling opens new possibilities in exploring spin and valley degree of freedom in graphene with the realization of new concepts in spin manipulation.

Received 15 December 2017
Revised 22 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.075434

Physics Subject Headings (PhySH)

Spin relaxation Spin-orbit coupling Weak antilocalization

Graphene Transition metal dichalcogenides

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Simon Zihlmann^1,*, Aron W. Cummings², Jose H. Garcia², Máté Kedves³, Kenji Watanabe⁴, Takashi Taniguchi⁴, Christian Schönenberger¹, and Péter Makk^1,3,†

¹Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
²Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain
³Department of Physics, Budapest University of Technology and Economics and Nanoelectronics “Momentum” Research Group of the Hungarian Academy of Sciences, Budafoki ut 8, 1111 Budapest, Hungary
⁴National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan

^*simon.zihlmann@unibas.ch
^†peter.makk@mail.bme.hu

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Vol. 97, Iss. 7 — 15 February 2018

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Figure 1
Device layout and basic characterization of ${WSe}_{2}$ /graphene/ $h$ -BN vdW heterostructures. (a) An optical image of device A before the fabrication of the top gate, whose outline is indicated by the dashed white rectangle. On the right is a schematic cross section and the directions of the magnetic fields are indicated. The scale bar is 1 $μ m$ . The data in (b)–(e) are from device B. The two-terminal resistance measured from lead 1 to lead 2 is shown as a function of top and back gate voltage. A pronounced resistance maximum tunable by both gates indicates the charge neutrality point (CNP) of the bulk device, whereas a fainter line only changing with $V_{BG}$ indicates the CNP from the device area close to the contacts that are not covered by the top gate. (c) Cuts in $V_{TG}$ at different $V_{BG}$ of the conductivity measured in a four-terminal configuration, which are also used to extract field effect mobility (linear fit indicated by the dashed black line) and residual doping as indicated. (d) The fan plot of longitudinal resistance $R_{xx}$ versus $V_{BG}$ and $B_{z}$ at $V_{TG} = - 1.42$ V and (e) a cut at $B_{z} = 7$ T. Clear plateaus are observed at filling factors $ν = \pm 2, \pm 3, \pm 4, \dots$ , indicating full lifting of the fourfold degeneracy of graphene for magnetic fields $> 6$ T.
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Figure 2
Magnetoconductivity of device A. (a) Magnetoconductivity versus $B_{z}$ and $n$ is shown at $T = 0.25$ K. A clear feature is observed around $B = 0$ mT and large modulations due to UCF are observed in $B_{z}$ and $n$ . (b) Magnetoconductivity averaged over all traces at different $n$ . The WAL peak completely disappears at $T = 30$ K, leaving the classical magnetoconductivity as a background. The 30 K trace is offset vertically for clarity. The quantum correction to the magnetoconductivity is then obtained by subtracting the high-temperature background from the magnetoconductivity; see (b) on the right for different temperatures. With increasing temperature the phase coherence time shortens and therefore the WAL peak broadens and reduces in height. (c) Autocorrelation of the magnetoconductivity in red and its derivative in blue (without scale). The minimum of the derivative indicates the inflection point ( $B_{i p}$ ) of the autocorrelation, which is a measure of $τ_{ϕ}$ .
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Figure 3
Fitting of quantum correction to the magnetoconductivity of device A. The quantum correction to the magnetoconductivity is fit using Eq. (2). The results for three different limits are shown and their parameters are indicated (in units of picoseconds). $τ_{ϕ}$ is estimated to be 8 ps from the autocorrelation of UCF in the magnetic field [see Fig. 2].
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Figure 4
Density dependence of device C. The dependence of the spin-orbit scattering rates $τ_{sym}^{- 1}$ and $τ_{asy}^{- 1}$ as a function of $τ_{p}$ are shown for device C. The error bars on the spin-orbit scattering rates are given by a conservative estimate of $50 %$ . The two-terminal conductivity is shown in the inset and the extracted mobilities for the $n$ and $p$ side are indicated. The density of each data point is indicated in blue above the top graph. The magnetoconductivity was averaged over a density range of $3.3 \times 10^{12}$ ${cm}^{- 2}$ centered around the value given at the top.
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Figure 5
In-plane magnetic field dependence of device A. (a) The quantum correction to the magnetoconductivity at the CNP and at zero perpendicular electric field is shown for different in-plane magnetic field strengths $B_{∥}$ . Here, $n$ was averaged in the range of $- 1 \times 10^{11}$ to $1 \times 10^{11}$ ${cm}^{- 2}$ . The WAL peak gradually decreases in height and broadens as $B_{∥}$ is increased. The traces at $B_{∥} = 5$ , 7, and 9 T are offset by $0.03 e^{2} / h$ for clarity. (b) The extracted phase coherence time $τ_{ϕ}$ and the total spin-orbit scattering time $τ_{SO}$ are plotted versus $B_{∥}$ . $τ_{ϕ}$ clearly reduces, whereas $τ_{SO}$ remains roughly constant over the full $B_{∥}$ range investigated. The error bars on $τ_{SO}$ and $τ_{ϕ}$ are given by a conservative estimate of 50%.
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Figure 6
Possible low-energy band structures: (a), (b) band structures using the Hamiltonian of Eq. (1) with the parameters listed in (a). The unknown parameters $Δ$ and $λ_{I}$ were taken from Ref. [22]. In (a), the band structure is shown in the density range of $- 2.5 \times 10^{11}$ to $2.5 \times 10^{11}$ ${cm}^{- 2}$ (CNP), which corresponds the one investigated above. The energy range dominated by charge puddles is indicated by the grey shaded region. (b) Zoom-in at low energy. (c) $λ_{I}$ of 5 meV is assumed to show the changes due to the unknown $λ_{I}$ at low energy.
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Physical Review B

covering condensed matter and materials physics

Large spin relaxation anisotropy and valley-Zeeman spin-orbit coupling in ${WSe}_{2}$ /graphene/ $h$ -BN heterostructures

Simon Zihlmann, Aron W. Cummings, Jose H. Garcia, Máté Kedves, Kenji Watanabe, Takashi Taniguchi, Christian Schönenberger, and Péter Makk

Phys. Rev. B 97, 075434 – Published 22 February 2018

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Physical Review B

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Large spin relaxation anisotropy and valley-Zeeman spin-orbit coupling in WSe2/graphene/h-BN heterostructures

Simon Zihlmann, Aron W. Cummings, Jose H. Garcia, Máté Kedves, Kenji Watanabe, Takashi Taniguchi, Christian Schönenberger, and Péter Makk

Phys. Rev. B 97, 075434 – Published 22 February 2018

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Large spin relaxation anisotropy and valley-Zeeman spin-orbit coupling in ${WSe}_{2}$ /graphene/ $h$ -BN heterostructures