Misorientation-Controlled Cross-Plane Thermoelectricity in Twisted Bilayer Graphene

Phanibhusan S. Mahapatra, Bhaskar Ghawri, Manjari Garg, Shinjan Mandal, K. Watanabe, T. Taniguchi, Manish Jain, Subroto Mukerjee, and Arindam Ghosh

Phys. Rev. Lett. 125, 226802 – Published 24 November 2020

Abstract

The introduction of “twist” or relative rotation between two atomically thin van der Waals membranes gives rise to periodic moiré potential, leading to a substantial alteration of the band structure of the planar assembly. While most of the recent experiments primarily focus on the electronic-band hybridization by probing in-plane transport properties, here we report out-of-plane thermoelectric measurements across the van der Waals gap in twisted bilayer graphene, which exhibits an interplay of twist-dependent interlayer electronic and phononic hybridization. We show that at large twist angles, the thermopower is entirely driven by a novel phonon-drag effect at subnanometer scale, while the electronic component of the thermopower is recovered only when the misorientation between the layers is reduced to $< 6 °$ . Our experiment shows that cross-plane thermoelectricity at low angles is exceptionally sensitive to the nature of band dispersion and may provide fundamental insights into the coherence of electronic states in twisted bilayer graphene.

Received 17 September 2019
Revised 8 May 2020
Accepted 15 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.226802

Physics Subject Headings (PhySH)

Thermoelectric effects Thermopower Transport phenomena

Graphene

Raman spectroscopy Scanning electron microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Phanibhusan S. Mahapatra ^1,*, Bhaskar Ghawri^1,†, Manjari Garg², Shinjan Mandal¹, K. Watanabe³, T. Taniguchi³, Manish Jain¹, Subroto Mukerjee¹, and Arindam Ghosh^1,‡

¹Department of Physics, Indian Institute of Science, Bangalore 560 012, India
²Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012, India
³National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan

^*Corresponding author. phanis@iisc.ac.in
^†Corresponding author. gbhaskar@iisc.ac.in
^‡Also at Centre for Nano Science and Engineering, Indian Institute of Science, Bangalore 560 012, India.

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Issue

Vol. 125, Iss. 22 — 27 November 2020

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Images

Figure 1
Device structure and characterization. (a) Moiré superlattice when a relative rotation ( $θ$ ) is introduced between two graphene layers. (b) The Raman spectra for $G$ peak and 2D peak (shaded region) are compared for $θ \sim 12.5 °$ , $θ \sim 2 °$ , $θ = 0 °$ , and single layer graphene with relative offset in the intensity for clarity. (c) SEM image of a device with twist angle $θ = 0 °$ (Bernal stacking). The scale bar represents a length of $5 μ m$ . (d) Device schematic for the cross-plane electrical and thermoelectric measurements.
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Figure 2
Cross-plane electrical transport. (a) Schematic for the four-terminal cross-plane conductance measurements. (b) The cross-plane resistance ( $R_{cp}$ ) as a function of top-gate ( $V_{tg}$ ) and bottom-gate ( $V_{bg}$ ) potentials for $θ \sim 4 °$ . $R_{cp}$ as a function of $V_{tg}$ is shown by cyan curve from a line cut at fixed $V_{bg} = - 34 V$ (dotted line). Temperature dependence of $G_{cp}$ for (c) $θ \sim 12.5 °$ and (d) $θ \sim 2 °$ , respectively, for different values of carrier density ( $n$ ) measured from the charge neutrality point (CNP).
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Figure 3
Thermoelectric transport at large twist angle ( $θ \sim 12.5 °$ ). (a) In-plane heating and measurement scheme for cross-plane thermovoltage $V_{2 ω}$ . (b) $V_{2 ω}$ with varying top-gate voltages $| V_{tg} - V_{D} |$ for different in-plane heating currents ( $1 - 4 μ A$ ) at 84 K. (c) $V_{2 ω}$ normalized with $I_{ω}^{2}$ . The inset shows that the measured temperature difference $Δ T \propto I_{ω}^{2}$ . (d) Temperature dependence of $S = V_{2 ω} / Δ T$ for $θ \sim 12.5 °$ device for various $n$ . The solid lines show the fit of the TEP described in Eq. (1). The inset shows the obtained phonon energy as a function of Fermi wave vector $k_{F}$ . (e) The density dependence of the measured $S$ for three representative temperatures (circles). The dashed lines show the fitted $S$ from the phonon-drag TEP [Eq. (1)]. The inset shows the comparison between the measured $S$ (gray line) and the calculated $S$ (green line) from the Mott relation [Eq. (2)] at $T = 30 K$ . The red lines show the fit of the phonon-drag-mediated TEP.
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Figure 4
Cross-plane thermoelectricity at low twist angle. Temperature dependence of $S$ for (a) $θ \sim 2 °$ and (b) $θ = 0 °$ (Bernal stacking) for various $n$ . The dashed lines show the linear $T$ behavior as a guide for the eye. The doping dependence of experimentally measured $S$ (colored circles) is compared to $S_{Mott}$ (gray solid lines) for (c) $θ \sim 2 °$ and (d) $θ = 0 °$ at various temperatures. $S_{Mott}$ is calculated using the (c) single layer Dirac dispersion and (d) parabolic band dispersion of bilayer graphene. The inset in (d) shows the density dependence of $S$ for $θ = 0 °$ compared to that of normalized $S_{Mott}$ (black line) evaluated from the single layer Dirac dispersion at a fixed representative temperature $T = 150 K$ .
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Figure 5
Twist-controlled cross-plane thermoelectricity. (a) Seebeck coefficient as a function of temperature for seven different $θ$ at a fixed doping of $n \sim 3 \times 10^{11} {cm}^{- 2}$ . The solid lines show the fit of the phonon-driven TEP, while the dotted lines show the linear $T$ dependence as a guide for the eye. The $S − T$ data for $θ \sim 13 °$ are taken from Ref. [15]. (b) A schematic showing the interplay of the timescales associated with interlayer hybridization, dephasing, and electron-phonon scattering.
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