Interlayer Electron-Hole Friction in Tunable Twisted Bilayer Graphene Semimetal

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Interlayer Electron-Hole Friction in Tunable Twisted Bilayer Graphene Semimetal

D. A. Bandurin, A. Principi, I. Y. Phinney, T. Taniguchi, K. Watanabe, and P. Jarillo-Herrero

Phys. Rev. Lett. 129, 206802 – Published 10 November 2022

Abstract

Charge-neutral conducting systems represent a class of materials with unusual properties governed by electron-hole ( $e − h$ ) interactions. Depending on the quasiparticle statistics, band structure, and device geometry these semimetallic phases of matter can feature unconventional responses to external fields that often defy simple interpretations in terms of single-particle physics. Here we show that small-angle twisted bilayer graphene (SA TBG) offers a highly tunable system in which to explore interactions-limited electron conduction. By employing a dual-gated device architecture we tune our devices from a nondegenerate charge-neutral Dirac fluid to a compensated two-component $e − h$ Fermi liquid where spatially separated electrons and holes experience strong mutual friction. This friction is revealed through the $T^{2}$ resistivity that accurately follows the $e − h$ drag theory we develop. Our results provide a textbook illustration of a smooth transition between different interaction-limited transport regimes and clarify the conduction mechanisms in charge-neutral SA TBG.

Received 4 June 2022
Revised 22 August 2022
Accepted 21 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.206802

Physics Subject Headings (PhySH)

Electrical conductivity Transport phenomena

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. A. Bandurin ^1,*, A. Principi^2,†, I. Y. Phinney³, T. Taniguchi⁴, K. Watanabe ⁵, and P. Jarillo-Herrero^3,‡

¹Department of Materials Science and Engineering, National University of Singapore, 117575 Singapore
²School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
³Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁴International Center for Materials Nanoarchitectonics, National Institute of Material Science, Tsukuba 305-0044, Japan
⁵Research Center for Functional Materials, National Institute of Material Science, Tsukuba 305-0044, Japan

^*Corresponding author. dab@nus.edu.sg
^†Corresponding author. alepr85@gmail.com
^‡Corresponding author. pjarillo@mit.edu

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Issue

Vol. 129, Iss. 20 — 11 November 2022

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Images

Figure 1
Biased SA TBG. (a),(b) Single-particle band structure for SA TBG [34, 35]. At low energies, two Dirac cones are formed in the vicinity of the $k_{m}$ and $k_{m}^{'}$ points (a); when $D \neq 0$ , the cones are shifted with respect to each other (b). The horizontal dashed lines represent the Fermi level in the neutral SA TBG. (c) Phase diagram for the charge-neutral $e − h$ mixture in SA TBG mapped onto a $T − D$ plane. Dashed lines: the dependence of $T_{F}$ in each minivalley on $D$ for $n = 0$ . (d) Schematic of the dual-gated encapsulated SA TBG device.
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Figure 2
Effect of displacement on the transport properties of the SA TBG. (a) $ρ_{x x}$ as a function of $V_{BG}$ and $V_{TG}$ measured in the 1.65° SA TBG device. Blue and red lines correspond to the $(V_{TG}, V_{BG})$ points where $D = 0$ and $D = 0.7 V / nm$ respectively. (b) $ρ_{x x} (n)$ traces for $D = 0$ and $D = 0.7 V / nm$ measured at $T = 4.2 K$ . Inset: Optical photograph of an encapsulated SA TBG device. We attribute low- $T$ bulges in the resistivity at $| n | ≃ 10^{11} {cm}^{- 2}$ to the manifestation of composite supermoiré lattices with a very long wavelength that could form due to unintentional and coarse alignment of graphene sheets with both boron nitride flakes [42]. (c) Same as (b) but for $T = 20 K$ . Inset: enlarged region of the NP vicinity for $D = 0.7 V / nm$ .
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Figure 3
Temperature dependence of the SA TBG resistivity. (a) $ρ_{x x} (n)$ for different $T$ for the case of $D = 0$ . Inset: $ρ_{x x} (T)$ at the NP and $D = 0$ . (b) Same as (a) but for $D = 0.7 V / nm$ . Inset: $ρ_{x x} (T)$ at the compensation point ( $n = 0$ ) and $D = 0.7 V / nm$ . Dashed line: guide for the eye that represents the $a + b T^{2}$ dependence. The deviation from the $T^{2}$ scaling can be attributed to the thermal smearing of the distribution function that leads to the exit of the SA TBG $e − h$ system from the degenerate state: at $n = 1.3 \times 10^{11} {cm}^{- 2}$ , the Fermi temperature of the 1.65° SA TBG is of the order of 220K. (c) $ρ_{x x} (n)$ for BLG at $D = 0$ . (d) Resistivity as a function of $T$ for the charge-neutral SA TBG at $D = 0$ (blue) and $D = 0.7 V / nm$ (red) and for BLG at $D = 0$ (gray). The data are normalized to the lowest- $T$ value of $ρ_{x x} (n)$ : 4.2 K for SA TBG and 10 K for BLG. (e) $Δ ρ = ρ_{x x} (T) - ρ_{x x} (4.2 K)$ as a function of $T$ measured at $D = 0.7 V / nm$ and $n = 0$ (symbols). Note, $Δ ρ (T)$ exhibits somewhat faster $T$ dependence at $T < 15 K$ . This apparent behavior is spurious and is related to the subtraction operation of the $ρ_{0} = ρ_{x x} (4.2 K)$ from the experimental dataset rather than $ρ_{x x}$ at $T \to 0$ . Solid line: theoretical dependence, Eq. (1). Upper left inset: schematic illustration of the interlayer $e − h$ friction in SA TBG at finite $D$ . Lower right inset: Prefactor $B$ as a function of twist angle, $θ$ .
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