Probing many-body interactions in the cyclotron resonance of $h$-BN/bilayer graphene/$h$-BN

Probing many-body interactions in the cyclotron resonance of $h$ -BN/bilayer graphene/ $h$ -BN

Rai Moriya, Sabin Park, Satoru Masubuchi, Kenji Watanabe, Takashi Taniguchi, and Tomoki Machida

Phys. Rev. B 104, 245137 – Published 27 December 2021

Abstract

Unlike a conventional two-dimensional electron gas system, which has parabolic band structure, the nonparabolic band dispersion of mono- to few-layer graphene violates Kohn's theorem. Thus, Landau levels (LLs) in graphene are sensitive to many-body interactions. This modifies the LL spacing, depending on the location of the Fermi energy ( $E_{F}$ ). Such effects have been extensively studied in $h$ -BN/monolayer graphene/ $h$ -BN through observation of inter-LL optical transitions known as cyclotron resonances (CRs). However, thus far, the influence of many-body interactions on the CR of bilayer graphene (BLG) has been rarely studied, even though BLG also possesses nonparabolic band dispersion. Here, we investigate CR in the $h$ -BN/BLG/ $h$ -BN structure via magneto-photothermoelectric measurements under infrared laser irradiation. This method enables sensitive detection of cyclotron resonances while tuning $E_{F}$ of BLG. The CR magnetic field value shifted significantly when $E_{F}$ of BLG approached the charge-neutrality point (the Dirac point, DP). We attribute this to a change in the Fermi velocity of BLG near the DP, which occurs as a result of many-body interactions.

Received 5 July 2021
Revised 1 December 2021
Accepted 3 December 2021

DOI:https://doi.org/10.1103/PhysRevB.104.245137

Physics Subject Headings (PhySH)

Landau levels Quantum Hall effect

Graphene

Cyclotron resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rai Moriya ^1,*, Sabin Park¹, Satoru Masubuchi¹, Kenji Watanabe ², Takashi Taniguchi ^3,1, and Tomoki Machida ^1,†

¹Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505, Japan
²Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
³International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

^*moriyar@iis.u-tokyo.ac.jp
^†tmachida@iis.u-tokyo.ac.jp

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Vol. 104, Iss. 24 — 15 December 2021

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Images

Figure 1
(a) Schematic illustration of device structure. (b) Two-terminal conductance $G$ as a function of carrier density $n$ . (c) Photovoltage $V_{ph}$ as a function of $n$ . (d) $V_{ph}$ as a function of magnetic field $B$ at fixed $n (n = 5.94 \times 10^{10} c m^{- 2})$ . (e) $V_{ph}$ as a function of $B$ and $n$ . (f) Energies of LLs with LL indices in the range of $N = - 6$ to $+ 6$ ; cyclotron resonance transitions $T_{3}$ to $T_{6}$ are indicated by arrows. All the experimental data shown in this figure were acquired at a temperature of 2.0 K.
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Figure 2
(a), (b) Detailed mapping of $V_{ph}$ as a function of magnetic field $B$ and carrier density $n$ at $T = 2.0 K$ under irradiation at a wavelength $λ$ of $10.675 μ m$ for (a) $T_{4}$ and $T_{5}$ transitions, and (b) $T_{3}$ transition. (c) $V_{ph}$ vs $B$ traces at selected $λ$ (or $E_{ph}$ ). The red lines correspond to the case where Fermi energy $E_{F}$ being located close to the Dirac point, while black lines correspond to $E_{F}$ being away from the DP. Traces are offset for clarity and the baselines (corresponding to $V_{ph} = 0$ ) for each trace are indicated by the horizontal dashed lines. (d) Relationship between irradiation energy for the $T_{3}$ transition and the magnetic field value of the cyclotron resonance. Solid and dashed lines indicate calculated results for the energies of each transition based on Eq. (1). In the figure, $υ_{0}$ is defined as $1 \times 10^{6} m / s$ . (e) Schematic energy level diagram illustrating the $E_{F}$ dependence of cyclotron resonance transitions.
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Figure 3
(a), (c) Image plot of $V_{ph}$ as a function of magnetic field $B$ and quantum Hall filling factor $v$ at $T = 2.0 K$ under irradiation at a wavelength $λ$ of $10.675 μ m$ for the (a) $T_{4}$ and $T_{5}$ transitions and (c) $T_{3}$ transition. (b), (d) Positions of CR transition estimated from the theoretical calculation using a many-body correction for the (b) $T_{4}$ and $T_{5}$ transitions, and (d) $T_{3}$ transition plotted vs the number of filled Landau levels $N_{f}$ . The theoretical calculation results are extracted from Ref. [22].
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Figure 4
(a), (c) Detailed mapping of $V_{ph}$ as a function of magnetic field $B$ and carrier density $n$ at $T = 2.0 K$ under irradiation at a wavelength $λ$ of $10.675 μ m$ for the (a) $T_{4}$ and $T_{5}$ transitions and (c) $T_{3}$ transition. (b), (d) $V_{ph}$ vs $B$ traces at selected $n$ values for (b) the $T_{4}$ and $T_{5}$ transitions and (d) the $T_{3}$ transition. The corresponding $n$ values are indicated by circles, squares, triangles, and diamonds in panels (a) and (c). The traces are offset for clarity, and those indicated by blue and green dashed circles are multiplied by a factor of 0.5 and 2.0, respectively.
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Figure 5
(a), (c) Image plot of $V_{ph}$ as a function of magnetic field $B$ and quantum Hall filling factor $ν$ at $T = 2.0 K$ under irradiation at a wavelength $λ$ of $10.675 μ m$ for the (a) $T_{4}$ and $T_{5}$ transitions and (c) $T_{3}$ transition. (b), (d) Cross section of panels (a), (c) at constant $B$ . The corresponding $B$ values are indicated by arrows in panels (a), (c). The traces shown by thick lines are data at the cyclotron resonance and thin lines are the data corresponding to the background nonresonant thermoelectric signal.
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