Momentum-resolved view of highly tunable many-body effects in a graphene/hBN field-effect device

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Momentum-resolved view of highly tunable many-body effects in a graphene/hBN field-effect device

Ryan Muzzio, Alfred J. H. Jones, Davide Curcio, Deepnarayan Biswas, Jill A. Miwa, Philip Hofmann, Kenji Watanabe, Takashi Taniguchi, Simranjeet Singh, Chris Jozwiak, Eli Rotenberg, Aaron Bostwick, Roland J. Koch, Søren Ulstrup, and Jyoti Katoch

Phys. Rev. B 101, 201409(R) – Published 26 May 2020

Abstract

Integrating the carrier tunability of a functional two-dimensional material electronic device with a direct probe of energy- and momentum-resolved electronic excitations is essential to gain insights on how many-body interactions are influenced during device operation. Here, we use microfocused angle-resolved photoemission in order to analyze many-body interactions in back-gated graphene supported on hexagonal boron nitride. By extracting the doping-dependent quasiparticle dispersion and self-energy, we observe how these interactions renormalize the Dirac cone and impact the electron mobility of our device. Our results are not only limited to a finite energy range around the Fermi level, as in electron transport measurements, but describe interactions on a much wider energy scale, extending beyond the regime of hot carrier excitations.

Received 16 February 2020
Accepted 8 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.201409

Physics Subject Headings (PhySH)

Carrier dynamics Electrical conductivity Fermi surface

Devices Graphene

Angle-resolved photoemission spectroscopy Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ryan Muzzio^1,*, Alfred J. H. Jones ^2,*, Davide Curcio ², Deepnarayan Biswas², Jill A. Miwa², Philip Hofmann², Kenji Watanabe³, Takashi Taniguchi³, Simranjeet Singh¹, Chris Jozwiak⁴, Eli Rotenberg⁴, Aaron Bostwick⁴, Roland J. Koch⁴, Søren Ulstrup ^2,†, and Jyoti Katoch^1,‡

¹Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
²Department of Physics and Astronomy, Aarhus University, 8000 Aarhus C, Denmark
³National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
⁴Advanced Light Source, E. O. Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

^*These authors contributed equally to this work.
^†Corresponding author: ulstrup@phys.au.dk
^‡Corresponding author: jkatoch@andrew.cmu.edu

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Vol. 101, Iss. 20 — 15 May 2020

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Images

Figure 1
(a) Optical micrograph of device. (b) Sketch of the experimental setup integrating microscale photoemission with source ( $S$ ), drain ( $D$ ), and gate ( $G$ ) contacts fabricated on a graphene/hBN/graphite stack placed on a ${SiO}_{2}$ /Si wafer. (c) Map of $(x, y)$ -dependent photoemission intensity corresponding to the region shown in (a). The graphene flake is demarcated by dashed lines and an arrow in (a) and (c). (d) Dirac dispersion collected from the graphene flake in the spot marked by a yellow circle in (c). The purple arrows point to faint minibands originating from the graphene/hBN interface. The map in (c) is composed from the integrated intensity enclosed between the dashed lines in (d).
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Figure 2
(a) Snapshots of Dirac dispersion at the given gate voltages. (b) Dirac cone at the highest achieved gate voltage for $n$ -type doping. The branches below (above) the Dirac crossing are labeled $v$ ( $c$ ). The dashed curves represent linearly extrapolated bands determined from momentum distribution curve (MDC) fits to the $v$ branches (blue dashed bands) and $c$ branches (red dashed bands) [24]. The $v$ ( $c$ ) branches cross at $E_{D v}$ ( $E_{D c}$ ). (c)–(e) Constant energy contours at $E_{F}$ for (c) $p$ -type doping, (d) near charge neutrality, and (e) $n$ -type doping. The purple dashed circle outlines the circular Fermi surface with radius $k_{F}$ indicated by a purple arrow. (f) MDCs extracted at $E_{F}$ (thick colored curves) with Lorentzian fits (black thin curves). (g) Energy distribution curves (EDCs) at $\bar{K}_{G}$ with tick marks indicating simple estimates of the $v$ crossing $E_{v}$ (blue tick) and the $c$ crossing $E_{c}$ (red tick). Each curve in (f) and (g) corresponds to a different value of $V_{G}$ as noted on the right of panel (g). (h),(i) Gate voltage dependence of (h) $k_{F}$ determined from the MDC peak positions in (f), and (i) the EDC peak positions in (g) along with their separation ( $E_{v} - E_{c}$ ).
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Figure 3
(a) Carrier density determined as $k_{F}^{2} / π$ using the data in Fig. 2. The curve is a fit to the expected linear dependence on $V_{G}$ [1]. (b) Resistance $R$ as a function of gate voltage obtained before exposure to the synchrotron beam [24]. (c) Sheet conductivity $σ_{2 D}$ as a function of carrier density based on the fitted dependence in (a). (d) Binding energy positions of $E_{D v}$ and $E_{D c}$ (see definitions of these energies in the inset) determined by extrapolating the linear dispersion from below (blue squares) and from above (red squares) the Dirac point region, respectively. The curves are fits to $\sqrt{n}$ -dependent functions. (e) Band velocities $v_{F}$ and $v^{*}$ measured at the Fermi level (orange circles) and 300 meV below $E_{D v}$ (purple circles), respectively. The diagram illustrates the extraction of $v_{F}$ and $v^{*}$ from the slopes of the dispersion. The purple line is a fit to a linear dependence to guide the eye, and the orange curve is the analytic dependence of $v_{F}$ on doping for an effective Coulomb coupling constant given by $α = 0.5$ . The noninteracting velocity $v$ is indicated by a horizontal dashed line. (f) Imaginary part of the self-energy determined from the linewidth of Lorentzian fits to MDCs at the Fermi level. The curve is a fit to a $\sqrt{n}$ dependence, which follows from scattering processes that scale with the size of the Fermi surface $k_{F}$ as illustrated in the inset.
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