Magnetoexciton limit of quantum Hall breakdown in graphene

A. Schmitt, M. Rosticher, T. Taniguchi, K. Watanabe, J. M. Berroir, G. Ménard, C. Voisin, G. Fève, M. O. Goerbig, B. Plaçais, and E. Baudin

Phys. Rev. B 108, 085438 – Published 31 August 2023

Abstract

One of the intrinsic drift velocity limits of the quantum Hall effect is the collective magnetoexciton (ME) instability. It has been demonstrated in bilayer graphene (BLG) using noise measurements [W. Yang et al., Phys. Rev. Lett. 121, 136804 (2018)]. We reproduce this experiment in monolayer graphene (MLG), and show that the same mechanism carries a direct relativistic signature on the breakdown velocity. Based on theoretical calculations of MLG- and BLG-ME spectra, we show that Doppler-induced instabilities manifest for a ME phase velocity determined by a universal value of the ME conductivity, set by the Hall conductance.

Received 10 March 2023
Revised 13 July 2023
Accepted 1 August 2023

DOI:https://doi.org/10.1103/PhysRevB.108.085438

Physics Subject Headings (PhySH)

Integer quantum Hall effect Quantum Hall effect

Graphene

Noise measurements Random phase approximation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Schmitt ^1,*, M. Rosticher¹, T. Taniguchi², K. Watanabe ², J. M. Berroir¹, G. Ménard ¹, C. Voisin¹, G. Fève¹, M. O. Goerbig³, B. Plaçais ^1,†, and E. Baudin ^1,‡

¹Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 24 rue Lhomond, 75005 Paris, France
²Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan
³Laboratoire de Physique des Solides, CNRS UMR 8502, Univ. Paris-Sud, Université Paris-Saclay, F-91405 Orsay Cedex, France

^*aurelien.schmitt@phys.ens.fr
^†bernard.placais@phys.ens.fr
^‡emmanuel.baudin@phys.ens.fr

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Vol. 108, Iss. 8 — 15 August 2023

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Images

Figure 1
Low-bias magnetotransport and noise in high-mobility bottom-gated hBN-encapsulated graphene sample AuS2 measured at $T = 4 K$ . Sample dimensions are $L \times W \times t_{h B N} = 16 \times 10.6 \times 0.032 µ m$ . The contact resistance and mobility are $R_{c} = 36 Ohms$ and $μ = 32 m^{2} / Vs$ . (a) sketch of the measuring setup. (b) Low-bias ( $V = 3 mV$ ) conductance quantization steps in units of $e^{2} / h$ , obeying the MLG quantization sequence $ν = 2 (2 N + 1)$ for the filling factor $ν$ as function of the Landau index $N$ . (c) Fan chart of the zero-bias differential conductance $\partial G_{d s} / \partial V_{g}$ showing a series of Landau levels. In (b) and (c), the feature inside the N=7 Landau level (at $G ≃ 27 e^{2} / h$ ) is a measurement artifact. (d) Typical shot-noise spectra in increasing bias at $n = 2 . 10^{12} {cm}^{- 2}, B = 0.5 T$ .
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Figure 2
MLG magnetotransport and noise scaling in sample AuS2. (a) High-bias transport current $I (V)$ at $B = 0.5 T$ for $n = 0.5 - 2 . 10^{12} {cm}^{- 2}$ deviate from quantum Hall current $I = n e V / B$ at the breakdown voltage $V_{b d} ≃ 0.6 V$ (black line). Inset shows the measured low-bias mobility $I / n e V$ (squares, in $m^{2} / Vs$ ) and the $1 / B$ Hall line. (b) Noise current $I_{N} (V) = S_{I} / 2 e$ at the same magnetic field and doping sequence, showing the onset of a large breakdown noise at the same $V_{b d}$ , above a low noise quantum Hall background $I_{N} / V ≃ 0.1 mS$ due to contact noise. (c) Voltage dependence of $I_{N} (V) = S_{I} / 2 e$ for various magnetic fields, at large doping $n = 2 . 10^{12} {cm}^{- 2}$ . Inset shows the linear dependence $V_{b d} (B)$ corresponding to $v_{b d} = 0.14 v_{F}$ (solid line), which strongly exceeds the Zener velocity (dashed line) at low field. (d) Scaling of breakdown noise with Hall velocity $E_{H} / B$ for $n = 1 - 2 . 10^{12} {cm}^{- 2}$ and $B = 0.5 - 2 T$ corresponding to $V_{b d} = 0.6 - 2.4 V$ . It is represented by the master line $I_{N} / W = γ n^{2} [E_{H} / B v_{b d} - 1]$ (dashed line), with $v_{b d} (n, B) = 1.4 10^{5} m / s$ (solid line), and $γ = 4 . 10^{- 31} {Am}^{3}$ corresponding to large breakdown noise currents $I_{N} / W \sim 40 A / m$ (at $n = 1 . 10^{12} {cm}^{- 2}$ ).
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Figure 3
Effect of gate and dielectric screening on the velocity-induced magnetoexciton (ME) instability in MLG and BLG. RPA magneto-optical conductivity spectra $σ_{M O} (q, ω)$ (in units of $N G_{K}$ ) are plotted for the AuS2 MLG-sample geometry at $B = 2 T$ for $N = 3$ in (a) and $N = 12$ in (b), and a similar BLG sample at $N = 6$ for $B = 5 T$ in (d) and $B = 1 T$ in (e). White lines correspond to the Doppler shifted drifting-electron spectrum for $v_{b d}^{M L G} = 0.14 v_{F}$ in (a) and (b) and $v_{b d}^{B L G} = ℏ / m^{*} l_{B} \sqrt{N} \propto \sqrt{B}$ in (d) and (e). They separate the high-conductivity domain $σ_{M O} ≳ 10^{- 2} N G_{K}$ from the low-conductivity one. (c) Experimental data of $v_{b d}^{M L G}$ (blue squares) and $v_{b d}^{B L G}$ (red squares from Ref. [11]), measured at the same $n = 2 . 10^{12} {cm}^{- 2}$ , support these scalings and illustrate the main difference between MLG and BLG.
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Figure 4
RPA calculations of the MLG magneto-optical conductivity $σ_{M O}$ for $N = 7$ and $B = 2 T$ , and role of gate screening and interactions. The conductivity values are represented in units of the Hall conductance $N G_{K}$ . Panel (a) shows the case of hBN encapsulation with an Au gate mimicking the AuS2 device (Eq. (2), with $d_{1} = 32 nm, d_{2} = 60 nm$ , and dielectric functions for hBN $ε_{x}$ and $ε_{z}$ described in Ref. [24]). The conductivity PHES is very similar to that of an interactionless [ $ε_{b} = 100$ for an unscreened 2D Coulomb potential $v (q) = \frac{2 π e^{2}}{ε_{b} q}$ ] ungated sample shown in panel (b). Panels (c) and (d) focus on the role of interactions in the ungated case ( $v (q) = \frac{2 π e^{2}}{ε_{b} q}$ , with $ε_{b} = 1$ [panel (c)] and $ε_{b} = 3.4$ [panel (d)]). The white line in panels (a) and (b) correspond to the measured breakdown velocity for the AuS2 device $ω = v_{b d} q$ with $v_{b d} = 0.14 v_{F}$ . The lines in panels (c) and (d) correspond to higher breakdown velocities following the discussion in the text. In all cases, the breakdown Doppler line separates the high-conductivity and low-conductivity PHES sectors at $σ_{M O} \sim 10^{- 2} N G_{K}$ .
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