Landau Velocity for Collective Quantum Hall Breakdown in Bilayer Graphene

Breakdown of the quantum Hall effect (QHE) is commonly associated with an electric field approaching the inter-Landau-level (LL) Zener field, the ratio of the Landau gap and the cyclotron radius. Eluded in semiconducting heterostructures, in spite of extensive investigation, the intrinsic Zener limit is reported here using high-mobility bilayer graphene and high-frequency current noise. We show that collective excitations arising from electron-electron interactions are essential. Beyond a noiseless ballistic QHE regime a large super-Poissonian shot noise signals the breakdown via inter-LL scattering. The breakdown is ultimately limited by collective excitations in a regime where phonon and impurity scattering are quenched. The breakdown mechanism can be described by a Landau critical velocity as it bears strong similarities with the roton mechanism of superfluids. In addition, we show that breakdown is a precursor of an electric-field induced QHE-metal transition.

Figure 1

High electric-field magnetostransport and 5 GHz shot noise in bilayer graphene of dimensions $L\times W=4\times 3\mu \mathrm{m}$ at $T=4\mathrm{K}$. (a)–(h) High-bias transport current $I_{\mathrm{ds}}(V_{\mathrm{ds}})$ and shot-noise current $S_I/2e(V_{\mathrm{ds}})$ in the hole doping QHE regime $|n|=0–4.3\times {10}^{12}{\mathrm{cm}}^{-2}$ corresponding to $V_g=0\to -6\mathrm{V}$. In quantizing fields ($B\gtrsim 2\mathrm{T}$) shot noise is suppressed at low bias where $G_{\mathrm{ds}}=|n|e/B$, rises up abruptly at a breakdown voltage (dashed black lines), peaks to a large value eventually reaching the full shot-noise limit $S_I\approx 2e{I}_{\mathrm{ds}}$ ($B=5\mathrm{T}$), and vanishes as conductance saturates to a field-independent value $G_{\text{sat}}\simeq 0.6\mathrm{mS}$.

Figure 2

Scaling behavior of current and noise in the QHE regime. (a) Bias dependence of the drift velocity $v_D=J_{\mathrm{ds}}/|n|e$ deduced from current data in Fig. 1. The $B=2\to 7\mathrm{T}$ data of different densities bunch in the QHE regime and stray above the breakdown field. The slopes, represented as a Hall mobility in the inset, obey the expected law $\mu =1/B$ (blue dashed line in ${\mathrm{m}}^2/\mathrm{Vs}$). Black squares correspond to a typical breakdown voltage deduced from the onset of noise [dashed lines in Figs. 1]. They can be fitted to the Zener tunneling limit $v_c={(E_c\hslash e/N{m}^{*2})}^{1/3}$ (black dashed line) by taking a constant landau level $N=5$ corresponding to the median experimental value [dashed yellow line in Figs. 1]. (b) Bias dependence of $|n|=2.15\times {10}^{12}{\mathrm{cm}}^{-2}$ shot-noise data [from Figs. 1] in increasing magnetic fields $B=0\to 7\mathrm{T}$. Ballistic transport is characterized by a suppression of noise below a critical voltage ranging from $V_c\simeq 0.6$ (at $B=2$) to $V_c\simeq 4\mathrm{V}$ (at $B=7\mathrm{T}$). Current noise is scaled by the constant saturation conductance $G_{\text{sat}}=0.6\mathrm{mS}$ to be expressed as a noise temperature. (c) The above noise data obey a quantum Hall scaling at breakdown where Hall voltage and noise temperature are scaled to the maximum Zener field $E_c=\hslash {\omega }_c/e{l}_B$ and cyclotron energy $\hslash {\omega }_c$, respectively.

Figure 3

Super-Poissonian inter-Landau level tunneling and a sketch of the magnetoexciton instability scenario of QHE breakdown. (a) Shot noise (solid lines, left axis) and backscattering current $I_{\mathrm{bs}}=G_H{V}_{\mathrm{ds}}-I_{\mathrm{ds}}$ (dashed lines, right axis) at $B=3\mathrm{T}$ for $V_g=-2\to -5\mathrm{V}$ (blue, green, orange, red) obey a similar bias dependence at breakdown yielding a doping independent Fano factor $\mathcal{F}=S_I/2e{I}_{\mathrm{bs}}\simeq 7.5$. Inset $\mathcal{F}(B)\simeq (2.7T^{-1})B\approx \hslash {\omega }_c/{ϵ}_c$ obeys a linear law with ${ϵ}_c=1.4\mathrm{meV}$. (b) ME spectrum according to Eq. (1), at rest ($v_D=0$), for a subcritical ($v_D=0.5\times {10}^5\mathrm{m}/\mathrm{s}$) and the critical ($v_D=1\times {10}^5\mathrm{m}/\mathrm{s}$) drift velocities. For clarity we have chosen a large $r_s\simeq 4$, $B=4\mathrm{T}$ and $|n|=2\times {10}^{12}{\mathrm{cm}}^{12}$ ($N=5$), corresponding to the $V_g=-3\mathrm{V}$ median working point in (Fig. SM1 [33]). The line thickness illustrates the spectral weight which, according to Ref. [48], vanishes at $q\sim k_F$. The Landau critical velocity $v_c=1\times {10}^5\mathrm{m}/\mathrm{s}$ is estimated by the vanishing of the ME gap at $q/k_F\sim 1$. It agrees with the noise determination of breakdown, $v_{\mathrm{bd}}=1.1\times {10}^5\mathrm{m}/\mathrm{s}$ [$B=4\mathrm{T}$ square in Fig. 2].