Puddle-Induced Resistance Oscillations in the Breakdown of the Graphene Quantum Hall Effect

We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The $\nu =2$ quantized plateau appears from fields $B\simeq 5\mathrm{T}$ and persists up to $B\simeq 80\mathrm{T}$. At high current density, in the breakdown regime, the longitudinal resistance oscillates with a $1/B$ periodicity and an anomalous phase, which we relate to the presence of additional electron reservoirs. The high field experimental data suggest that these reservoirs induce a continuous increase of the carrier density up to the highest available magnetic field, thus enlarging the quantum plateaus. These in-plane inhomogeneities, in the form of high carrier density graphene pockets, modulate the quantum Hall effect breakdown and decrease the breakdown current.

Figure 1

(a) Longitudinal and Hall magnetoresistances of sample S1 measured at $T=4\mathrm{K}$ up to $B=80\mathrm{T}$. The inset is a sketch of the Hall bar covered by the resists.

Figure 2

(a) Longitudinal (solid lines) and transverse (dashed lines) symmetrized resistances for sample S1, at $T=1.6\mathrm{K}$ up to $T=120\mathrm{K}$. (b) solid lines, open symbols: $T{\sigma }_{xx}$ vs $T^{-1/2}$ from $B=20\mathrm{T}$ up to $B=60\mathrm{T}$ with a step of 10 T. Dashed lines: linear fits with the soft Coulomb gap VRH model. The data of Ref. [14] at $B=19\mathrm{T}$ are reported for comparison (red dashed line). (c) Open symbols: localization length $\xi$ extracted from the VRH fit. The blue and red lines are guides for the eye, following the magnetic length $l_B$ and the prediction $\xi \sim 1/{\nu }^{2.3}$, respectively. (d) Parameters $T_0$ and ${\sigma }_0$ extracted from the fit.

Figure 3

(a) Longitudinal resistance $R_{xx}$ for currents higher than the breakdown current $I_c\simeq 10\mu \mathrm{A}$. $1/B$-periodic oscillations are visible. (b) Landau plot for the minima and maxima of these oscillations. The period corresponds to a carrier concentration $n_{\mathrm{HD}}\approx 1.15\times 10^{13}{\mathrm{cm}}^{-2}$. The $R_{xx}$ maxima plotted as a function of their index $N$ go to $N=1/2$ when $B_N\to \infty$, which is usually a signature of a zero Berry phase. (c) The observed oscillation damping by the temperature does not agree with the usual Shubnikov–de Haas theory. The oscillation period may change from one cooldown (solid line) to another (dashed lines).

Figure 4

(a) Charge density in LD and HD regions as a function of the magnetic field. The proportion of highly doped regions $\alpha$ is fixed to 30% of the total surface (thick blue and red lines: $n_{\mathrm{HD}}$ and $n_{\mathrm{LD}}$, respectively), $A=0.4\mathrm{eV}$ and $\mathrm{\Gamma }=15\mathrm{meV}$. The thin dashed lines represent the LL carrier density in the LD region. The inset is a sketch of the inhomogeneous Hall bar embedding several highly doped regions, a deflected current line is sketched by open arrows. (b) Chemical potential $\mu$ as a function of $B$ for $\alpha =30\%$ (red line) and $\alpha =0$ (black line). The thin blue dashed lines represent the positions of the Landau Levels in the HD puddles. (c) Longitudinal resistance $R_{xx}$ as a function of $B$, at various currents, calculated within the model described in the text. The curves from the bottom to the top correspond to currents of 100, 250, and $400\mu \mathrm{A}$, respectively. The inset is a Landau plot (blue circles: maxima indexed with integers; red circles: minima indexed with half-integers).