Phase Space for the Breakdown of the Quantum Hall Effect in Epitaxial Graphene

We report the phase space defined by the quantum Hall effect breakdown in polymer gated epitaxial graphene on SiC $(\mathrm{SiC}/\mathrm{G})$ as a function of temperature, current, carrier density, and magnetic fields up to 30 T. At 2 K, breakdown currents ($I_c$) almost 2 orders of magnitude greater than in GaAs devices are observed. The phase boundary of the dissipationless state (${\rho }_{xx}=0$) shows a [$1-(T/T_c{)}^2$] dependence and persists up to $T_c>45\mathrm{K}$ at 29 T. With magnetic field $I_c$ was found to increase $\propto B^{3/2}$ and $T_c\propto B^2$. As the Fermi energy approaches the Dirac point, the $\nu =2$ quantized Hall plateau appears continuously from fields as low as 1 T up to at least 19 T due to a strong magnetic field dependence of the carrier density.

Figure 1

(a) $I-V_{xx}$ characteristics of sample 1 at 2.0 K, with a breakdown condition of $V_{xx}=10\mu \mathrm{V}$, giving a maximum critical current density $j_c=43\mathrm{A}/\mathrm{m}$ at 23 T. (b) Combined magnetotransport [${\rho }_{xy}$ and ${\rho }_{xx}$] data and $I-V_{xx}-B$ contour plot; the hashed region represents $V_{xx}<10\mu \mathrm{V}$, the dissipationless quantum Hall regime. Extrapolating the low field Hall coefficient to ${\rho }_{xy}=h/2e^2$ (dashed red line) gives the expected field for the peak breakdown of $\nu =2$ without a field dependent $n$. (c) Magnetic field dependence of the carrier density (thick black line), following lines of constant filling factor (thin red lines) while $E_F$ lies between Landau levels and then the charge transferred from surface donors in SiC, $n(B,N)$ (thin green curves), while the Landau levels fill, from the model in Ref. 7.

Figure 2

(a) Magnetotransport [${\rho }_{xy}$ and ${\rho }_{xx}$] and corresponding $I-V_{xx}-B$ contour plot for the $35\mu \mathrm{m}$ wide device at $T=1.5\mathrm{K}$. (b) Theoretical prediction of magnetic field dependent carrier density (thick black line) as descibed for Fig. 1 [18]. (c) $\Delta$ as a function of magnetic field and the resulting $E_F$. Also shown are the $N=0$ and 1 Landau levels (black curves) and the midpoint where $E_F=1/2E(N=1)$ corresponding to $\nu =2$.

Figure 3

(a) Normalized temperature dependence of breakdown current at several magnetic fields, fitted with Eq. (1). (b) The magnetic field dependence of $T_c$, with a best fit of $0.055B^2$. (c) The magnetic field dependence of $j_c$ for the two Hall bars with the sequence of illumination shown by arrows.