Magnetoconductance of the Corbino disk in graphene

Electron transport through the Corbino disk in graphene is studied in the presence of uniform magnetic fields. At the Dirac point, we observe conductance oscillations with the flux piercing the disk area ${\Phi }_d$, characterized by the period ${\Phi }_0=2\left(h/e\right)\text{ln}\left(R_{\text{o}}/R_{\text{i}}\right)$, where $R_{\text{o}}\left(R_{\text{i}}\right)$ is the outer (inner) disk radius. The oscillations magnitude increase with the radii ratio and exceed 10% of the average conductance for $R_{\text{o}}/R_{\text{i}}\ge 5$ in the case of the normal Corbino setup or for $R_{\text{o}}/R_{\text{i}}\ge 2.2$ in the case of the Andreev-Corbino setup. At a finite but weak doping, the oscillations still appear in a limited range of $\left|{\Phi }_d\right|\le {\Phi }_d^{\text{max}}$, away from which the conductance is strongly suppressed. At large dopings and weak fields we identify the crossover to a normal ballistic transport regime.

Figure 1

(Color online) The Corbino magnetometer in graphene. The current is passed through the disk-shaped area with the inner radius $R_{\text{i}}$ and the outer radius $R_{\text{o}}$ in a perpendicular magnetic field $\mathbf{B}=\left(0,0,B\right)$. The leads (yellow/light gray) are modeled as infinitely doped graphene regions. The gate electrode (not shown) is placed underneath to tune the doping in the disk area.

Figure 2

(Color online) Conductance as a function of the magnetic field and the doping for $R_{\text{o}}/R_{\text{i}}=10$. (a) Magnetoconductance at weak doping (specified for each curve by $k_0{R}_{\text{i}}={10}^{-4}–{10}^{-1}$ with $k_0=\left|E-U_0\right|/\hslash v_F$). The zero-doping magnetoconductance is also shown (red/gray line). (b) Magnetoconductance at large doping $\left(k_0{R}_{\text{i}}=0.2–0.6\right)$. (c) Conductance as a function of doping at fixed magnetic field [specified by the flux piercing the disk area ${\Phi }_d=0–4{\Phi }_0$, with ${\Phi }_0=2\left(h/e\right)\text{ln}{R}_{\text{o}}/R_{\text{i}}$].

Figure 3

(Color online) Phase diagram representing the tunneling field-suppressed and ballistic transport regimes in the field-doping parameter plane. Solid lines corresponds to $G=G_0$ for the radii ratio $R_{\text{o}}/R_{\text{i}}=10$. Dashed lines depict borders of the tunneling (${\Phi }_d<{\Phi }_d^{\text{max}}$, red/gray line) and ballistic ($2r_c>R_{\text{o}}-R_{\text{i}}$, blue/dark gray line) transport regimes. [Notice the logarithmic scale for $k_0\left(R_{\text{o}}-R_{\text{i}}\right)<1$.] Inset shows the crossover into the tunneling behavior for the first Landau level $\left(n=1\right)$ in the magnified horizontal scale $\left({\delta }_n\equiv \frac{1}{2}{k}_0^2{l}_B^2-n\right)$.