Boundary Scattering in Ballistic Graphene

We report magnetotransport measurements in ballistic graphene mesoscopic wires where the charge carrier mean free path is comparable to the wire width $W$. Magnetoresistance curves show characteristic peak structures where the peak field scales with the ratio of cyclotron radius $R_{\mathrm{c}}$ and wire width $W$ as $W/R_{\mathrm{c}}=0.9\pm 0.1$, due to diffusive boundary scattering. The obtained proportionality constant between $R_{\mathrm{c}}$ and $W$ differs from that of a classical semiconductor two-dimensional electron system in which $W/R_{\mathrm{c}}=0.55$.

Figure 1

(a) Conductivity $\sigma$ as a function of back-gate bias voltage $V_{\mathrm{g}}$ measured at $T=4$, 16, 60, 120, 180, 240, and 300 K (top to bottom). For clarity, each curve was offset by 2 mS. Dashed curves are the calculated conductivity based on the Boltzmann equation discussed in the main text. The inset shows the atomic force microscopy image of the GBN sample studied in this work. The white region indicates the region of Pd metal electrodes. The white dashed lines indicate the outline of the graphene flake. (b) Short-range mean free path $l_{\mathrm{short}}$ and (c) long-range mean free path $l_{\mathrm{long}}$ as a function of gate bias voltage $V_{\mathrm{g}}$, for $T=4$, 16, 60, 120, 180, 240, and 300 K (top to bottom).

Figure 2

(a) Two-terminal resistance $R$ as a function of $B$ measured at $T=4\mathrm{K}$ for the device with channel length $L=2.3\mu \mathrm{m}$ with applied gate bias voltage $V_{\mathrm{g}}=-45\mathrm{V}$. (inset) Schematic of electrotrajectories in mesoscopic wire for (solid curve) $R_{\mathrm{c}}>W$ and (dotted curve) $R_{\mathrm{c}}<W$. (b) $R$ as a function of $B$ measured at $T=4\mathrm{K}$ for (top curve) $L=1.4\mu \mathrm{m}$ and (bottom curve) $L=0.6\mu \mathrm{m}$. (c) Amplitude of magnetoresistance signal $\Delta R$ vs channel length $L$.

Figure 3

(a) $R$ as a function of $B$ measured at $T=(\mathrm{a})$ 4 and (b) 1.6 K for the device with $(L,W)=(\mathrm{a})$ ($2.3\mu \mathrm{m}$, $1.0\mu \mathrm{m}$) and (b) ($3.1\mu \mathrm{m}$, $1.5\mu \mathrm{m}$) with applied gate bias voltage $V_{\mathrm{g}}=-50,-48,\cdots ,-28\mathrm{V}$ (bottom to top). Each curve was offset vertically so that the peak positions were separated by $0.01\mathrm{k}\Omega$. The blue dotted curves and colored area indicate the expected peak positions for $\alpha =0.55$ and $0.9\pm 0.1$, respectively.

Figure 4

(a) $\Delta R$ (top panel), $l_{\mathrm{long}}$ (blue curve in bottom panel), and $l_{\mathrm{short}}$ (black curve in bottom panel) as a function of $T$ measured in the device with channel length $L=2.3\mu \mathrm{m}$ at $V_{\mathrm{g}}=-35\mathrm{V}$. (b) $\Delta R$ (top panel), $l_{\mathrm{long}}$ (blue curve in bottom panel), and $l_{\mathrm{short}}$ (black curve in bottom panel) as a function of $V_{\mathrm{g}}$ at $T=4\mathrm{K}$. The dotted line is the channel width of the GBN mesoscopic wire.