Carrier Drift Velocity and Edge Magnetoplasmons in Graphene

We investigate electron dynamics at the graphene edge by studying the propagation of collective edge magnetoplasmon excitations. By timing the travel of narrow wave packets on picosecond time scales around exfoliated samples, we find chiral propagation with low attenuation at a velocity that is quantized on Hall plateaus. We extract the carrier drift contribution from the edge magnetoplasmon propagation and find it to be slightly less than the Fermi velocity, as expected for an abrupt edge. We also extract the characteristic length for Coulomb interaction at the edge and find it to be smaller than that for soft depletion-edge systems.

Figure 1

(a) Optical photograph of a graphene sample with edge coupling electrodes terminating the coplanar wave guides. (b) Measurement configuration: An EMP wave packet excited by a 7 or 11 ps rise time 100 mV step function propagates along the edge. (c) Demodulated responses, offset for clarity, at $B=\pm 18\mathrm{T}$ (filling factor $\nu =2$) constructed by subtraction of waveforms at a $\pm 15\mathrm{V}$ side gate potential for an 11 ps excitation. The arrival time difference arises from unequal left and right path lengths for oppositely directed magnetic fields. The overlay in red (thin solid line) is best fit to the weighted sum of the first (blue dotted line) and second (blue dashed line) derivatives of a Fermi function (see the text). The blue dots are at the fitted arrival time: 21.4 ps for $+18\mathrm{T}$ and 11 ps for $-18\mathrm{T}$. (d) Direct measurement of the 7 ps rise time excitation pulse broadened to 13 ps by the receiver amplifier.

Figure 2

(a) 3D color (grayscale) plot of the modulated signal amplitude in the propagation time and magnetic field plane. (b) Five signals chosen at filling factors $\nu =2$, 6, and 10, offset for clarity. From top to bottom: 18, 6, 3.6, 0, $-3.6$, $-6$, and $-18\mathrm{T}$. These data correspond to 11 ps excitation and 5 ps sampling resolution.

Figure 3

(a) Propagation times between emitter and receiver structures as a function of the perpendicular magnetic field for opposing orientations. The determination of zero time is described in the text. Filling factors $\nu =10$, 6, and 2 are at 3.6, 6, and 18 T, respectively. Black squares (red circles) correspond to the positive (negative) sign of the magnetic field. These data correspond to 7 ps excitation and 2 ps sampling resolution.