Electromechanical oscillations in bilayer graphene

Abstract

Nanoelectromechanical systems constitute a class of devices lying at the interface between fundamental research and technological applications. Realizing nanoelectromechanical devices based on novel materials such as graphene allows studying their mechanical and electromechanical characteristics at the nanoscale and addressing fundamental questions such as electron-phonon interaction and bandgap engineering. In this work, we realize electromechanical devices using single and bilayer graphene and probe the interplay between their mechanical and electrical properties. We show that the deflection of monolayer graphene nanoribbons results in a linear increase in their electrical resistance. Surprisingly, we observe oscillations in the electromechanical response of bilayer graphene. The proposed theoretical model suggests that these oscillations arise from quantum mechanical interference in the transition region induced by sliding of individual graphene layers with respect to each other. Our work shows that bilayer graphene conceals unexpectedly rich and novel physics with promising potential in applications based on nanoelectromechanical systems.

Figure 1. Device and experimental set-up.

(a) Scanning electron microscope (SEM) image of the device. A 60-nm-wide graphene nanoribbon is suspended above a substrate and contacted by electrodes. Scale bar, 500-nm long. (b) Schematic drawing of the experimental set-up and geometry. The suspended graphene ribbon is deformed in the centre using an AFM probe attached to a piezo scanner. The vertical displacement of the scanner Z_piezo results in the deflection of the cantilever D_cantilever and nanoribbon deflection D_GNR. The device is biased by an a.c. voltage with a root mean squared amplitude of 4 mV. The resulting drain current I_d is monitored using a lock-in amplifier.

Figure 2. Electromechanical response of monolayer graphene.

(a) Electromechanical experiment shows simultaneous measurements of the current (upper curve) and the cantilever's deflection (lower part) as a function of the piezo scanner extension. The electromechanical response is reproducible for both extension (red) and retraction (black) curves. The measurement is performed for an a.c. voltage with a root mean squared amplitude of 4 mV and with the grounded back-gate. Further analysis (see equations in the main text) allows extraction of b, relative variation of the resistance as a function of nanoribbon deflection. All monolayer graphene devices show a response with varying slopes depending on the GNR width. In most cases, the resistance increases under strain, however, we observed one case of decreasing resistance under strain (blue curve, device #5).

Figure 3. Electromechanical response of bilayer graphene.

(a) Simultaneous measurements of the current (upper curve) and the cantilever's deflection (lower part) as a function of the piezo scanner extension show oscillations in the electrical response of bilayer GNRs. Oscillations are reproducible and slightly out of phase for both extension and retraction cycles. The measurement is performed for an a.c. voltage with a root mean squared amplitude of 4 mV and with the back-gate grounded. (b) Relative resistance of a bilayer graphene nanoribbon as a function of nanoribbon deflection for several successive cycles of mechanical deformation. Curves for deformations #2, #3 and #4 are offset for clarity. Oscillations in resistance with an amplitude of ∼2% are superposed on a slowly increasing background. (c) Electromechanical response of an additional bilayer GNR device. Curves for deformations #2, #3 and #4 are offset for clarity.

Figure 4. Theoretical simulations of charge-carrier transport.

(a) Schematic illustration of the lateral shift of individual graphene layers with respect to each other subjected to the AFM tip action. The AB-stacked bilayer graphene domains are separated by a region of decoupled monolayers of different effective width. (b) Calculated charge-carrier transmission probability across a region of decoupled graphene monolayers as a function of E and k_|| for various charge-carrier path differences ΔW, given in units of lattice constant of graphene a. The dashed lines show the contours of the massive Dirac fermion band of bilayer graphene and the massless Dirac cone of monolayer graphene, respectively. (c) Relative electrical resistance ΔR/R₀ of the simulated nanoelectromechanical device based on a bilayer GNR with a width of 50 nm under V_s=4 mV with a contact resistance R_c=41 kΩ as a function of charge-carrier path difference ΔW given in units of lattice constant of graphene a. The line is a guide to the eye.