Fig. 2: Evidence for dynamically-enhanced strain in graphene.

All measurements are performed on device 1 at V_dc = −8 V. a Calibrated RMS mechanical amplitude at the drive frequency Ω/2π (z_rms) recorded as the frequency is swept downwards, for V_ac increasing from 0 to 150 mV. The red dashed line is the backbone curve evidencing non-linear resonance frequency softening. The red arrow indicates the jump-down frequency at V_ac = 150 mV. The grey dashed line denotes the onset of non-linearity. b Raman spectra measured under V_ac = 0 mV (open symbols and fit) and 150 mV (filled symbols and fit, vertically flipped for clarity). c, d G-mode and 2D-mode frequency shifts Δω_G,2D and full-width at half maximum variations (ΔΓ_G,2D), relative to the values at V_ac = 0 mV, as a function of V_ac. Inset in c: correlation between Δω_2D and Δω_G. The symbol colour encodes the increase of V_ac as in a. The straight black line with a slope of 2.2 is a guide to the eye for strain-induced phonon softening. e Normalised integrated intensity of G-mode and 2D-mode features as a function of V_ac. The inset illustrates the equilibrium position shift (Δξ_eq between the two red circles) in the non-linear regime, with U(ξ) the potential energy. f Time-averaged dynamical strain ε_d extracted from the softening of G-mode and 2D-mode features (open red and filled blue triangles, respectively) as a function of the corresponding \({z}_{{\rm{rms}}}^{0}\). The right axis (grey triangles) shows the relative non-linear mechanical resonance frequency shift \(\delta =\left|{\widetilde{\Omega }}_{0}-{\Omega }_{0}\right|/{\Omega }_{0}\), where \({\widetilde{\Omega }}_{0}\) is the jump-down frequency in a. The grey dashed line is a parabolic fit (Supplementary Note 6). Error bars in c, d, f are extracted from the fits of Raman spectra. Only one error bar is included in each plot for visibility.