Rippling ultrafast dynamics of suspended 2D monolayers, graphene

Abstract

Here, using ultrafast electron crystallography (UEC), we report the observation of rippling dynamics in suspended monolayer graphene, the prototypical and most-studied 2D material. The high scattering cross-section for electron/matter interaction, the atomicscale spatial resolution, and the ultrafast temporal resolution of UEC represent the key elements that make this technique a unique tool for the dynamic investigation of 2D materials, and nanostructures in general. We find that, at early time after the ultrafast optical excitation, graphene undergoes a lattice expansion on a time scale of 5 ps, which is due to the excitation of short-wavelength in-plane acoustic phonon modes that stretch the graphene plane. On a longer time scale, a slower thermal contraction with a time constant of 50 ps is observed and associated with the excitation of out-of-plane phonon modes, which drive the lattice toward thermal equilibrium with the well-known negative thermal expansion coefficient of graphene. From our results and first-principles lattice dynamics and out-of-equilibrium relaxation calculations, we quantitatively elucidate the deformation dynamics of the graphene unit cell.rippling dynamics | monolayer graphene | 2D materials | ultrafast electron diffraction | first-principles lattice dynamics F or a long time it was believed that 2D materials could not exist in nature due to a crumpling effect induced by long-wavelength thermal fluctuations (1-3). Recently, however, graphene was isolated from graphite by Novoselov et al. using the simple Scotch tape idea (4), and since then more and more 2D materials have been produced from bulk layered crystals (5, 6). In a strict definition, so far no isolated 2D layers have been found to be perfectly flat due to the presence of ripples, a microscopic roughening of the 2D plane, as observed in almost all cases (7,8), apart from those in perfect contact with a substrate (9). Accordingly, rippling can be considered as an intrinsic feature of 2D materials, and is widely accepted to be at the origin of their structural stability (7,10,11).Graphene, as the first 2D material, has attracted enormous interest due to extraordinary properties originating from the quasi-relativistic character of its electronic band dispersion (12). Most impressively, graphene's excellent transport properties, such as ultrahigh carrier mobility and electrical conductivity, have found a wide range of applications in new generations of nanoelectronic devices (13,14). Considering that ripples can strongly affect the transport properties of graphene by inducing effective magnetic fields (15-17) and changing local potentials (18,19), one of the remaining open questions is whether it is possible to modulate the rippling such that active control of the transport properties can be achieved. To address this issue, the main challenge lies in the ability to modulate ripples in a controlled manner at the mesoscopic and microscopic length scales. Bao et al. (20) have introduced a strain-engineering method to create period...

Stacking transition in rhombohedral graphite

“…4j and k. Here, no clear transition from ABC to ABA was observed, although there were some alternations in the ABA area (dark fringes in the bottom part in Fig. 4k), which can also be an effect of enhanced rippling in graphene after photo-excitation [28].…”

Anisotropic structural dynamics of monolayer crystals revealed by femtosecond surface X-ray scattering

“…2C). The time constant of τ 1 = 2.9 ± 1.2 ps shows characteristic time of the in-plane lattice expansion, as a result of an in-plane acoustic wave propagation 22,23 . Comparing with the freestanding multilayer samples 18,19 , the lack of oscillatory Bragg peak shift suggests an overdamped mode that may result from the interaction with the substrate.…”

“…(right) Integrated intensity values for the ground state {10l} CTR, obtained by integration at different out-of-plane momentum transfer values q z . used to characterize in-plane structural dynamics of monolayer 2D materials 22,23 , while the out-of-plane structural dynamics of a monolayer crystal was only inferred 23 . Comparing with ultrafast electron diffraction, ultrafast x-ray diffraction has been an indispensable tool for studying structural dynamics in thin films, providing evidence on non-thermal structural response in transition metal dichacogenides 24 and electron-phonon coupling in superconducting FeSe 14 .…”

Ultrafast rotational motions of supported nanoclusters probed by electron diffraction

“…22,23 The timescale for generation of flexural ZA phonons (out of graphene plane atomic vibrations) and dynamic rippling is in the order of 50 ps. 24 Detailed theoretical considerations by Panizon et al 2 have shown that transfer of momentum from graphene to adsorbed Au NCs is carried out by flexural ZA phonons or by and the (220) peaks (red and blue data-points, respectively) and biexponential fittings (solid lines). The two data-sets presented in this figure disentangle the two processes that affect peak decay dynamics, namely, lattice heating (a) and disorientation of NCs (b).…”