The discovery of piezoelectricity in two-dimensional (2D) nanomaterials represents a milestone towards embedding the low-dimensional materials into future technologies. This paper reviews recent progress in the characterization, properties evaluation and applications of piezoelectricity of 2D piezoelectric nanomaterials (PNs). To begin, an introduction to the existing 2D PNs which exhibit a wide range of atomic structures and configurations is presented. The nanoscale measurements and the associated experimental techniques as well as the atomic simulations of the piezoelectric properties of 2D PNs are then summarised. Some of the pertinent parameters which govern the piezoelectric properties of 2D PNs are discussed. Furthermore, our paper concludes with some potential applications including piezotronics, piezophototronics and energy harvesting of 2D PNs, which can open the doors to the innovative design of next-generation nanoelectronics and nanodevices. Finally, perspectives and challenges for the future development of 2D PNs are pointed out.

https://iopscience.iop.org/article/10.1088/1361-6641/aa5cfb/pdf

Piezoelectricity of 2D nanomaterials: characterization, properties, and applications

We propose an analytical framework to study the propagation of transition waves in one-dimensional free-standing lattices comprising concentrated masses and bistable springs. Starting from the discrete model, we derive the partial differential equation that describes the non-linear dynamic response of the system and obtain its exact closed-form solution. Such solution enables us to uncover the effect of the system’s parameters on the characteristics of the supported transition waves as well as to characterize the rarefaction front that precedes the pulse. As such, this work provides new opportunities to elucidate how transition waves propagate in systems in which the phase transition results in macroscopic volumetric changes.

Nonlinear transition waves in free-standing bistable chains

Phase transformations in substrate-free dissipative multistable metamaterials

The dark and bright solitons in different systems are already known. If the intrinsic field is only considered, then the modal dynamics for small oscillations could be characterized by the bound state in a limited range of frequency, revealed via associated Legendre polynomial. The pairing and interplay between the dark and bright solitons occur. The disappearance of the bound state after a critical frequency gives rise to dark solitons in the unbound states that propagate through the domains. Above the upper boundary of the bound states, the estimated frequencies of dark solitons match with those experimentally found for ‘acoustical memory’.

Bound to unbound state route and propagation of dark solitons showing acoustical memory

The presence of discrete breathers (DBs) has already been described in nonlinear photonic materials, such as ferroelectrics and metamaterials (MMs) by the Klein?Gordon (K?G) approach. Rectification of energy transport in MMs in the presence of an appropriate external field is studied via symmetry breaking leading to directed energy transport or ratchet behaviour. Based on the earlier development of the K?G equation in a MM system with a split-ring resonator for antenna applications, a theoretical model for current density is worked out by symmetry analysis and its violation to characterize the ratchet effect. The time-averaged current shows interesting results against phase shift in the ac driver. These data are further related to various parameters, such as coupling and damping in the system. For MMs, this opens a new application for rectification using ratchets.

Rectification of energy transport in nonlinear metamaterials via ratchets

In the framework of a simple model of a one-dimensional array of a ferroelectric slab of domains, the polarization with time and space is explained by the Klein-Gordon equation. A perturbation of the K-G equation makes it possible to use this continuum model through a progressive-wave nonlinear Schr\"odinger equation (NLSE). The latter gives rise to a bright soliton that moves with a certain velocity. The bright soliton controls itself so that both bright and dark solitons appear at the same time with discrete energy levels that are estimated from a hypergeometric function, but the dark soliton is not visible as it is part of the complex solution that indicates absorption of energy, i.e., the presence of an energy gap. The pulse width for switching of ferroelectrics can be estimated from the analysis of the NLSE and matches that calculated from this model.

Arghya Dey

Papers

Discrete energy levels of bright solitons in lithium niobate ferroelectrics