Flexoelectricity in atomic monolayers from first principles

Giant In-Plane Flexoelectricity and Radial Polarization in Janus IV-VI Monolayers and Nanotubes

Nanotubes have established a new paradigm in nanoscience because of their atomically thin geometries and intriguing properties. However, because of their typical metastability compared to their 2D and 3D counterparts, it is still fundamentally challenging to synthesize nanotubes with controlled size. New strategies have been suggested for synthesizing nanotubes with a controlled geometry. One of these is considering Janus 2D layers, which can self-roll to form a nanotube. Herein, we study 412 nanotubes (along the armchair and zigzag directions) based on 36 Janus IV-VI compounds using density functional theory (DFT) calculations. By investigating the energy-radius relationship using structural models and Bayesian predictions, the most stable nanotubes show negative strain energies and radii below 20 Å, where curvature effects can play a significant role. The band structures show that the selected nanotubes exhibit sizable band gaps and size-dependent electronic properties. More strikingly, the flexoelectricity along the in-plane directions and radial directions in these nanotubes is significantly larger than that in other nanotubes and their 2D counterparts. This work opens up an avenue of structure-property relationships of Janus IV-VI nanotubes and demonstrates giant flexoelectricity in these nanotubes for future electronic and energy applications.

Strain engineering of Zeeman and Rashba effects in transition metal dichalcogenide nanotubes and their Janus variants: anab initiostudy

We study the influence of mechanical deformations on the Zeeman and Rashba effects in transition metal dichalcogenide nanotubes and their Janus variants from first principles. In particular, we perform symmetry-adapted density functional theory simulations with spin-orbit coupling to determine the variation in the electronic band structure splittings with axial and torsional deformations. We find significant effects in molybdenum and tungsten nanotubes, for which the Zeeman splitting decreases with increase in strain, going to zero for large enough tensile/shear strains, while the Rashba splitting coefficient increases linearly with shear strain, while being zero for all tensile strains, a consequence of the inversion symmetry remaining unbroken. In addition, the Zeeman splitting is relatively unaffected by nanotube diameter, whereas the Rashba coefficient decreases with increase in diameter. Overall, mechanical deformations represent a powerful tool for spintronics in nanotubes.

In-Plane Flexoelectricity in Two-Dimensional D_{3d} Crystals

We predict a large in-plane polarization response to bending in a broad class of trigonal two-dimensional crystals. We define and compute the relevant flexoelectric coefficients from first principles as linear-response properties of the undistorted layer by using the primitive crystal cell. The ensuing response (evaluated for SnS_{2}, silicene, phosphorene, and RhI_{3} monolayers and for a hexagonal BN bilayer) is up to 1 order of magnitude larger than the out-of-plane components in the same material. We illustrate the topological implications of our findings by calculating the polarization textures that are associated with a variety of rippled and bent structures. We also determine the longitudinal electric fields induced by a flexural phonon at leading order in amplitude and momentum.

Directly measuring flexoelectric coefficients μ11 of the van der Waals materials

Flexoelectricity originates from the electromechanical coupling interaction between strain gradient and polarization, broadly applied in developing electromechanical and energy devices. However, the study of quantifying the longitudinal flexoelectric coefficient (μ₁₁) which is important for the application of atomic-scale two-dimensional (2D) materials is still in a slow-moving stage, owing to the technical challenges. Based on the free-standing suspension structure, this paper proposes a widely applicable method and a mensurable formula for determining the μ₁₁ constant of layer-dependent 2D materials with high precision. A combination of in situ micro-Raman spectroscopy and piezoresponse force microscopy (PFM) imaging was used to quantify the strain distribution and effective out-of-plane electromechanical coupling, respectively, for μ₁₁ constant calculation. The μ₁₁ constants and their physical correlation with the variable mechanical conditions of naturally bent structures have been obtained extensively for the representative mono-to-few layered MX₂ family (M = W and Mo; X = S and Se), and the result is perfectly consistent with the estimated order-of-magnitude of the μ₁₁ value (about 0.065) of monolayer MoS₂. The quantification of the flexoelectric constant in this work not only promotes the understanding of mechanical and electromechanical properties in van der Waals materials, but also paves the way for developing novel 2D nano-energy devices and mechanical transducers based on flexoelectric effects.

On the bending of rectangular atomic monolayers along different directions: anab initiostudy

We study the bending of rectangular atomic monolayers along different directions from first principles. Specifically, choosing the phosphorene, GeS, TiS₃, and As₂S₃monolayers as representative examples, we perform Kohn-Sham density functional theory calculations to determine the variation in transverse flexoelectric coefficient and bending modulus with the direction of bending. We find that while the flexoelectric coefficient is nearly isotropic, there is significant and complex anisotropy in bending modulus that also differs between the monolayers, with extremal values not necessarily occurring along the principal directions. In particular, the commonly adopted orthotropic continuum plate model with uniform thickness fails to describe the observed variations in bending modulus for GeS, TiS₃, and As₂S₃. We determine the direction-dependent effective thickness for use in such continuum models. We also show that the anisotropy in bending modulus is not associated with the rehybridization of atomic orbitals.

Synthesis and Characterization of Biotene: A New 2D Natural Oxide From Biotite

In this work, the synthesis and characterization of ultrathin metal oxide, called biotene, using liquid-phase exfoliation from naturally abundant biotite are demonstrated. The atomically thin biotene is used for energy harvesting using its flexoelectric response under multiple bending. The effective flexoelectric response increases due to the presence of surface charges, and the voltage increases up to ≈8 V, with a high mechano-sensitivity of 0.79 V N^-1 for normal force. This flexoelectric response is further validated by density functional theory (DFT) simulations. The atomically thin biotene shows an increased response in the magnetic field and thermal heating. The synthesis of two-dimensional (2D) metal-oxide biotene suggests a wealth of future 2D-oxide material for energy generation and energy harvesting applications.

Computation of Flexoelectric Coefficients of a MoS2 monolayer with a Model of Self-consistently Distributed Effective Charges and Dipoles

Flexoelectricity is an electromechanical coupling phenomenon, that can generate noticeable electric polarization in dielectric materials for nanoscale strain gradients. It is gaining an increasing attention because of its potential applications, and the fact that experimental results were initially an order of magnitude higher than initial theoretical predictions. This stimulated intense experimental and theoretical researches to investigate flexoelectric coefficients in dielectric materials such as two-dimensional materials. In this work, we concentrate on the calculation of the flexoelectric coefficients of 2D-MoS2 thanks to a model using self-consistently determined charges and dipoles on the atoms. More specifically, we study the importance of two contributions which were neglected/omitted in previous papers using this model, namely the charge term in the total polarization and the conservation of electric charge through a Lagrange multiplier. Our calculations demonstrate that the results for flexoelectric coefficient computed with this improved definition of polarization agree better with experimental measurements, provided consistent definitions for signs are used. Additionally, we show how two physical contributions with opposite signs compete to give net values of flexoelectric coefficients that can be either positive of negative depending on their relative importance, and give net values for the case of MoS2.

Torsional strain engineering of transition metal dichalcogenide nanotubes: anab initiostudy

We study the effect of torsional deformations on the electronic properties of single-walled transition metal dichalcogenide (TMD) nanotubes. In particular, considering forty-five select armchair and zigzag TMD nanotubes, we perform symmetry-adapted Kohn-Sham density functional theory calculations to determine the variation in bandgap and effective mass of charge carriers with twist. We find that metallic nanotubes remain so even after deformation, whereas semiconducting nanotubes experience a decrease in bandgap with twist-originally direct bandgaps become indirect-resulting in semiconductor to metal transitions. In addition, the effective mass of holes and electrons continuously decrease and increase with twist, respectively, resulting in n-type to p-type semiconductor transitions. We find that this behavior is likely due to rehybridization of orbitals in the metal and chalcogen atoms, rather than charge transfer between them. Overall, torsional deformations represent a powerful avenue to engineer the electronic properties of semiconducting TMD nanotubes, with applications to devices like sensors and semiconductor switches.

Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity

Soft robotics requires materials that are capable of large deformation and amenable to actuation with external stimuli such as electric fields. Energy harvesting, biomedical devices, flexible electronics, and sensors are some other applications enabled by electroactive soft materials. The phenomenon of flexoelectricity is an enticing alternative that refers to the development of electric polarization in dielectrics when subjected to strain gradients. In particular, flexoelectricity offers a direct linear coupling between a highly desirable deformation mode (flexure) and electric stimulus. Unfortunately, barring some exceptions, the flexoelectric effect is quite weak and rather substantial bending curvatures are required for an appreciable electromechanical response. Most experiments in the literature appear to confirm modest flexoelectricity in polymers although perplexingly, a singular work has measured a "giant" effect in elastomers under some specific conditions. Due to the lack of an understanding of the microscopic underpinnings of flexoelectricity in elastomers and a commensurate theory, it is not currently possible to either explain the contradictory experimental results on elastomers or pursue avenues for possible design of large flexoelectricity. In this work, we present a statistical-mechanics theory for the emergent flexoelectricity of elastomers consisting of polar monomers. The theory is shown to be valid in broad generality and leads to key insights regarding both giant flexoelectricity and material design. In particular, the theory shows that, in standard elastomer networks, combining stretching and bending is a mechanism for obtaining giant flexoelectricity, which also explains the aforementioned, surprising experimental discovery.

Torsional moduli of transition metal dichalcogenide nanotubes from first principles

We calculate the torsional moduli of single-walled transition metal dichalcogenide (TMD) nanotubes usingab initiodensity functional theory (DFT). Specifically, considering forty-five select TMD nanotubes, we perform symmetry-adapted DFT calculations to calculate the torsional moduli for the armchair and zigzag variants of these materials in the low-twist regime and at practically relevant diameters. We find that the torsional moduli follow the trend: MS₂> MSe₂> MTe₂. In addition, the moduli display a power law dependence on diameter, with the scaling generally close to cubic, as predicted by the isotropic elastic continuum model. In particular, the shear moduli so computed are in good agreement with those predicted by the isotropic relation in terms of the Young's modulus and Poisson's ratio, both of which are also calculated using symmetry-adapted DFT. Finally, we develop a linear regression model for the torsional moduli of TMD nanotubes based on the nature/characteristics of the metal-chalcogen bond, and show that it is capable of making reasonably accurate predictions.