Lattice Relaxation Effects Research Articles

Effect of lattice relaxation on electronic spectra of helically twisted trilayer graphene: large-scale atomistic simulation approach

Effect of lattice relaxation on electronic spectra of helically twisted trilayer graphene: large-scale atomistic simulation approach

Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe2

Large-scale moiré systems are extraordinarily sensitive, with even minute atomic shifts leading to significant changes in electronic structures. Here, we investigate the lattice relaxation effect on moiré band structures in twisted bilayer MoTe2 with two approaches: (a) large-scale plane-wave basis first principle calculation down to 2.88°, (b) transfer learning structure relaxation + local-basis first principles calculation down to 1.1°. We use two types of van der Waals corrections: the D2 method of Grimme and the density-dependent energy correction, and find that the density-dependent energy correction yields a continuous evolution of bandwidth with twist angles. Based on the above results. we develop a complete continuum model with a single set of parameters for a wide range of twist angles, and perform many-body simulations at ν = −1, −2/3, −1/3.

Relaxation effects in transition metal dichalcogenide bilayer heterostructures

While moiré structures in twisted bilayer transition metal dichalcogenides (TMDCs) have been studied for over a decade, the importance of lattice relaxation effects was pointed out only in 2021 by DiAngelo and MacDonald1, who reported the emergence of a Dirac cone upon relaxation. TMDCs of group 6 transition metals MX2 (M = Mo, W, X = S, Se) share layered structures with pronounced interlayer interactions, exhibiting a direct band gap when exfoliated to a two-dimensional (2D) monolayer. As their heterolayers are incommensurable, moiré structures are present in the bilayers even if stacked without a twist angle. This study addresses the challenge of accurately modeling and understanding the structural relaxation in twisted TMDC heterobilayers. We show that the typical experimental situation of finite-size flakes stacked upon larger flakes can reliably be modeled by fully periodic commensurate models. Our findings reveal significant lattice reconstruction in TMDC heterobilayers, which strongly depend on the twist angle. We can categorize the results in two principal cases: at or near the untwisted configurations of 0° and 60°, domains with matching lattice constants form and the two constituting layers exhibit significant in-phase corrugation—their out-of-plane displacements are oriented towards the same direction in all local stackings—while at large twist angles—deviating from the 0° and 60°—the two layers show an out-of-phase corrugation. In particular, we reveal that the lattice reconstruction results from the competition between the strain energy cost and the van der Waals energy gain. Additionally, our systematical study highlights structural disparities between heterostructures composed of different or identical chalcogen atoms. Our research not only confirms the reliability of using periodic commensurate models to predict heterostructure behavior but also enriches the understanding of TMDC bilayer heterostructures.

Electronic transport in graphene with out-of-plane disorder

Real-world samples of graphene often exhibit various types of out-of-plane disorder–ripples, wrinkles and folds–introduced at the stage of growth and transfer processes. These complex out-of-plane defects resulting from the interplay between self-adhesion of graphene and its bending rigidity inevitably lead to the scattering of charge carriers thus affecting the electronic transport properties of graphene. We address the ballistic charge-carrier transmission across the models of out-of-plane defects using tight-binding and density functional calculations while fully taking into account lattice relaxation effects. The observed transmission oscillations in commensurate graphene wrinkles are attributed to the interference between intra- and interlayer transport channels, while the incommensurate wrinkles show vanishing backscattering and retain the transport properties of flat graphene. The suppression of backscattering reveals the crucial role of lattice commensuration in the electronic transmission. Our results provide guidelines to controlling the transport properties of graphene in presence of this ubiquitous type of disorder.

Twist-Induced Modification in the Electronic Structure of Bilayer WSe2.

The recent discovery of strongly correlated phases in twisted transition-metal dichalcogenides (TMDs) highlights the significant impact of twist-induced modifications on electronic structures. In this study, we employed angle-resolved photoemission spectroscopy with submicrometer spatial resolution (μ-ARPES) to investigate these modifications by comparing valence band structures of twisted (5.3°) and nontwisted (AB-stacked) bilayer regions within the same WSe2 device. Relative to the nontwisted region, the twisted area exhibits pronounced moiré bands and ∼90 meV renormalization at the Γ-valley, substantial momentum separation between different layers, and an absence of flat bands at the K-valley. We further simulated the effects of lattice relaxation, which can flatten the Γ-valley edge but not the K-valley edge. Our results provide a direct visualization of twist-induced modifications in the electronic structures of twisted TMDs and elucidate their valley-dependent responses to lattice relaxation.

Structure, magnetic morphology and magnetization correlations in pulsed laser deposited CoFe[formula omitted]O[formula omitted] ([formula omitted]) thin films

The present paper reports a complete study on the correlation between structure, morphology, and magnetic properties of (111)-oriented cobalt ferrite (CoFe2O4) thin films with varying film thickness. The CoFe2O4 (CFO) thin films were deposited on Pt-coated Si substrate by pulsed laser deposition (PLD) at 550 °C. The x-ray diffraction (XRD) data confirms the (111)-oriented growth of the cobalt ferrite films. The in-plane morphology of the films in the field emission scanning electron micrographs ensure the Stranski–Krastanov growth mechanism, and the atomic force micrographs confirms the effect of lattice relaxation on the morphology of the films with varying thickness. The possible cation distributions for the samples were determined from the Raman spectroscopy, which revealed the crystal structure-magnetic property correlations in cobalt ferrite films. The magnetic hysteresis (M−H) loops show a significant spin reorientation by showing the variation between the in-plane (IP) and out-of-plane (OP) magnetization. The presence of a kink on the OP M−H loops and its variation with film thickness clearly establishes the existence of competing magnetic anisotropies in the films. The high coercivity (HC) values observed for OP magnetization of cobalt ferrite films with thicknesses 115 nm and 125 nm may be explored for possible room-temperature (RT) device applications.

Commensurate and incommensurate double moiré interference in twisted trilayer graphene

Twisted graphene multi-layers have been recently demonstrated to share several correlation-driven behaviours with twisted bilayer graphene. In general, the van Hove singularities (VHSs) can be used as a proxy of the tendency for correlated behaviours. In this paper, we adopt an atomistic method by combining tight-binding method with the semi-classical molecular dynamics to investigate the electronic structures of twisted trilayer graphene (TTG) with two independent twist angles. The two independent twist angles can lead to the interference of the moir\'e patterns forming a variety of commensurate/incommensurate complex supermoir\'e patterns. In particular, the lattice relaxation, twist angle and angle disorder effects on the VHS are discussed. We find that the lattice relaxation significantly influence the position and magnitude of the VHSs. In the supermoir\'e TTG, the moir\'e interference provides constructive or destructive effects depending on the relative twist angle. By modulating the two independent twist angles, novel superstructures, for instance, the Kagome-like lattice, could constructed via the moir\'e pattern. Moreover, we demonstrate that a slight change in twist angles (angle disorder) provides a significant suppression of the peak of the VHSs. Apart from the moir\'e length, the evolution of the VHSs and the LDOS mapping in real space could be used to identify the twist angles in the complicated TTG. In practice, our work could provide a guide for exploring the flat band behaviours in the supermoir\'e TTG experimentally.

Lattice relaxation effects on the collective resonance spectra of a finite dipole array.

Dielectric/plasmonic lattice relaxation spectroscopy is theoretically discussed in this work. A lattice relaxation effect generally occurs in nanocrystals, which means that from the bulk phase to the crystal surface, lattice parameters show a gradual shift. Here, lattice relaxation is introduced into finite polarizable point arrays or rod arrays as an adjusting tool, and its effect on lattice resonance extinction spectrum peaks is calculated. DDA (discrete dipole approximation) and FDTD (finite difference time domain) methods are applied. Different from an ideal infinite array, a finite array exhibits a broad, rippled extinction spectral peak. The application of an expanded/contracted lattice relaxation to the finite array can compress the ripple on one shoulder of the peak, as a cost, and the other shoulder of the peak gets more rippled, showing a "ripple transfer" effect. The strategy introduced in this work can contribute to the micro/nano optical measurement, on-chip adjustable optical cavity for OPOs (optical parameter oscillators)/lasers and controlling of fluorescence or hot-electron chemistry.

Kinetics of laser-induced melting of thin gold film: How slow can it get?

Melting is a common and well-studied phenomenon that still reveals new facets when triggered by laser excitation and probed with ultrafast electron diffraction. Recent experimental evidence of anomalously slow nanosecond-scale melting of thin gold films irradiated by femtosecond laser pulses motivates computational efforts aimed at revealing the underlying mechanisms of melting. Atomistic simulations reveal that a combined effect of lattice superheating and relaxation of laser-induced stresses ensures the dominance of the homogeneous melting mechanism at all energies down to the melting threshold and keeps the time scale of melting within ~100 picoseconds. The much longer melting times and the prominent contribution of heterogeneous melting inferred from the experiments cannot be reconciled with the atomistic simulations by any reasonable variation of the electron-phonon coupling strength, thus suggesting the need for further coordinated experimental and theoretical efforts aimed at addressing the mechanisms and kinetics of laser-induced melting in the vicinity of melting threshold.

Color coordination of emerald on CIE color space based on first-principles calculations

Be3Al2(SiO3)6 including Cr3+ known as emerald have been widely studied and utilized for solid-state laser materials. Numerous theoretical investigations on these systems have also been published in the literature since the electronic energy levels, optical properties, and structures of Cr3+ impurities in emerald systems have been thoroughly investigated using a variety of experimental approaches. In general, semi-empirical computations have been used to accomplish the majority of theoretical interpretations of experimental data. Although in the case of non-empirical calculations, the agreement between theoretical and experimental optical properties was improved by taking into account the energy corrections, quantitative evaluation of the color of emitted light was not feasible until recently. Here, the color coordinates of emerald under the standard illuminant has been calculated to perform a quantitative evaluation based on the optical spectra. The “theoretical” color was calculated and presented visually on the Commission Internationale d’Eclairage (CIE) color space based on the theoretical spectra obtained non-empirically using the so-called first-principles discrete variational multi-electron method, known as DVME. The absorption spectra of emerald were calculated using CrO69− model cluster with D3 symmetry. Several key effects in reproducing optical spectra were investigated in detail, such as lattice relaxation, energy correction, and orbital effects. The accuracy of this approach in predicting absorption spectra was analyzed thoroughly under various computational conditions. The results show that accounting for all of the above effects is important to producing the absorption spectra. Specifically, enlarging the considered orbital in the calculation improved the agreement between the computed and experimentally-observed colors. This study is crucial for validating the non-empirical calculations made using the DVME approach to assess the color of emitted light quantitatively.

Flat-band plasmons in twisted bilayer transition metal dichalcogenides

Twisted bilayer transition metal dichalcogenides are ideal platforms to study flat-band phenomena. In this paper, we investigate flat-band plasmons in the hole-doped twisted bilayer ${\mathrm{MoS}}_{2}$ (tb-${\mathrm{MoS}}_{2}$) by employing a full tight-binding model and the random phase approximation. When considering lattice relaxations in tb-${\mathrm{MoS}}_{2}$, the flat band is not separated from remote valence bands, which makes the contribution of interband transitions in transforming the plasmon dispersion and energy significantly different. In particular, low-damped and quasiflat plasmons emerge if we only consider intraband transitions in the doped flat band, whereas a $\sqrt{q}$ plasmon dispersion emerges if we also take into account interband transitions between the flat band and remote bands. Furthermore, the plasmon energies are tunable with twist angles and doping levels. However, in a rigid sample that suffers no lattice relaxations, lower-energy quasiflat plasmons and higher-energy interband plasmons can coexist. For rigid tb-${\mathrm{MoS}}_{2}$ with a high doping level, strongly enhanced interband transitions quench the quasiflat plasmons. Based on the lattice relaxation and doping effects, we conclude that two conditions, the isolated flat band and a proper hole-doping level, are essential for observing the low-damped and quasiflat plasmon mode in twisted bilayer transition metal dichalcogenides. We hope that our study on flat-band plasmons can be instructive for studying the possibility of plasmon-mediated superconductivity in twisted bilayer transition metal dichalcogenides in the future.

Strong suppression of near-field thermal transport between twisted bilayer graphene near the magic angle

Twisted bilayer graphene (TBLG) has recently emerged as a versatile platform for studying a variety of exotic transport phenomena. Here, we present a theoretical study of near-field thermal radiation between suspended TBLG with a focus on the magic angle. Within the chirally symmetric continuum model, we observe a suppressed heat flow when approaching the magic angle owing to a reduced Drude weight, with greater suppressions at lower temperatures and larger gap sizes. When the chemical potential lies in the energy gap near the charge neutrality point, more than 100-fold heat-flow variation can be achieved at 50 K within 0.25° of twist. By reducing the electron scattering rate, the radiation spectrum near the magic angle dramatically narrows, leading to over 10,000-fold of suppression. In addition, supported TBLG is briefly considered to facilitate experimental measurement. With rationally tailored substrates, the heat-flow contrast can still exceed 1000. We also discuss lattice relaxation effect in terms of the interlayer coupling energy, finding that a stronger coupling leads to a smaller heat-flow contrast and more prominent multiband transport. Our results highlight the great potential of magic-angle TBLG in thermal transport, especially for controlling thermal radiation.

Correction to: Lattice relaxation effect in RbxMA(1−x)PbBr3 single crystal to enhance optoelectronic performance of perovskite photodetectors

Correction to: Lattice relaxation effect in RbxMA(1−x)PbBr3 single crystal to enhance optoelectronic performance of perovskite photodetectors

Lattice relaxation effect in RbxMA(1−x)PbBr3 single crystal to enhance optoelectronic performance of perovskite photodetectors

Lattice relaxation effect in RbxMA(1−x)PbBr3 single crystal to enhance optoelectronic performance of perovskite photodetectors

Lattice relaxation and substrate effects of graphene moiré superlattice

When two two-dimensional (2D) materials with different lattice constants or with different rotation angles are superimposed, a moiré superlattice can be constructed. The electronic properties of the superlattice are strongly dependent on the stacking configuration, twist angle and substrate. For instance, theoretically, when the rotation angle of twisted bilayer graphene is reduced to a set of specific values, the so-called magic angles, flat bands appear near the charge neutrality, and the electron-electron interaction is significantly enhanced. The Mott insulator and unconventional superconductivity are detected in the twisted bilayer graphene with a twist angle around 1.1°. For a moiré pattern with a large enough periodicity, lattice relaxation caused by an interplay between van der Waals force and the in-plane elasticity force comes into being. The atomic relaxation forces atoms to deviate from their equilibrium positions, and thus making the system reconstructed. This review mainly focuses on the effects of the lattice relaxation and substrates on the electronic properties of the graphene superlattices. From both theoretical and experimental point of view, the lattice relaxation effects on the atomic structure and electronic properties of graphene-based superlattices, for example, the twisted bilayer graphene, twisted trilayer graphene, graphene-hexagonal boron nitride superlattice and twisted bilayer graphene-boron nitride superlattice are discussed. Finally, a summary and perspective of the investigation of the 2D material superlattice are presented.

Lattice relaxation effect in CsxMA(1-x)PbBr3 single crystal to enhance optoelectronic performance of perovskite photodetectors

Single crystal (SC) MAPbBr3 perovskite is regarded as a promising material to fabricate high-performance photodetectors (PDs) due to its impressive optoelectronic properties and good chemical stability. Cs+ doping has been proved to be an effective method to significantly improve the optoelectronic properties of MAPbBr3 SC. However, the intrinsic effect of Cs+ on the crystal structure is still unclear. Herein, we grew a series CsxMA(1-x)PbBr3 SCs. X-ray rocking curves (XRC) of CsxMA(1-x)PbBr3 SCs prove that appropriate Cs-doping concentration could reduce defect density effectively. X-ray photoelectron spectroscopy (XPS) measurements indicate that Cs-doping enhances the atoms interaction in CsxMA(1-x)PbBr3 lattice due to isoelectronic impurity effect. Single-crystal PDs were fabricated to compare the optoelectronic properties of MAPbBr3 SCs with different Cs-doping concentration, and the 2% Cs-doped CsxMA(1-x)PbBr3 PD shows the optimum performance. Density functional theory (DFT) calculations demonstrate that Cs-doping leads to lattice relaxation effect which is benefit to reduce trap density of CsxMA(1-x)PbBr3 SCs. The Pb-6p level of CsxMA(1-x)PbBr3 slightly shifts to lower energy region compared with MAPbBr3, resulting in the decrease of band gap of CsxMA(1-x)PbBr3.

Optical spectra of the quantum defects in metal halide perovskites

Defects in metal halide perovskites (MHPs) are of fundamental importance to understand optical properties of materials. Here, optical transitions of negative, positive, and neutral defects in MHPs are studied based on the quantum defect model. We find that the intensities of emission peaks are obviously enhanced along with a nonlinear redshift as the depth of defect levels increases in the bandgap. Moreover, the full width at half-maximum of emission spectra can be broadened from tens to hundreds of meV with the increasing temperature. This can be attributed to the strong defect-longitudinal optical phonon coupling, resulting in the enhanced lattice relaxation effect, which could be used as a judging criterion between defects and exciton emission. These results not only provide deep insight for the properties of defect's spectra but also shed light on the influence of defects on the potential applications of MHP-based optoelectronic devices.

First-Principles calculations of the interconfigurational transition energies of 4f - 4f-15d of Ln3+ ions in LiYF4 and CaF2

In studying the design of novel phosphors and solid-state laser materials, luminescence with a characteristically long lifetime originates from f - f emissions (infrared, visible and ultraviolet). However, due to high demand for novel luminescence materials which excite in the ultraviolet (UV) and vacuum ultraviolet (VUV) ranges, the interconfigurational f - d transition has been of great interest. In this work, we investigated the 4 f n - 4 f n -1 5 d transition energy of trivalent lanthanide ions in LiYF 4 and CaF 2 host crystals (LiYF 4 : Ln 3+ and CaF 2 : Ln 3+ ) without referring to any empirical parameters. These crystals are considered to be promising fluoride hosts for solid-state laser crystals. LnF 8 5− atomic clusters were built based on the crystal structures of LiYF 4 and CaF 2 . The relativistic MO calculations were done using the relativistic Discrete Variational Xα (DV-Xα) algorithm. The relativistic version of discrete variational multi-electron method (DVME) algorithm was used to calculate the multiplet energies. We considered the effect of lattice relaxation by a simple estimation using Shannon's crystal radii. Given that the theoretical transition energies are typically underestimated due to the underestimation of the corresponding effects, the absolute transitional energies have received corrections based on one-electron calculations utilizing the Slater's transition-state technique. The in-depth study indicates that the lattice-relaxation effect does not substantially impact LiYF 4 : Ln 3+ , but greatly affects the transitional energy of heavy lanthanides doped in CaF 2 from 4 f n - 4 f n -1 5 d . The energy corrections based on Slater's transition-state method are necessary to improve the accuracy of our calculations. By a combination of these two methods, the transition energies of 4 f n - 4 f n -1 5 d of LiYF 4 : Ln 3+ and CaF 2 : Ln 3+ agree very well with the experimental data. This research is important to providing guidance in the search for new lanthanide-based phosphors in UV or VUV regions. • The 4 f n - 4 f n -1 5 d transition energies of LiYF 4 :Ln 3+ and CaF 2 :Ln 3+ have been studied. • Effect of lattice relaxation was simply estimated based on Shannon's crystal radii. • Energy corrections utilizing Slater's transition-state method were considered. • The lattice relaxation greatly affects the transitional energy of heavy CaF 2 :Ln 3+ . • The energy corrections are necessary to improve the accuracy.

Facet-dependent stability of near-surface oxygen vacancies and excess charge localization at CeO2 surfaces

To study the dependence of the relative stability of surface (V A ) and subsurface (VB ) oxygen vacancies with the crystal facet of CeO2, the reduced (100), (110) and (111) surfaces, with two different concentrations of vacancies, were investigated by means of density functional theory (DFT + U) calculations. The results show that the trend in the near-surface vacancy formation energies for comparable vacancy spacings, i.e. (110) < (100) < (111), does not follow the one in the surface stability of the facets, i.e. (111) < (110) < (100). The results also reveal that the preference of vacancies for surface or subsurface sites, as well as the preferred location of the associated Ce3+ polarons, are facet- and concentration-dependent. At the higher vacancy concentration, the V A is more stable than the V B at the (110) facet whereas at the (111), it is the other way around, and at the (100) facet, both the V A and the VB have similar stability. The stability of the V A vacancies, compared to that of the V B , is accentuated as the concentration decreases. Nearest neighbor polarons to the vacant sites are only observed for the less densely packed (110) and (100) facets. These findings are rationalized in terms of the packing density of the facets, the lattice relaxation effects induced by vacancy formation and the localization of the excess charge, as well as the repulsive Ce3+−Ce3+ interactions.

Effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene

We present a theoretical study of the effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene (TBG) at small twist angle, based on the band structures obtained from a continuum model. We find that heterostrain, lattice relaxation, and their combination give rise to very distinctive spectroscopic features in the optical conductivity, which can be used to probe and distinguish these effects. From the spectrum at various Fermi energies, important features in the strain- and relaxation-modified band structure, such as the band gap, bandwidth, and van Hove singularities, can be directly measured. The peak associated with the transition between the flat bands in the optical conductivity with twist angle $\ensuremath{\theta}=1.{05}^{\ensuremath{\circ}}$ are highly sensitive to the direction of the strain, which can provide direct information on the strain-modified flat bands. Moreover, discussing $\ensuremath{\theta}=1.{47}^{\ensuremath{\circ}}$ and $1.{81}^{\ensuremath{\circ}}$ as two more examples, we show that the qualitative changes of optical conductivity under the influence of strain and lattice relaxation are quite general in small-angle TBG.