Imaginary Modes Research Articles

Generalized Path Integral Energy and Heat Capacity Estimators of Quantum Oscillators and Crystals Using Harmonic Mapping.

Imaginary-time path integral (PI) is a rigorous tool to treat nuclear quantum effects in static properties. However, with its high computational demand, it is crucial to devise precise estimators. We introduce generalized PI estimators for the energy and heat capacity that utilize coordinate mapping. While it can reduce to the standard thermodynamic and centroid virial (CVir) estimators, the formulation can also take advantage of harmonic character of quantum oscillators and crystals to construct a coordinate mapping. The method is not applicable to fluids or systems with imaginary modes such as double-well potentials. This yields harmonically mapped averaging (HMA) estimators, with mappings that decouple (HMAc) or couple (HMAq) the centroid and internal modes. The HMAq is constructed with normal mode coordinates (HMAq-NM) with quadratic scaling of cost or harmonic oscillator staging (HMAq-SG) coordinates with linear scaling. The estimator performance is examined for a 1D anharmonic oscillator and a 3D Lennard-Jones crystal using path integral molecular dynamics (PIMD) simulation. The HMA estimators consistently provide more precise estimates compared to CVir, with the best performance obtained by HMAq-NM, followed by HMAq-SG, and then HMAc. We also examine the effect of anharmonicity (for AO), intrinsic quantumness, and Trotter number. The HMA formulation introduced assumes the availability of forces and Hessian matrix; however, an equally efficient finite difference alternative is possible when these derivatives are inaccessible. The remarkable improvement in precision offered by HMAq estimators provides a framework for efficient PI simulation of more challenging systems, such as those based on ab initio calculations.

Janus Monolayer of 1T-TaSSe: A Computational Study.

Materials exhibiting charge density waves are attracting increasing attention owing to their complex physics and potential for applications. In this paper, we present a computational, first principles-based study of the Janus monolayer of 1T-TaSSe transition metal dichalcogenide. We extensively compare the results with those obtained for parent compounds, TaS2 and TaSe2 monolayers, with confirmed presence of 13×13 charge density waves. The structural and electronic properties of the normal (undistorted) phase and distorted phase with 13×13 periodic lattice distortion are discussed. In particular, for a normal phase, the emergence of dipolar moment due to symmetry breaking is demonstrated, and its sensitivity to an external electric field perpendicular to the monolayer is investigated. Moreover, the appearance of imaginary energy phonon modes suggesting structural instability is shown. For the distorted phase, we predict the presence of a flat, weakly dispersive band related to the appearance of charge density waves, similar to the one observed in parent compounds. The results suggest a novel platform for studying charge density waves in two-dimensional transition metal dichalcogenides.

Quasinormal mode of Schwarzschild black hole with geometric correction

We investigated the quasinormal modes (QNMs) for scalar, Dirac and electromagnetic fields of a Schwarzschild black hole with geometric corrections. In addition to the inherent modes of the Schwarzschild black hole, we discovered the existence of purely imaginary modes induced by the geometric corrections, which dominated the behavior of the perturbation when geometric corrections were pretty small. Notably, we found that these purely imaginary modes are prominent, and their imaginary parts are proportional to the correction parameter ϵ. We also explored the large-l limit using the WKB approximation for scalar field. This opens up the possibility of observed geometric corrections in the future.

X[formula omitted]CoH[formula omitted] (X = Ca, Sr) for hydrogen storage: First-principles computations

The structural, electronic, elastic, optical, phonon, and thermo-physical properties of the tetragonal X2CoH5 (X = Ca, Sr) hydrogen storage compounds were thoroughly examined using first-principles calculations. The negative formation enthalpies (−76.03 kJ/mol.H2 for Ca2CoH5 and −72.55 kJ/mol.H2 for Sr2CoH5) highlight the structural stability of these materials. Phonon calculations revealed no imaginary frequency modes, confirming the dynamic stability of X2CoH5. The mechanical stability of Ca2CoH5 and Sr2CoH5 was evidenced by the compliance of the elastic constants with Born stability criteria. The electronic band structure indicates that Ca2CoH5 and Sr2CoH5 are direct bandgap semiconductors with narrow bandgaps of ∼0.27 and 0.34 eV, respectively. The appraisal of Poisson’s ratio (ν = 0.22 for X = Ca and 0.23 for Sr) and Pugh’s ratio (B/G = 1.47 for X = Ca and 1.56 for Sr) suggests that both metal hydrides exhibit brittle mechanical behavior. Moreover, 3D plots of Young’s modulus (E), shear modulus (G), linear compressibility (β), and Poisson’s ratio (ν) uncover anisotropy within X2CoH5. The hydrogen storage capabilities were scrutinized, and the present materials feature excellent volumetric hydrogen density (95.65 gH2l−1 for Ca2CoH5 and 80.24 gH2l−1 for Sr2CoH5), moderate gravimetric hydrogen density (3.38 wt% for Ca2CoH5 and 2.06 wt% for Sr2CoH5) and high hydrogen desorption temperature (584 K for Ca2CoH5 and 558 K for Sr2CoH5). Notably, the obtained volumetric hydrogen densities are in line with the volumetric capacity criteria set by the U.S. Department of Energy (DOE) for 2025. Finally, the optical and thermo-physical characteristics of X2CoH5 compounds were also investigated in this work.

Anomalous dimension and quasinormal modes of flavor branes

We study scalar quasinormal modes in a D3/D7 system holographically dual to a quantum field theory with chiral symmetry breaking at finite temperature. From the bottom-up approach, we consider a nontrivial dilaton profile which is responsible for the anomalous dimension of the quark condensate. It depends on a new parameter q in the model. By varying this parameter, we study the behavior of the massive and massless scalar quasinormal modes. The numerical method that we use is the spectral method, and we find that there is no pure imaginary mode for the massless case but it appears by increasing the parameter q. It is known that this mode becomes tachyonic for massive cases. Then we turn on a pseudoscalar field and using a simple ansatz study its effect on the quasinormal modes of the scalar field. By varying the parameter of the nontrivial dilaton profile in the model, we qualitatively study quasinormal modes in walking theories.

Harmonic Oscillator Staging Coordinates for Efficient Path Integral Simulations of Quantum Oscillators and Crystals.

Imaginary-time path integral (PI) is a rigorous quantum mechanical tool to compute static properties at finite temperatures. However, the stiff nature of the internal PI modes poses a sampling challenge. This is commonly tackled using staging coordinates, in which the free particle (FP) contribution of the PI action is diagonalized. We introduce novel and simple staging coordinates that diagonalize the entire action of the harmonic oscillator (HO) model, rendering it efficiently applicable to (exclusively) systems with harmonic character, such as quantum oscillators and crystals. The method is not applicable to fluids or systems with imaginary modes. Unlike FP staging, the HO staging provides a unique treatment of the centroid mode. We provide implementation schemes for PIMC and PIMD simulations in NVT ensemble. Sampling efficiency is assessed in terms of the precision and accuracy of estimating the energy and heat capacity of a one-dimensional HO and an asymmetric anharmonic oscillator (AO). In PIMC, the HO coordinates propose collective moves that perfectly sample the HO contribution, then (for AO) the residual anharmonic term is sampled using standard Metropolis method. This results in a high acceptance rate and, hence, high precision, in comparison to the FP staging. In PIMD, the HO coordinates naturally prescribe definitions for the fictitious masses, yielding equal frequencies of all modes when applied to the HO model. This allows for a substantially larger time step sizes relative to standard staging, without affecting accuracy or integrator stability. For completeness, we also present results using normal mode (NM) coordinates, based on both HO and FP models. While staging and NM coordinates show similar performance (for FP or HO), staging is computationally preferable due to its cheaper scaling with the number of beads. The simplicity and the enhanced sampling gained by the HO coordinates open avenues for efficient estimation of nuclear quantum effects in more complex systems with harmonic character, such as real molecular bonds and quantum crystals.

FP-LAPW calculations of the structural, and optoelectronic properties of vanadium silicide compound for optoelectronic applications

Optoelectronic devices play an essential part in our daily lives by seamlessly integrating optics and electronics, leading to technologies such as smartphones, solar cells, and optical communication. In this study, the structural and optoelectronic characteristics of the hexagonal vanadium silicide are determined using the density functional theory (DFT). The structural parameters such as the zero-pressure bulk modulus B0, its pressure derivative B0′; equilibrium energy, and the volume of the primitive cell at equilibrium V0 are compared with experiment results. The metallic character of VSi2 is confirmed by calculating the density of states and band structure. Moreover, the optical properties like the dielectric function, reflectivity, energy loss function, refractive index, absorption coefficient, and optical conductivity are studied deeply, using the Drude model, within the energy interval from 0 to 14 eV and they are compared with experiment results of a polycrystalline and single crystal. However, the phonon dispersion spectrum shows the presence of imaginary modes, which indicates instability in the structure of vanadium silicide. The results indicate that the VSi2 material has the potential to be used in many applications, including mirrors, glass coatings, optoelectronic devices, optical networks, electronics, optical communications, and waveguide components.

Innovative approach to modeling propagative, non-propagative and complex modes of ultrasonic guided waves

In the present paper are developed a new hybrid-spectral approach that deals with the dispersion of propagative, non-propagative and complex ultrasonic guided waves in different types of waveguides. First, a mathematical formulation of the eigenvalue and eigenvector problem has been presented. Then, the hybrid approach based on eigenvector processing is presented. A comparison is then made with the frequency and wavenumber approaches, to highlight the strengths of our method. The dispersion curves of propagative, non-propagative and complex modes are plotted in 2D and 3D. From these representations, several observations on mode behavior have been highlighted, notably the phenomenon of conversion of non-propagative modes into propagative modes, and also conversions specific to imaginary modes. The braiding phenomenon between symmetrical and antisymmetrical modes was also analyzed. Single and multi-layer planar and cylindrical geometries were treated with different degrees of anisotropy. The accuracy of the results was checked by comparison with analytical dispersion curves for planar structures and based on the thin plate limit for cylindrical structures. The error evaluated is of the order of 10 − 5 . A computation time analysis has been carried out, showing that the approach developed is the fastest in comparison with those available in the literature. On the basis of the results obtained, the hybrid approach applied to eigenvalue problems resulting from a spectral formulation presents a very good alternative for obtaining dispersion curves. It is stable, convergent, easy to implement and requires very little computing time and it can generate all types of modes (propagative, non-propagative and complex), in contrast to existing approaches in the reference.

Band structure of the one-dimensional tetrameric Kitaev chain induced by imaginary potentials

We investigate the one-dimensional tetramerised Kitaev chain induced by imaginary potentials {iγ,−iγ,−iγ,iγ} applied to the dimerised Kitaev chain. It is found that the imaginary potentials cause a variety of topological phase transitions. When the chemical potential μ is tuned to the energy zero point, they lead to the appearance of the mixed phase of the system consisting of two purely real Kitaev-like modes and four purely imaginary energy SSH-like zero-energy modes, which appear as the transition of the Kitaev-like-mixed-SSH-like phase. In addition, the Kitaev-like phase can be broadened by imaginary potentials, manifested as the widening of the quantised Andreev reflection plateau. When μ≠0, the same topological phase transition occurs, from the topologically-trivial phase to the Kitaev-like phase. One can believe that this work provides theoretical support for probing the generation of Majorana zero modes in new topological superconducting systems.

Investigation of structural, electronic, mechanical, and thermoelectric properties of the defect chalcopyrite semiconductor ZnIn[formula omitted]Se[formula omitted] from density functional theory

In this study, the detailed structural, electronic, mechanical, and thermoelectric properties of ZnIn2Se4 defect chalcopyrite semiconductor are carried out using density functional theory & semi-classical Boltzmann transport theory. From the band structure analysis, the compound is confirmed to be a direct band gap semiconductor with a band gap of 1.20 eV. The presence of flat valence bands near the Fermi level indicates a higher effective mass of holes. From the elastic and mechanical properties, it has been found that the compound is mechanically stable and revealed to be ductile. The phonon dispersion study of the compounds shows that the compound is dynamically stable with no imaginary phonon modes. The electronic transport properties were studied within a temperature range of 300K to 900K as a function of chemical potential (μ), temperature(T), and carrier concentrations (n). The μ dependent electronic transport properties show enhanced values in the p-type doping region because of the cationic site vacancy. The dependency of electronic transport properties on n and T agrees well with Mott’s relation. The highest ZT is found to be 0.96 at 900K for a low carrier concentration of 1019cm−3. The phonon thermal conductivity of the compound is found to be 2.52 W/mK near room temperature and 0.84 W/mK at 900K using the Slack method. All these results support ZnIn2Se4, a defect chalcopyrite semiconductor, as a favorable candidate for thermoelectric applications.

Elastic anisotropy, mechanical, lattice dynamics, and electronic properties of MPdZ (M = Hf, Zr, Ti; Z = Sn, Ge, Si). DFT study

Elastic anisotropy, mechanical, lattice dynamics, and electronic properties of MPdZ (M = Hf, Zr, Ti; Z = Sn, Ge, Si) compounds have all been computed from first principles. All compounds are ductile according to Pugh’s ratio, Cauchy’s pressure, and Poisson’s ratio values. Based on the Born stability criteria, each MPdZ compound is mechanically stable. The high machinability index values of TiPdSn and ZrPdSi indicate their high quality of machinability. The hardness of the compounds is between 5.5 and 8.0 GPa, and the highest hardness is found in the HfPdSn (7.966 GPa) compound. The computed Kleinman parameter indicates that the bond stretching for all MPdZ compounds is minimal. The anisotropy indices incorporating graphical presentation indicate all MPdZ compounds are anisotropic. Young’s modulus elastic anisotropy is less compared to the Zener anisotropy index, equivalent Zener anisotropy measure, and anisotropy ratio of the maximum and minimum shear moduli. Prominent anisotropy for sound velocities is observed in HfPdSi, ZrPdSi, and TiPdSi compounds. With the exception of TiPdGe, other compounds in this work are dynamically stable due to the lack of imaginary phonon modes. HfPdSn, ZrPdSn, and TiPdSn have narrow energy band gaps among the compounds that were studied.

DFT based study of copper calcium halide perovskite nanomaterials for optoelectronic and energy applications

The mechanical, electronic, optical, and thermoelectric analyses of CuCaX3 (X = Cl, Br, I) have been done using DFT based TB-mBJ approach. The stability of CuCaX3 (X = Cl, Br, I) has been confirmed from the enthalpy of formation; values for CuCaCl3, CuCaBr3, and CuCaI3 are −1.07 eV, −1.55 eV, and −2.15 eV, respectively. The phonon spectra plot is also discussed, and the phonon dispersion analysis confirms that the CuCaX3 systems are dynamically stable since no imaginary modes are observed. The modified Becke-Johnson exchange potential is used to evaluate the opto-electronic and thermo-electric properties. By replacing anions (Cl to I), the band gap of the studied material in the visible region has been tailored, from 2.9 eV to 2.65 eV, for renewable energy devices. In addition, various optical properties such as dielectric constant, refraction, absorption, optical conductivity, and optical loss factor have been analyzed for optoelectronic applications. With the replacement of anions (Cl to I), the peaks of maximum intensities shifted to lower energy to values of 7.2 eV, 6.2 eV and 5 eV for CuCaCl3, CuCaBr3 and CuCaI3 respectively. Furthermore, the BoltzTrap code has been used to discuss thermal conductivity, power factor, Hall coefficient, specific capacitance and electron densities in detail for thermoelectric applications. The CuCaX3 family of perovskites has been found to have bandgaps falling in the visible region for light-emitting diodes (LEDs). These also exhibit high thermal efficiency, making them potential multifunctional candidates for optoelectronic and energy harvesting applications.

Robust Ferroelasticity and Carrier Dynamics Across the Domain Wall in Perovskite‐Like van der Waals WO2I2

AbstractAs a new group of van der Waals (vdWs) ferroic materials, transition metal dioxydihalides MO2X2 (M: Mo, W; X: halogen) with a perovskite‐like structure are theoretically predicted to exhibit intriguing physics and versatile ferroic characteristics, which is not achieved experimentally as far as it is known. In this work, the robust ferroelasticity in vdWs WO2I2 with the switching strain as low as ≈0.3%, accompanied with the striped optical contrast between adjacent domains, spot splitting of selected area electron diffraction (SAED) patterns at domain wall, and 90° domain wall is demonstrated. With the aid of ab‐initio calculations, the origin of ferroelasticity in WO2I2 is unveiled, where the imaginary phonon mode in the high‐symmetry paraelastic phase leads to the spontaneous displacement of W atom away from the center of the [WO4I2] octahedron, resulting in the switchable spontaneous strain under an external strain field. Moreover, transient absorption microscopy (TAM) measurements demonstrate that the diffusion of photogenerated carriers is significantly hindered by the ferroelastic domain walls. This study provides deep insights into the ferroic order and domain wall in perovskite‐like vdWs MO2X2 for new physics and functionalities.

Theoretical study of two-dimensional BeB<sub>2</sub> monolayer as anode material for magnesium ion batteries

<sec>Rechargeable lithium-ion batteries as the main energy storage equipment should possess high power density, excellent reversible capacity, and long cycle life. However, due to the high cost and dendrite growth of Li, searching for non-Li-ion batteries is urgent. Compared with lithium, magnesium has abundant resources, small ionic radius, and high energy density. Therefore, magnesium-ion batteries (MIBs) can serve as the next generation metal-ion batteries. Two-dimensional materials based on Be or B element acting as the anode of metal-ion batteries always exhibit high theoretical storage capacity. Using first-principles calculations, we systematically explore the potential of BeB<sub>2</sub> as MIBs anode. The optimized BeB<sub>2</sub> monolayer structure shown in Fig. (a) consists of two atomic layers, where each Be atom is coordinated with six B atoms, and each B atom is coordinated with three Be atoms.</sec><sec>The lattice constants are <i>a</i> = <i>b</i> = 3.037 Å with a thickness of 0.554 Å. From the phonon spectrum calculations, the absence of imaginary modes indicates the dynamic stability of BeB<sub>2</sub> monolayer. The presence of a Dirac cone further suggests the excellent conductivity (Fig.(b)). Three stable adsorption sites (Be<sub>1</sub>: top of Be atoms; Be<sub>2</sub> and B<sub>2</sub>: bottom of Be and B atoms) are labeled in Fig. (a). Taking symmetry into account, we consider three pathways to evaluate the migration of Mg atom on BeB<sub>2</sub> monolayer (Fig.(c)). The corresponding lowest diffusion energy barrier is 0.04 eV along Path III. The stable configuration with the maximum adsorption Mg concentration is shown in Fig.(d), which generates a theoretical capacity of 5250 mA·h·g<sup>–1</sup>. The calculated average open-circuit voltage is 0.33 V. Based on <i>ab initio</i> molecular dynamics simulations, the total energy of BeB<sub>2,</sub> with Mg adsorbed, fluctuates within a narrow range, suggesting that BeB<sub>2</sub> can sustain structural stability after storing Mg at room temperature (Fig.(e)). Finally, for practical application, we investigate the adsorption and diffusion behavior of Mg on bilayer BeB<sub>2</sub>. Three configurations are considered: <i>AA</i> stacking (overlapping of Be atoms in upper layer with Be atoms in lower layer), <i>AB</i> stacking (overlapping of Be atoms in upper layer with B atoms in lower layer), and <i>AC</i> stacking (overlapping of Be atoms in upper layer with B—B bonds in lower layer). The most stable configuration is <i>AB</i> stacking (shown in Fig.(f)) with the interlayer spacing of 3.12 Å and the binding energy of –120.97 meV/atom. Comparing with the BeB<sub>2</sub> monolayer structure, the adsorption energy of Mg is –2.24 eV for Be<sub>1</sub>, –1.38 eV for B<sub>5</sub> site, and –1.90 eV for B<sub>4</sub> site, while the lowest diffusion energy barrier is 0.13 eV along the path of B<sub>5</sub>-Be<sub>3</sub>-B<sub>5</sub>. Therefore, according to the above-mentioned properties, we believe that BeB<sub>2</sub> monolayer can serve as an excellent MIBs anode material.</sec>

Bernstein spectral method for quasinormal modes and other eigenvalue problems

Spectral methods are now common in the solution of ordinary differential eigenvalue problems in a wide variety of fields, such as in the computation of black hole quasinormal modes. Most of these spectral codes are based on standard Chebyshev, Fourier, or some other orthogonal basis functions. In this work we highlight the usefulness of a relatively unknown set of non-orthogonal basis functions, known as Bernstein polynomials, and their advantages for handling boundary conditions in ordinary differential eigenvalue problems. We also report on a new user-friendly package, called SpectralBP, that implements Berstein-polynomial-based pseudospectral routines for eigenvalue problems. We demonstrate the functionalities of the package by applying it to a number of model problems in quantum mechanics and to the problem of computing scalar and gravitational quasinormal modes in a Schwarzschild background. We validate our code against some known results and achieve excellent agreement. Compared to continued-fraction or series methods, global approximation methods are particularly well-suited for computing purely imaginary modes such as the algebraically special modes for Schwarzschild gravitational perturbations.

Complex Modal Characteristic Analysis of a Tensegrity Robotic Fish's Body Waves.

A bionic robotic fish based on compliant structure can excite the natural modes of vibration, thereby mimicking the body waves of real fish to generate thrust and realize undulate propulsion. The fish body wave is a result of the fish body's mechanical characteristics interacting with the surrounding fluid. Thoroughly analyzing the complex modal characteristics in such robotic fish contributes to a better understanding of the locomotion behavior, consequently enhancing the swimming performance. Therefore, the complex orthogonal decomposition (COD) method is used in this article. The traveling index is used to quantitatively describe the difference between the real and imaginary modes of the fish body wave. It is defined as the reciprocal of the condition number between the real and imaginary components. After introducing the BCF (body and/or caudal fin) the fish's body wave curves and the COD method, the structural design and parameter configuration of the tensegrity robotic fish are introduced. The complex modal characteristics of the tensegrity robotic fish and real fish are analyzed. The results show that their traveling indexes are close, with two similar complex mode shapes. Subsequently, the relationship between the traveling index and swimming performance is expressed using indicators reflecting linear correlation (correlation coefficient (Rc) and p value). Based on this correlation, a preliminary optimization strategy for the traveling index is proposed, with the potential to improve the swimming performance of the robotic fish.

Crystal structure, mechanical, electronic, optical and thermoelectric characteristics of Cs2MCl6 (M = Se, Sn, Te and Ti) cubic double perovskites

The crystal structure, mechanical, electronic, optical and thermoelectric characteristics of Cs2MCl6 (M = Se, Sn, Te and Ti) cubic double perovskites are studied within GGA, GGA-mBJ and EV-GGA functionals. The M − Cl bond lengths are shorter and especially in Cs2TiCl6 double perovskite, which reflects the strong interaction between M and Cl atoms and this is correlated with its better chemical stability. The negativity of formation energy and Helmholtz free energy and no imaginary phonon modes throughout the Brillouin zone confirm the thermal, thermodynamic and dynamical stability of these double perovskites. Semiconductors Cs2MCl6 (M = Se, Sn, Te and Ti) double perovskites with flat conduction and valence bands, and an indirect band gap are p-type carriers. A high Seebeck coefficient, adequate ZT values ​​and non-toxicity make these compounds attractive for thermoelectric applications at high temperature and spintronic technology. The empty first conduction band corresponds to their band gap, and the transition occurs from Cl-p to (Se-p, Sn-p, Te-p and Ti-d). The high static dielectric constant and the intense peak of the real part in the ultraviolet energy range favor less the recombination rate of charge carriers and their use in optoelectronic devices. The indirect band gap, high absorption in ultraviolet energy, high static refractive index make these cubic double perovskites as ideal materials for solar cell applications.

DFT studies on structural stability, vibrational and linear and nonlinear optical properties of low-dimensional zinc sulfide: from the 3D bulk to the 2D monolayer and the 1D zigzag single-walled nanotubes

Through first-principles calculations, we investigate structural stability, vibrational and linear and nonlinear optical properties of the zinc sulfide (ZnS) in different periodic forms ranging from the 3D bulk to the 2D hexagonal monolayer and their corresponding 1D zigzag single-walled nanotubes. To first order, the electronic wave function on the ground state was constructed using linear combinations of Gaussian-type functions at the DFT/B3LYP level. Then, the Raman and IR spectrum is computed by adopting a Coupled-Perturbed-Hartree–Fock/Kohn–Sham (CPHF/KS) approach. Cohesive, relaxation, and rolling energies, elastic and piezoelectric constants, electronic and nuclear contributions to the polarizability tensor, and nonlinear first and second-order hyperpolarizability tensor components are reported. Our study shows that 3D and 2D forms are stable and show semiconducting behavior, good piezoelectric responses, and fascinating linear and nonlinear optical properties. For 1D single-walled nanotubes, dynamic stability is observed only for the smallest (6,0) nanotubes. For n > 6, imaginary mode frequencies in the simulated IR and Raman spectra indicate dynamic instability. A scanning mode procedure along the largest imaginary vibrational mode is applied in order to determine the stable structures of the largest (14,0), (18,0) and (22,0) ZnS nanotubes. After that, no more imaginary phonon frequencies are detected in their vibrational spectra. Their potential energy surface contains two minima between a saddle point corresponding to a slightly distorted nanotube structure. Our study proves that the zinc sulfide nanostructures possess diverse physical properties so useful for potential applications in nanoelectronics and for nanodevices.

Global structure optimization following imaginary phonon modes accelerated by machine learning potentials in Cu, Ag, and Au

Global structure optimization following imaginary phonon modes accelerated by machine learning potentials in Cu, Ag, and Au

Twists and Puckers: Tuning Crystal Chemistry in the La(AuxGe1-x)2 Compositional Series.

The physical properties of solid-state materials are closely tied to their crystal structure, yet our understanding of how competing structural arrangements energetically compare is limited. In this work, we explore how small differences in composition affect the structure in the La(AuxGe1-x)2 series of compounds, which comprises four unique structure types between LaGe2 and LaAu2. This family includes the previously unknown AlB2-type compound with stoichiometry La(Au0.375Ge0.625)2 as well as La(Au0.25Ge0.75)2, an intergrowth of the AlB2 and ThSi2 structure types. We then study the chemical forces driving the structure changes and use phonon band structure calculations and DFT-Chemical Pressure to evaluate atomic-size effects. These calculations show that the parent AlB2 structure type is disfavored in Au-rich compounds due to soft atomic motions along the c axis. The instability of AlB2-type LaAuGe is confirmed by the presence of imaginary modes in the phonon band structure that correspond to a "puckering" of the hexagonal AlB2-type lattice, resulting in the experimentally observed LiGaGe structure type. The impact of size effects is less clear for Au-poor compositions; instead, twisting the AlB2 structure type to form the ThSi2 type opens a pseudogap at the Fermi level in the electronic density of states. This investigation demonstrates how crystal structure in solid-state materials can be compositionally tuned based on balancing size and electronics when multiple structure types are in close thermodynamic competition.