Semiclassical Theory Research Articles

Thermoelectric transport properties of XAgP (X = Sr and Ba) from first principles

For thermoelectric applications those materials are of interest that have significant power factor (PF) and low lattice thermal conductivity, . Here we theoretically explore of two novel materials SrAgP and BaAgP using linearized Boltzmann transport equation with a single-mode relaxation time approach. We estimate the figure of merit zT by employing ab-initio calculations based on density functional theory and semiclassical Boltzmann transport theory. It is observed that at room temperature SrAgP exhibits slightly higher lattice thermal conductivity than BaAgP, which is mainly due to the large phonon group velocity. The relaxation time derived from deformation potential theory indicates a higher p-type PF for SrAgP compared to BaAgP over the entire temperature range. This provides an estimate for the figure of merit for the two materials. The low lattice thermal conductivity and higher PF make SrAgP a more promising thermoelectric material.

Dynamics and Entanglement in Quantum and Quantum-Classical Systems: Lessons for Gravity.

Motivated by quantum gravity, semiclassical theory, and quantum theory on curved spacetimes, we study the system of an oscillator coupled to two spin-1/2 particles. This model provides a prototype for comparing three types of dynamics: the full quantum theory, the classical oscillator with spin backreaction, and spins propagating on a fixed oscillator background. From calculations of oscillator and entanglement entropy evolution, we find the three systems give equivalent dynamics for sufficiently weak oscillator-spin couplings but deviate significantly for intermediate couplings. These results suggest that semiclassical dynamics with backreaction does not provide a suitable intermediate regime between quantum gravity and quantum theory on curved spacetime.

The electronic, thermoelectric and optical properties of Janus In2STe monolayer: A first-principles investigation

In this present work, comprehensive investigations of the electronic structure, thermoelectric and optical properties of the Janus In2STe monolayer have been performed using density functional theory combined with the semi-classical Boltzmann transport theory. A direct bandgap semiconductor has been predicted for Janus In2STe monolayer. Compared to the InS and InTe monolayers, it is observed that the electrical conductivity was enhanced for the Janus In2STe monolayer, reaching 10.81×1019(Ω−1m−1s−1) with small p-type doping. At room temperature, our calculations predicted high Seebeck coefficients and electronic figure of merit for InS, InTe and Janus In2STe monolayers. Of interest, the Janus In2STe monolayer exhibited the highest Seebeck coefficient value of around 1110 μV/K, with an electronic figure of merit of 0.97, indicating its high potential for thermoelectric applications. Moreover, we have addressed the optical properties such as dielectric constant, refractive index, reflectivity, extinction coefficient, and absorption coefficient, versus the energy for InS, InTe, and Janus In2STe monolayers. The predicted absorption coefficient in the visible region was found to be high with a value of 107 cm−1, showing the future potential applications of InS, InTe, and Janus In2STe monolayers in optoelectronic and optical devices.

Hot and cold phonons in electrically biased graphene

Based on first-principles calculations and semiclassical transport theory, we study the nonequilibrium phonon distribution in graphene in the presence of electrical current. In addition to the hot-phonon effect, we observe a cooling of phonon modes at the same time. Interestingly, the presence of electric current along the direction connecting $K$ and ${K}^{\ensuremath{'}}$ valleys induces an opposite dipolelike temperature distribution in the two valleys and at the $\mathrm{\ensuremath{\Gamma}}$ point. This leads to a ``high-order'' valley polarization of phonon distribution between $K$ and ${K}^{\ensuremath{'}}$. Based on the nonequilibrium phonon distribution, we furthermore study their effect on the lattice parameters and find a negative current-induced expansion coefficient. Similar to graphene's negative thermal expansion, this is rooted in the dominant contribution of out-of-plane acoustic phonons, which do not couple directly to electrons, but gain energy from in-plane phonons through anharmonic scattering.

Bulk second-order optical nonlinearities in centrosymmetric materials

The semiclassical theory of electrical susceptibility predicts null even-order susceptibilities for all centrosymmetric materials. However, second harmonic generation and other even-order nonlinear optical phenomena are often seen in them. Contributions due to magnetic dipoles, bulk quadrupoles, or symmetry ruptures describe many of these effects, but not all of them, as can be seen in some experiments recalled here. This work presents an extension of the theory that renders more general expressions for susceptibilities. According to these expressions, bulk even-order susceptibilities may eventually transform as pseudo-tensors and, therefore, may have nonzero values in centrosymmetric structures. We show examples of how this fact provides an alternative or simpler explanation of the conflicting experiments. Our result may have important implications in lasing, communications, imaging, quantum optics, quantum computing, and other fields, as it widens the family of materials in which to look for nonlinear effects such as second harmonic generation, the Pockels effect, spontaneous parametric downconversion, and other phenomena.

Radical addition and H abstraction reactions in C2H2, C2H4, and C2H6: A gateway for ethyl- and vinyl-bearing molecules in the interstellar medium

Context. Recent interstellar detections include a significant number of molecules containing vinyl (C2H3) and ethyl (C2H5) groups in their structure. For several of these molecules, there is no clear experimental or theoretical evidence that supports their formation from simpler precursors. Aims. We carried out a systematic search of viable reactions starting from closed-shell hydrocarbons containing two carbon atoms (ethane, C2H6; ethylene, C2H4; and acetylene, C2H2), with the goal of determining viable chemical routes for the formation of vinyl and ethyl molecules on top of interstellar dust grains. Methods. We used density functional theory calculations in combination with semiclassical instantem theory to derive the rate coefficients for the radical-neutral surface reactions. The effect of a surface was modeled through an implicit surface approach, profiting from the weak interaction between the considered hydrocarbons and the dust surfaces. Results. Our results show that both H and OH radicals are key in converting acetylene and ethylene into more complex radicals that are liable to continue reacting and to form interstellar complex organic molecules. The relevant reactions, for example OH additions, present rate constants above 101 s−1 that are likely competitive with OH diffusion on grains. Similarly, H atom addition to acetylene and ethylene is a very fast process, with rate constants above 104 s−1 in all cases, and is greatly enhanced by quantum tunneling. Hydrogen abstraction reactions are less relevant, but may play a role in specific cases involving the OH radical. Reactions with other radicals NH2 and CH3 are likely to have much less impact on the chemistry of ethyl- and vinyl-bearing molecules. Conclusions. The effective formation at low temperatures of four radicals (C2H3, C2H5, C2H2OH, and C2H4OH) through our proposed mechanism opens the gate for the formation of complex organic molecules, and indicates a potential prevalence of OH-bearing molecules on the grain. Following our suggested reaction pathway, we explain the formation of many of the newly detected molecules, and propose new molecules for detection. Our results reinforce the recent view on the importance of the OH radical in interstellar surface chemistry.

ℏ2 expansion of the transmission probability through a barrier.

Ninety years ago, Wigner derived the leading order expansion term in ℏ2 for the tunneling rate through a symmetric barrier. His derivation included two contributions: one came from the parabolic barrier, but a second term involved the fourth-order derivative of the potential at the barrier top. He left us with a challenge, which is answered in this paper, to derive the same but for an asymmetric barrier. A crucial element of the derivation is obtaining the ℏ2 expansion term for the projection operator, which appears in the flux-side expression for the rate. It is also reassuring that an analytical calculation of semiclassical transition state theory (TST) reproduces the anharmonic corrections to the leading order of ℏ2. The efficacy of the resulting expression is demonstrated for an Eckart barrier, leading to the conclusion that especially when considering heavy atom tunneling, one should use the expansion derived in this paper, rather than the parabolic barrier approximation. The rate expression derived here reveals how the classical TST limit is approached as a function of ℏ and, thus, provides critical insights to understand the validity of popular approximate theories, such as the classical Wigner, centroid molecular dynamics, and ring polymer molecular dynamics methods.

Evaluating the Atmospheric Loss of H2 by NO3 Radicals: A Theoretical Study

Molecular hydrogen (H2) is now considered among the most prominent substitute for fossil fuels. The environmental impacts of a hydrogen economy have received more attention in the last years, but still, the knowledge is relatively poor. In this work, the reaction of H2 with NO3 radical (the dominant night-time detergent of the atmosphere) is studied for the first time using high-level composite G3B3 and modification of high accuracy extrapolated ab initio thermochemistry (mHEAT) methods in combination with statistical kinetics analysis using non-separable semi-classical transition state theory (SCTST). The reaction mechanism is characterized, and it is found to proceed as a direct H-abstraction process to yield HNO3 plus H atom. The reaction enthalpy is calculated to be 12.8 kJ mol−1, in excellent agreement with a benchmark active thermochemical tables (ATcT) value of 12.2 ± 0.3 kJ mol−1. The energy barrier of the title reaction was calculated to be 74.6 and 76.7 kJ mol−1 with G3B3 and mHEAT methods, respectively. The kinetics calculations with the non-separable SCTST theory give a modified-Arrhenius expression of k(T) = 10−15 × T0.7 × exp(−6120/T) (cm3 s−1) for T = 200–400 K and provide an upper limit value of 10−22 cm3 s−1 at 298 K for the reaction rate coefficient. Therefore, as compared to the main consumption pathway of H2 by OH radicals, the title reaction plays an unimportant role in H2 loss in the Earth’s atmosphere and is a negligible source of HNO3.

Electron transport with the McKelvey–Shockley flux method: The effect of electric field and electron–phonon scattering

The McKelvey–Shockley (McK–S) flux method is a semi-classical transport theory that captures ballistic and non-equilibrium effects and can treat carrier flow from the nano-scale to the macro-scale. This work introduces a revised formulation of the McK–S flux equations for electron transport, in order to resolve the energy dependence of the fluxes, capture the effect of electric field, and include acoustic/optical phonon scattering. This updated McK–S formalism is validated by simulating electron transport across a finite-length semiconductor under the influence of a constant electric field under varying conditions, from ballistic to diffusive and from near-equilibrium to non-equilibrium, and benchmarked against solutions of the Boltzmann transport equation (BTE). The McK–S results display good agreement with those of the BTE, including the directed fluxes and heating profiles, with the electron density showing larger differences when far from equilibrium. Compared to other more rigorous techniques, the McK–S flux method is physically intuitive and computationally efficient and, thus, well suited to treat systems that are complex and/or span multiple length scales.

Evidence of two-spinon bound states in the magnetic spectrum of Ba3CoSb2O9

Recent inelastic neutron scattering (INS) experiments of the triangular antiferromagnet Ba$_3$CoSb$_2$O$_9$ revealed strong deviations from semiclassical theories. We demonstrate that key features of the INS data are well reproduced by a parton Schwinger boson theory beyond the saddle-point approximation. The measured magnon dispersion is well reproduced by the dispersion of two-spinon bound states (poles of the emergent gauge fields propagator), while the low-energy continuum scattering is reproduced by a quasifree two-spinon continuum, suggesting that a free-spinon gas is a good initial framework to study magnetically ordered states near a quantum melting point.

Hierarchical structure in the trace formula* *Dedicated to Michael Berry, to mark his 80th birthday.

Guztwiller’s trace formula is central to the semiclassical theory of quantum energy levels and spectral statistics in classically chaotic systems. Motivated by recent developments in random matrix theory and number theory, we elucidate a hierarchical structure in the way periodic orbits contribute to the trace formula that has implications for the value distribution of spectral determinants in quantum chaotic systems.

Signatures of Exciton Orbits in Quantum Mechanical Recurrence Spectra of Cu_{2}O.

The seminal work by Kazimierczuk etal. [Nature 514, 343 (2014)10.1038/nature13832] has shown the existence of highly excited exciton states in a regime, where the correspondence principle is applicable and quantum mechanics turns into classical mechanics; however, any interpretation of exciton spectra based on a classical approach to excitons is still missing. Here, we close this gap by computing and comparing quantum mechanical and semiclassical recurrence spectra of cuprous oxide. We show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a scaling transformation, can be directly related to classical periodic exciton orbits. The application of semiclassical theories to exciton physics requires the detailed analysis of the classical exciton dynamics, including three-dimensional orbits, which strongly deviate from hydrogenlike Keplerian orbits. Our findings illuminate important aspects of excitons in semiconductors by directly relating the quantum mechanical band structure splittings of excitons to the corresponding classical exciton dynamics.

Effective dynamics of interacting fermions from semiclassical theory to the random phase approximation

I review results concerning the derivation of effective equations for the dynamics of interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective theories, increasing in precision, can be distinguished: the semiclassical theory given by the Vlasov equation, the mean-field theory given by the Hartree–Fock equation, and the description of the dominant effects of non-trivial entanglement by the random phase approximation. Particular attention is given to the discussion of admissible initial data, and I present an example of a realistic quantum quench that can be approximated by Hartree–Fock dynamics.

First principles DFT analysis on the diffusion kinetics of hydrogen isotopes through bcc iron (Fe): Role of temperature and surface coverage

The diffusion of interstitial H, D, and T in Fe metal at different temperature are evaluated using ab-initio density functional theory and transition state theory. The thermal expansion coefficient, Helmholtz free energy of activation, jump factor of diffusion was determined by use of activation energy and phonon calculations. The calculated diffusion coefficient was well described by a constant activation energy, (D = D0exp (-Ea)/kT)) with Ea = 0.016, 0.041, and 0.050 eV and D0 = 1.042 × 10−7, 0.736 × 10−7 and 0.572x10−7 m2.s−1for H, D, and T, respectively using harmonic transition state theory (hTST) with temperature correction. The calculated permeability and solubility also followed the Arrhenius relation.The earlier experimentally reported higher diffusivity of H atom at lower temperatures than that at higher temperature (200–600 K) was well explained by Wigner + hTST model with temperature correction and semi-classical transition state theory (SC-TST). The present computed results followed the similar trend of experimental findings. Further, the ideal fracture energy was evaluated using the Born-Haber thermodynamic cycle for varied coverage of H, D and T to account for decohesion-based embrittlement. The lighter H atom was seen to cause more decohesion-based embrittlement compared to D and T due to reduced cohesion. Additionally, the effect of temperature on ideal fracture energy was evaluated for H, D and T in Fe. The decohesion-based embrittlement was increased with increase in the temperature for H, D and T up to certain temperature (for H lower than 500 K, for D around 500 K and for T above 500 K) but with further increase in the temperature, the ideal fracture energy was reduced due to decrease in the adsorption energy and increase in the solution enthalpy of H isotopes. Further, the path and kinetics of dissociation and reassociation of H2 molecule were established on Fe (100) surface at 0.5 and 2.0 ML coverage. At lower concentration (0.5 ML), dissociation of H2 molecule on Fe (100) surface was favored, whereas at high concentration (2.0 ML), reassociation of H2 molecule was favored.

Thickness and defect dependent electronic, optical and thermoelectric features of hbox {WTe}_2

Transition metal dichalcogenides (TMDs) receive significant attention due to their outstanding electronic and optical properties. In this study, we investigate the electronic, optical, and thermoelectric properties of single and few layer hbox {WTe}_2 in detail utilizing first-principles methods based on the density functional theory (DFT). Within the scope of both PBE and HSE06 including spin orbit coupling (SOC), the simulations predict the electronic band gap values to decrease as the number of layers increases. Moreover, spin-polarized DFT calculations combined with the semi-classical Boltzmann transport theory are applied to estimate the anisotropic thermoelectric power factor (Seebeck coefficient, S) for hbox {WTe}_2 in both the monolayer and multilayer limit, and S is obtained below the optimal value for practical applications. The optical absorbance of hbox {WTe}_2 monolayer is obtained to be slightly less than the values reported in literature for 2H TMD monolayers of hbox {MoS}_2, hbox {MoSe}_2, and hbox {WS}_2. Furthermore, we simulate the impact of defects, such as vacancy, antisite and substitution defects, on the electronic, optical and thermoelectric properties of monolayer hbox {WTe}_2. Particularly, the Te-hbox {O}_2 substitution defect in parallel orientation yields negative formation energy, indicating that the relevant defect may form spontaneously under relevant experimental conditions. We reveal that the electronic band structure of hbox {WTe}_2 monolayer is significantly influenced by the presence of the considered defects. According to the calculated band gap values, a lowering of the conduction band minimum gives rise to metallic characteristics to the structure for the single Te(1) vacancy, a diagonal Te line defect, and the Te(1)-hbox {O}_2 substitution, while the other investigated defects cause an opening of a small positive band gap at the Fermi level. Consequently, the real (varepsilon _1(omega )) and imaginary (varepsilon _2(omega )) parts of the dielectric constant at low frequencies are very sensitive to the applied defects, whereas we find that the absorbance (A) at optical frequencies is less significantly affected. We also predict that certain point defects can enhance the otherwise moderate value of S in pristine hbox {WTe}_2 to values relevant for thermoelectric applications. The described hbox {WTe}_2 monolayers, as functionalized with the considered defects, offer the possibility to be applied in optical, electronic, and thermoelectric devices.

Thermal transport and thermoelectric properties of alkali-metal telluride Na2Te from first-principles study

The excellent thermoelectric performance of alkali-metal telluride Na2Te has been systematically studied from the electronic and phonon transport properties within the density functional theory combined with the Boltzmann transport theory framework. The phonon dispersion without any imaginary mode demonstrates that the Na2Te compound is dynamically stable. The calculated lattice thermal conductivity is as small as 3.01 W m−1 K−1 at room temperature, suggesting that Na2Te can serve as a promising thermoelectric material. The related anharmonic effect parameters, phonon lifetime and Grüneisen parameter, are discussed to further explain the lattice thermal conductivity. Also, the electronic transport parameters, such as Seebeck coefficient S, electrical conductivity σ, and electronic thermal conductivity κe, are investigated to determine the thermoelectric performance by utilizing the semi-classical Boltzmann transport theory. The final figure of merit ZT can be evaluated based on the lattice thermal conductivity and the corresponding electronic transport coefficients. The maximum ZT of 1.53 can be achieved at a carrier concentration n = 3.08 × 1020 cm−3 for p-type Na2Te at T = 900 K, greatly larger than that of the n-type Na2Te (0.86), suggesting that the Na2Te can be a potential p-type thermoelectric material.

First-principles calculations to investigate new ferromagnetic quaternary Heusler alloys FeZrTiZ(Z=Si, Sn, Pb): Compatible for spin polarized device and waste heat recovery applications

In this article, we have studied the structural, electronic, magnetic, mechanical and thermoelectric properties of new quaternary Heusler alloys FeZrTiZ (Z = Si, Sn, Pb), using ab-initio simulation methods. Our structural phase stability studies show that all these compounds stabilize in Y1-type structure and showing ferromagnetic ground state. From the calculation based on Generalized Gradient Approximation method we found that all these alloys are having half metallic behavior with the band gap value of around 1eV in one of the spin channels. The half metallic nature of these alloys is a precursor for high spin polarization. These alloys also satisfy the Slater-Pauling rule with magnetic moment of MT = NV − 18 for half metallicity and as a result they have a total magnetic moment of 2μB. The calculated elastic constants convey the mechanical stability of these alloys and though they have a cubic structure they exhibit strong mechanical anisotropy with ductile behavior. The Seebeck coefficient and the thermoelectric figure of merit were calculated using semi-classical Boltzmann transport theory. The highest Seebeck coefficient value for FeZrTiZ (Z = Si, Sn, Pb) is 110.5 μV/K, 121.8 μV/K and 100.6 μV/K respectively at the temperature 900 K, 600 K and 750 K and the corresponding figure of merit is 0.85, 0.9 and 0.59. The observation of half metallicity indicates that these materials can be used in spintronic devices and the observation of substantial thermoelectric figure of merit suggests that these materials can be used in waste heat recovery.

Heavy-Atom Quantum Tunnelling in Spin Crossovers of Nitrenes.

We simulate two recent matrix‐isolation experiments at cryogenic temperatures, in which a nitrene undergoes spin crossover from its triplet state to a singlet state via quantum tunnelling. We detail the failure of the commonly applied weak‐coupling method (based on a linear approximation of the potentials) in describing these deep‐tunnelling reactions. The more rigorous approach of semiclassical golden‐rule instanton theory in conjunction with double‐hybrid density‐functional theory and multireference perturbation theory does, however, provide rate constants and kinetic isotope effects in good agreement with experiment. In addition, these calculations locate the optimal tunnelling pathways, which provide a molecular picture of the reaction mechanism. The reactions involve substantial heavy‐atom quantum tunnelling of carbon, nitrogen and oxygen atoms, which unexpectedly even continues to play a role at room temperature.

Measurement of n- and l-resolved State-selective Charge Exchange in Ar8+ Collision with He

The state-resolved capture cross sections for principal n and orbital angular momentum l play an important role in modeling soft X-ray emissions induced by charge exchange for many astrophysical environments. However, the empirical and semiclassical theories used to produce these data of n- and l-resolved state-selective capture have not been well tested. Using the cold target recoil ion momentum spectroscopy apparatus at Fudan University, we perform a series of measurements of Ar8+ ion charge exchange with He in the collision energy range from 1.4 to 20 keV u−1. We find that electrons are mainly captured in the n = 4 state of Ar7+ ions. This agrees with the prediction of the scaling law for n capture. Moreover, the relative cross sections are reported for 4s-, 4p-, 4d-, and 4f-resolved state-selective capture. The often used analytical l distributions in the astrophysical literature are evaluated by comparing to the measurements.

Large enhancement of thermoelectric properties of CoSb3 tuned by uniaxial strain

Skutterudite (CoSb3), as a promising thermoelectric material for medium-temperature applications, has attracted considerable interest. However, improving its thermoelectric properties is still an important problem. In this work, first-principles calculations combined with semiclassical Boltzmann theory are adopted to investigate the electronic transport and thermoelectric properties of CoSb3 under external strain. It is found that both tensile strain and compressive strain reduce the bandgap of the CoSb3 system and influence the Co_d orbitals near the Fermi level. Further, the steepness of the valence band near the Fermi level along the M–G and G–R directions are changed by external strain to different extents, which directly affects the Seebeck coefficient and the ratio of conductivity to relaxation time; both of these values are optimized under tensile and compressive strain. Therefore, the power factor of CoSb3 is greatly enhanced under external strain. At 700 K, the maximum power factors under strains of − 1% and 3% are 23.77% and 47.63% higher than those without strain, respectively. Thus, the thermoelectric properties of CoSb3 can be greatly improved by external strain.