Semiclassical Theory Research Articles

Asymptotically flat vacuum solutions in order-reduced semiclassical gravity

We investigate the effects of quantum backreaction on the Schwarzschild geometry in the semiclassical approximation. The renormalized stress-energy tensor (RSET) of a scalar field is modelled via an order reduction of the analytical approximation derived by Anderson, Hiscock and Samuel (AHS). As the resulting AHS semiclassical Einstein equations are of fourth-derivative order in the metric, we follow a reduction of order prescription to shrink the space of solutions. Motivated by this prescription, we develop a method that allows to obtain a novel analytic approximation for the RSET that exhibits all the desired properties for a well-posed RSET: conservation, regularity, and correct estimation of vacuum-state contributions. We derive a set of semiclassical equations sourced by the order-reduced AHS-RSET in the Boulware state. We classify the self-consistent solutions to this set of field equations, discuss their main features and address how well they resemble the solutions of the higher-order semiclassical theory. Finally, we establish a comparison with previous results in the literature obtained through the Polyakov approximation for minimally coupled scalar fields.

Transport and thermoelectric performance of Fluorine functionalized Ge-carbide sheets

Based on density functional theory simulations, GW approximation + BSE and the semi-classical Boltzmann transport theory, electronic ,optical and thermoelectric response of bidimensional fluorinated Ge-carbides are investigated. Three configurations are considered, namely F-CGe, CGe-F, F-CGe-F to explore the effect of both fluorination distribution and coverage. It is shown that the conduction (valence) band is shifted upwards (downwards) when F decorates C-atoms (Ge-atoms) which tunes the gap energy. Furthermore, full fluorination makes CGe sheet better dielectric structure. The maximum reflectivity and absorption reveal that F-CGe-F structure exhibits better optical response, unlike its two counterparts constrained to absorb incident photon energy to the UV region only. The maximum polarization values are found in the visible region for the half fluorinated structure F-CGe and in the UV spectrum for F-CGe-F and CGe-F. The Fluorination also improves the transport properties of CGe which significantly increases its merit factor (ZT) at room temperature. Th three compounds are found to exhibit an ultralow lattice conductivity which leads and a record high ZT up to 0.65, 0.77, and 0.81 at 900 K in CGe-F, F-CGe and F-CGe-F respectively. Our results evaluate the potential of fluorinated CGe sheets as suitable thermoelectric materials at the ambient temperature.

Molecular vibrations in the presence of velocity-dependent forces.

A semiclassical theory of small oscillations is developed for nuclei that are subject to velocity-dependent forces in addition to the usual interatomic forces. When the velocity-dependent forces are due to a strong magnetic field, novel effects arise-for example, the coupling of vibrational, rotational, and translational modes. The theory is first developed using Newtonian mechanics and we provide a simple quantification of the coupling between these types of modes. We also discuss the mathematical structure of the problem, which turns out to be a quadratic eigenvalue problem rather than a standard eigenvalue problem. The theory is then re-derived using the Hamiltonian formalism, which brings additional insight, including a close analogy to the quantum-mechanical treatment of the problem. Finally, we provide numerical examples for the H2, HT, and HCN molecules in a strong magnetic field.

Semiclassical initial value representation: From Møller to Miller. II.

As shown by W. H. Miller in a seminal article [J. Chem. Phys. 53, 3578 (1970)], the most convenient and accurate semiclassical (SC) theory of molecular scattering in action-angle coordinates is based on the initial value representation (IVR) and the use of shifted angles, which are different from the natural angles usually used in the quantum and classical treatments. Here, we show for an inelastic molecular collision that the initial and final shifted angles define three-segment classical paths that are exactly those involved in the classical-limit of Tannor-Weeks quantum scattering theory [J. Chem. Phys. 98, 3884 (1993)], provided that the translational wave packets |g+⟩ and |g-⟩ into play in this theory are both taken at |0⟩. Assuming this to be the case, using van Vleck propagators, and applying the stationary phase approximation, Miller's SCIVR expression of S-matrix elements is found, with an additional cut-off factor canceling the energetically forbidden transition probabilities. This factor, however, is close to unity in most practical cases. Furthermore, these developments show that the Møller operators underlie Miller's formulation, thus confirming, for molecular collisions, the results recently established in the simpler case of light-induced rotational transitions [L. Bonnet, J. Chem. Phys. 153, 174102 (2020)]. Last but not least, we show, based on the previous results, that for processes involving long-range anisotropic forces, implementing the Skinner-Miller method [Chem. Phys. Lett. 300, 20 (1999)] in shifted coordinates makes its predictions both easier and more accurate than in natural coordinates.

De Haas van Alphen oscillations in hybridization-gap insulators as a sudden change in the diamagnetic moment of Landau levels

This note revisits the semiclassical theory of quantum oscillations in hybridization-gap insulators, and shows that the physical origin of the oscillations, at T = 0 K, is a sudden change in the diamagnetic moment of each Landau level as it crosses the hybridized region of the valence band.

Negative transverse magnetoresistance due to the negative off-diagonal mass in linear dispersion materials

This study calculated the magnetoresistance (MR) in the Dirac electron system, Dresselhaus–Kip–Kittel (DKK) model, and nodal-line semimetals based on the semiclassical Boltzmann theory, with particular focus on the detailed energy dispersion structure. The negative off-diagonal effective-mass was found to induce negative transverse MR owing to the energy dispersion effect. The impact of the off-diagonal mass was more prominent in case of a linear energy dispersion. Further, Dirac electron systems could realize negative MR even if the Fermi surface was perfectly spherical. The obtained negative MR in the DKK model may explain the long-standing mystery in p-type Si.

Structural, electronic, elastic and thermal properties of Cr-doped U3Si2: A DFT study

Alloying has been considered as an effective strategy to make up for the poor oxidation corrosion resistance of U3Si2. However, the theoretical studies on alloyed U3Si2 are rarely reported. In this study, the structural, electronic, elastic and thermal properties of 10at% Cr-doped U3Si2 were studied using first principles calculations and semiclassical Boltzmann transport theory. Our results show that the U3Si1.5Cr0.5 phase is determined to be thermodynamically, dynamically and elastically stable, and U2.5Si2Cr0.5 phase is dynamically and elastically stable. U3Si1.5Cr0.5 is more stable than U2.5Si2Cr0.5 from the thermodynamic calculation results. From the calculated electronic structure results, a mixture of ionic and metallic bonds dominates the bonding of Cr-doped U3Si2. They are ductile materials compared to the brittleness of U3Si2 according to the results of B/G ratio, Cauchy pressure and Poisson's ratio. Moreover, U3Si1.5Cr0.5 is a nearly elastic isotropic material, while U2.5Si2Cr0.5 exhibits strong anisotropy. The thermal conductivity of Cr-alloyed U3Si2 is dominated by the electronic contribution at high temperature, which is lower than U3Si2 but higher than UO2 at service temperature and increases with temperature. Therefore, in addition to significantly improving the resistance to oxidation and corrosion of U3Si2, Cr doping can also convert the brittleness of U3Si2 into toughness and improve its machinability, albeit at the reasonable expense of some mechanical properties and thermal conductivities, while maintaining the high uranium density of U3Si2 fuel form. The results of this work may provide useful clues for the application and improvement of uranium silicide fuels.

Semiclassical Boltzmann magnetotransport theory in anisotropic systems with a nonvanishing Berry curvature

Understanding the transport behavior of an electronic system under the influence of a magnetic field remains a key subject in condensed matter physics. Particularly in topological materials, their nonvanishing Berry curvature can lead to many interesting phenomena in magnetotransport owing to the coupling between the magnetic field and Berry curvature. By fully incorporating both the field-driven anisotropy and inherent anisotropy in the band dispersion, we study the semiclassical Boltzmann magnetotransport theory in topological materials with a nonvanishing Berry curvature. We show that as a solution to the Boltzmann transport equation the effective mean-free-path vector is given by the integral equation, including the effective velocity arising from the coupling between the magnetic field, Berry curvature and mobility. We also calculate the conductivity of Weyl semimetals with an isotropic energy dispersion, and find that the coupling between the magnetic field and Berry curvature induces anisotropy in the relaxation time, showing a substantial deviation from the result obtained assuming a constant relaxation time.

Modification of Bekenstein-Hawking entropy of cylindrical symmetric black hole by Lorentz breaking theory

According to Lorentz breaking theory, WKB approximation theory, quantum tunneling radiation theory and the beyond semi-classical theory, the fermions dynamic equation in the space-time of a cylindrical symmetric black hole is modified more accurately. On this basis, the characteristics of the quantum tunneling radiation of such black holes and the new expressions of the modified temperature and Bekenstein-Hawking entropy of the black hole are studied. A series of results obtained in this paper are discussed in depth.

Significantly reinforced thermoelectric performance in the novel 1T-Au6Se2 monolayer

Ultra-low lattice thermal conductivity has long been a requirement for the high thermoelectric properties of materials. In this work, the novel 1T-Au6Se2 monolayer was obtained by introducing Au6 clusters into the selenide monolayer, and its electrical and thermal transport characteristics are investigated using first-principles computations supplemented with semi-classical Boltzmann transport theory. The calculation shows that the 1T-Au6Se2 monolayer exhibits ultra-low lattice thermal conductivity and excellent thermoelectric properties owing to its low phonon frequency, group velocity, and extremely strong anharmonicity. Based on strain engineering from 0% to 2%, the lattice thermal conductivity further reduces by restricting the thermal transport on the premise of maintaining outstanding electrical transport properties in the p-type doped system. Thence, the value of ZT for the p-type system increases nearly by 70% compared with the non-stressed state at 700 K. Our investigation indicates the ultra-low thermal conductivity and high ZT of the 1T-Au6Se2 monolayer that might be prepared in the lab, providing new insights into enhancing the thermoelectric performance of the material in the future.

Modeling and analyzing near-junction thermal transport in high-heat-flux GaN devices heterogeneously integrated with diamond

Gallium nitride (GaN) electronic devices possess excellent electrical characteristics that make them promising for advanced power and radiofrequency device applications. However, elevated channel temperatures associated with localized Joule heating degrade the device reliability and limit the device performance. To address this, recent intensive efforts have heterogeneously integrated diamond, the best thermal conductor among three-dimensional materials, near the device junction and have fabricated GaN-on-diamond devices. Numerous efforts have also been made to investigate their thermal characteristics via finite element simulations. The majority of these efforts have adopted several simplifying assumptions to facilitate thermal analysis and reduce computational loads. However, few have examined the impact of these assumptions on the device junction temperature. Here, we evaluate this impact by constructing a three-dimensional near-junction thermal transport model for GaN-on-diamond devices and calculating the temperature- and thickness-dependent GaN thermal conductivity utilizing semiclassical phonon transport theory. We further explore the influence of several near-junction thermal design parameters, including GaN layer and diamond substrate thicknesses, GaN/diamond thermal boundary resistance, and gate pitch and width, on the device junction temperature. Overall, this work may provide detailed guidelines and best practices for modeling and analyzing near-junction thermal transport in high-heat-flux GaN devices heterogeneously integrated with diamond.

Properties of the double half-heusler alloy ScNbNi2Sn2 with respect to structural, electronic, optical, and thermoelectric aspects

In the current work, the structural, electronic, thermoelectrics, and optical characteristics of the double half Heusler (DHH) ScNbNi2Sn2 compound are reported for the first time using density functional theory (DFT). The computed band structures show typical semiconductor behavior with an indirect bandgap (0.47 eV) using EV-GGA approximation. We also investigated the optical properties such as the dielectric function, optical conductivity, refractive index. Boltzmann's semiclassical theory attempts to explain a simulation concept in the BoltzTrap software, and the findings were presented and analyzed in terms of electrical conductivity, electronic and lattice thermal conductivities, the Seebeck coefficient, and the Figure of merit over a 50 K–1000 K temperature range. At room temperature, with a low magnitude of lattice thermal conductivity (κL) (5.30776 W/m. K) and a maximum value of the merit factor (ZT) is 0.64 at 900 K for ScNbNi2Sn2 compound is observed. These findings suggest that our material may be a viable option for use in high-temperature thermoelectric devices. We calculated (S, (σ/τ), (ke/τ)) along the x, y, and z axes utilizing the EV-GGA method. We found out that our compound is thermoelectrically anisotropic. We have also studied in EV-GGA the effect of the carrier concentration on the Seebeck coefficnet at T = 600 K. The maximum value of S is 356.9905 μV/K with n=3.04×1019Cm−3 within GGA and EV-GGA respectively.

Ground-state bistability of cold atoms in a cavity

We experimentally demonstrate an optical bistability between two hyperfine ground states of trapped, cold atoms, using a single mode of an optical resonator in the collective strong coupling regime. Whereas in the familiar case, the bistable region is created through atomic saturation, we report an effect between states of high quantum purity, which is essential for future information storage. The source of nonlinearity is a cavity-assisted pumping between ground states of the atoms and the stability depends on the intensity of two driving lasers. We interpret the phenomenon in terms of the recent paradigm of first-order, driven-dissipative phase transitions, where the transmitted and driving fields are understood as the order and control parameters, respectively. A semiclassical mean-field theory is invoked to describe the nontrivial two-dimensional phase diagram arising from the competition of the two drive. The saturation-induced bistability is recovered for infinite drive in one of the controls. The order of the transition is confirmed experimentally by hysteresis in the order parameter when either of the two control parameters is swept repeatedly across the bistability region.

First-principles study on the thermoelectric properties of Sr2Si and Sr2Ge

The development of environmentally friendly thermoelectric materials composed of earth-abundant, non-toxic elements is highly desirable in thermoelectric technology. In this study, the thermoelectric properties of n-type doped Sr2Si and Sr2Ge were systematically investigated using first-principles density functional theory calculations combined with semi-classical Boltzmann transport theory. The multi-band feature in the conduction band of Sr2Ge leads to a higher Seebeck coefficient than Sr2Si, resulting in a higher power factor. The phonon transport calculations using third-order perturbation theory predict ultra-low lattice thermal conductivity of 0.42 Wm−1K−1 for Sr2Si and 0.33 Wm−1K−1 for Sr2Ge at 900 K. The maximum figure of merit ZT is 1.44 for Sr2Ge, which is approximately 1.25 times higher than that of 1.15 for Sr2Si at 900 K. Our results indicate that the Sr2Ge and Sr2Si are promising candidates for high-performance thermoelectric materials.

Third-order intrinsic anomalous Hall effect with generalized semiclassical theory

The linear intrinsic anomalous Hall effect (IAHE) and second-order IAHE have been intensively investigated in time-reversal broken systems. However, as one of the important members of the nonlinear Hall family, the investigation of third-order IAHE remains absent due to the lack of an appropriate theoretical approach, although the third-order extrinsic AHE has been studied within the framework of first- and second-order semiclassical theory. Herein, we generalize the semiclassical theory for Bloch electrons under the uniform electric field up to the third-order using wavepacket method and based on which we predict that the third-order IAHE can also occur in time-reversal broken systems. Same as the second-order IAHE, we find the band geometric quantity, the second-order field-dependent Berry curvature arising from the second-order field-induced positional shift, plays a pivotal role to observe this effect. Moreover, with symmetry analysis, we find that the third-order IAHE, as the leading contribution, is supported by 15 time-reversal broken 3D magnetic point groups (MPGs), corresponding to a wide class of antiferromagnetic (AFM) materials. Guided by the symmetry arguments, a two-band model is chosen to demonstrate the generalized theory. Furthermore, the generalized third-order semiclassical theory depends only on the properties of Bloch bands, implying that it can also be employed to explore the IAHE in realistic AFM materials, by combining with first-principles calculations.

Thermal rate of transmission through a barrier: Exact expansion of up to and including terms of order ℏ4

Nine decades after Wigner's formulation of quantum rate theory, his celebrated result was recently generalized to the asymmetric barrier using an exact first-order expansion of the transmission probability in terms of ${\ensuremath{\hbar}}^{2}$. This paper extends the first-order quantum correction to second-order correction of order ${\ensuremath{\hbar}}^{4}$ for the thermally averaged transmission probability through an arbitrary barrier. The derivation employs a systematic expansion of the projection operator onto products and the thermal distribution which involves a Taylor expansion of the potential about the barrier up to eighth order. The resulting exact analytical expression is calibrated with numerical calculations of several model potentials and shows excellent agreement when the ${\ensuremath{\hbar}}^{4}$ term is included. In comparison, the semiclassical transition state theory cannot reproduce the correct ${\ensuremath{\hbar}}^{4}$ terms when the anharmonicity is treated on the level of VPT-4 (vibrational perturbation theory---fourth order) and will potentially need a VPT-6 expansion. Further analysis of the quartic barrier reveals suppressed transmission due to the dominant role of quantum reflection above the barrier. These results not only provide a conceptual framework but can also be applied to heavy atom tunneling and machine learning.

Phase transition enhanced thermoelectric performance for perovskites: The case of AgTaO3

In general, perovskite materials, such as AgTaO3, can exhibit complex structural phase transitions when the temperature changes. Different phase structures may show distinct thermoelectric properties. However, the effects of phase transition on the thermoelectric performance of AgTaO3 have yet to be systematically investigated. Thus, in this work, the electronic structures and thermoelectric properties of the p-type AgTaO3 in various phase structures are investigated by utilizing first-principles calculations and semi-classical Boltzmann transport theory. The results show that the p-type AgTaO3 in the cubic phase shows a superior power factor because the cubic phase possesses a large Seebeck coefficient and intermediate electrical conductivity. The calculated thermoelectric performance is consistent with the predictions and explanations from the analyses of the electronic structures. When the p-type AgTaO3 is transformed from the tetragonal phase to the cubic phase, its power factor is tripled, suggesting that a suitable phase transition can improve the thermoelectric properties of perovskites.

First principles study on structural, mechanical, and thermoelectric properties of half-Heusler alloy (KLiTe)

In this study, the structural, optoelectronics, elastic, and transport properties of KLiTe were estimated from first principles computations using the FP-LAPW technique and semi-classical Boltzmann transport theory The exchange–correlation is addressed employing the generalized gradient approximation with Perdew-Burke-Ernzerhof scheme (GGA-PBE). In order to distinguish between the brittle and ductile properties, the Poisson and Pugh's ratio was calculated. The semiconductor KLiTe is demonstrated to have a direct band gap. The compound under investigation exhibits significant Seebeck coefficient and power factor values. The high-power factor of 8.3 × 1011 W/K2ms. that KLiTe exhibits at 1200 K makes it a potentially viable material for thermoelectric applications. Due to their high figure of merit values, the results obtained indicate that KLiTe could be a strong contender for thermoelectric generator applications at low and moderate temperature.

Polarized Maser Emission with In-source Faraday Rotation

We discuss studies of polarization in astrophysical masers with particular emphasis on the case where the Zeeman splitting is small compared to the Doppler profile, resulting in a blend of the transitions between magnetic substates. A semiclassical theory of the molecular response is derived, and coupled to radiative transfer solutions for 1 and 2-beam linear masers, resulting in a set of nonlinear, algebraic equations for elements of the molecular density matrix. The new code, PRISM, implements numerical methods to compute these solutions. Using PRISM, we demonstrate a smooth transfer between this case and that of wider splitting. For a J = 1–0 system, with parameters based on the v = 1, J = 1–0 transition of SiO, we investigate the behavior of linear and circular polarization as a function of the angle between the propagation axis and the magnetic field, and with the optical depth, or saturation state, of the model. We demonstrate how solutions are modified by the presence of Faraday rotation, generated by various abundances of free electrons, and that strong Faraday rotation leads to additional angles where the Stokes Q changes sign. We compare our results to a number of previous models, from the analytical limits derived by Goldreich, Keeley, and Kwan in 1973, through computational results by W. Watson and coauthors, to the recent work by Lankhaar and Vlemmings in 2019. We find that our results are generally consistent with those of other authors given the differences in the approach and the approximations made.

A theoretical prediction of novel Janus NiSX (X = O, Se, Te) Monolayers: Electronic, optical, and thermoelectric properties

Using density functional theory and semi-classical Boltzmann transport theory were employed to investigate the electronic structure, phononic and optical properties, dynamic stability, and thermoelectric characteristics of Janus NiSX (X = O, Se, Te). The electronic band structure of NiSTe indicates metallic behavior while NiSO and NiSSe show semiconducting features with indirect bandgap. Phononic properties and dynamic stability analyses reveal the stability of Janus Ni compounds. These compounds can be utilized as promising wave reflectors in the infrared (IR) range. Moreover, NiSO and NiSSe are good optical absorbers in the range of far ultraviolet (FUV). NiSTe exhibits isotropic absorption in the visible as well as FUV ranges. Thermoelectric calculations at room temperature show high Seebeck coefficients of 650 and 550 µV/K for NiSO and NiSSe, respectively. The large power factor of 20.83 × 1010 and 25.16 × 1010 W/msK2 are respectively found for n-type NiSO and NiSSe. The results suggest NiSO and NiSSe as promising thermoelectric materials with figure of merit of one (ZT ∼ 1). Consequently, NiSO and NiSSe can serve as efficient alternatives to conventional thermoelectric devices. The results of the current research can be used in the design of novel nanoelectronic devices as well as providing an excellent database for future studies.