Semiclassical Theory Research Articles

Low-energy electrodynamics of Dirac semimetal phases in the doped Mott insulator Sr2IrO4

Correlated Dirac semimetal phases emerge in lightly doped (Tb- or La-doped) Mott insulator Sr$_2$IrO$_4$, where a d-wave symmetry-breaking order underlying a pseudogap plays a crucial role in determining the nature of Dirac degeneracy, i.e., whether it is a Dirac line node or Dirac point node. Here, using a realistic five-orbital tight-binding model with a Hubbard U and a semiclassical Boltzmann transport theory, we systematically study the low-energy electrodynamic properties of the Dirac semimetal phases in the paramagnetic lightly doped Sr$_2$IrO$_4$. We investigate the effects of the d-wave electronic order and electron doping concentration on the electronic band structures and optical properties of various Dirac semimetal phases. We calculate the intraband optical conductivity and obtain electrodynamic parameters of dc conductivity, scattering rate, and Drude weight for three Dirac semimetal phases: two are Dirac point-node states observed in the 3% Tb-doped and 5% La-doped Sr$_2$IrO$_4$, and the other is a Dirac line-node state. Our results show that the temperature dependence of the electrodynamic parameters is strong in the Tb-doped system while weak in the La-doped and Dirac line-node systems, which are consistent with available experimental data. Moreover, using the low-energy effective theory, we also compare the temperature-dependent screening effect in the Tb- and La-doped systems using graphene as a reference. Our paper provides valuable insight for understanding the transport and optical properties of correlated Dirac semimetal phases in the doped Sr$_2$IrO$_4$.

Investigation on Electronic and Thermoelectric Properties of (P, As, Sb) Doped ZrCoBi

Since the last decade, the half-Heusler (HH) compounds have taken an important place in the field of the condensed matter physics research. The multiplicity of substitutions of transition elements at the crystallographic sites X, Y and (III-V) elements at the Z sites, gives to the HH alloys a multitudes of remarkable properties. In the present study, we examined the structural, electronic and thermoelectric properties of ZrCoBi0.75Z0.25 (Z = P, As, Sb) using density functional theory (DFT). The computations have been done parallel to the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code. The thermoelectrically properties were predicted via the semi-classical Boltzmann transport theory, as performed in Boltztrap code. The obtained results for the band structure and densities of states confirm the semiconductor (SC) nature of the three compounds with an indirect band gap, which is around 1eV. The main thermoelectric parameters such as Seebeck coefficient, thermal conductivity, electrical conductivity and figure of merit were estimated for temperatures ranging from zero to 1200K. The positive values of Seebeck coefficient (S) confirm that the ZrCoBi0.75Z0.25 (x = 0 and 0.25) are a p-type SC. At the ambient temperature, ZrCoBi0.75P0.25 exhibit the large S value of 289 µV/K, which constitutes an improvement of 22% than the undoped ZrCoBi, and show also a reduction of 54% in thermal conductivity (κ/τ). The undoped ZrCoBi has the lowest ZT value at all temperatures and by substituting bismuth atom by one of the sp elements (P, As, Sb), a simultaneous improvement in κ/τ and S have led to maximum figure of merit (ZT) values of about 0.84 obtained at 1200 K for the three-doped compounds.

The impact of electron-phonon coupling on the figure of merit of Nb2SiTe4 and Nb2GeTe4 ternary monolayers.

We have comprehensively demonstrated the thermal transport properties of Nb2SiTe4 and Nb2GeTe4 ternary monolayers by employing first-principles calculations and the semi-classical Boltzmann transport theory, including the electron-phonon coupling. The appealing features uncovered here for the monolayers are their colossal Seebeck coefficient and power factor at a higher carrier concentration. For example, the room temperature Seebeck coefficient lasts as high as 200 μV K-1 even at an increased hole (electron) concentration 6.32 × 1020 cm-3 (5.17 × 1019 cm-3) and 1.47 × 1020 cm-3 (5.18 × 1019 cm-3) for Nb2SiTe4 and Nb2GeTe4 monolayers, respectively. Our findings disclose similar band structures and moderate indirect bandgaps of 0.55 eV and 0.41 eV for Nb2SiTe4 and Nb2GeTe4 monolayers. The absence of imaginary frequencies in phonon band dispersion confirms the dynamic stability of both monolayers. The lowest value of lattice thermal conductivity turns out to be 14.30 W m-1 K-1 (12.30 W m-1 K-1) for Nb2SiTe4 and 11.70 W m-1 K-1 (8.34 W m-1 K-1) for Nb2GeTe4 in the x(y) direction. Besides, both monolayers express tremendous potential to further reduced lattice thermal conductivity by nano-structuring without requiring a diminished sample size that is technically challenging to synthesize.

First principle calculations of GeTe and Ge2TeSe monolayers: Structural, electronic and thermoelectric properties

We have presented the structural, electronic and thermoelectric properties of GeTe and Ge2TeSe monolayers using density functional theory. It has been observed that Ge2TeSe monolayer is a direct band gap semiconductor opposite to GeTe monolayer which is an indirect band gap semiconductor. The electronic band structure and density of states for both monolayers have been calculated. An attempt is made to calculate and compare the temperature-dependent transport coefficients of both monolayers using the Boltzmann semi-classical theory. The Seebeck coefficient, electrical conductivity, power factor, and electronic thermal conductivity for both monolayers have been compared for different doping concentrations at 300 K, 500 K, and 700 K. It is found that the power factor of p-type Ge2TeSe monolayer is larger than that of p-type GeTe monolayer below carrier concentration ~1012 cm−2 at any temperature.

Semiclassic Models of the Dissipative Regime of Instability and Superradiation of a Quantum Radiator System

The paper discusses the similarity between dissipative generation and superradiance regimes for systems of excited quantum emitters placed in an open cavity. In the case of the existence of a resonator field due to reflections from the ends of the system, a dissipative generation regime is usually realized. In this case, the decrement of oscillations in the waveguide in the absence of radiators turns out to be greater than the increment of the arising instability of the system of radiators placed in the resonator. When describing this mode, the influence of the emitters on each other and the sum of their own fields is neglected. The resonator field forces the oscillators to emit or absorb quanta synchronously with it, depending on the local value of the population inversion. Lasing takes on a weakly oscillatory character due to an asynchronous change in the population inversion of the system of emitting dipoles (nutations), which have a ground and excited energy levels. To describe the process, the equations of the semiclassical theory based on the use of the density matrix are quite sufficient. In the case when there is no resonator or waveguide field, taking into account the eigenfields of the oscillators becomes essential. To simulate the superradiance process, large emitting particles are used, to describe which one should use the equations for the density matrix. It is shown that the interaction of quantum emitters in this case is due to electromagnetic fields under conditions when the overlap of their wave functions is insignificant. Equations are obtained that allow considering the process of interaction of emitters. When the emitters interact, an integral field is formed in the resonator, an increase in the intensity of which leads to synchronization of the emitters. It is shown that the characteristic times of the development of the process, as well as the attainable amplitudes of the excited fields for dissipative regimes of generation and regimes of superradiance of emitters filling an open resonator, are comparable.

Gravitational Dispersion Forces and Gravity Quantization

The parallel development of the theories of electrodynamical and gravitational dispersion forces reveals important differences. The former arose earlier than the formulation of quantum electrodynamics so that expressions for the unretarded, van der Waals forces were obtained by treating the field as classical. Even after the derivation of quantum electrodynamics, semiclassical considerations continued to play a critical role in the interpretation of the full results, including in the retarded regime. On the other hand, recent predictions about the existence of gravitational dispersion forces were obtained without any consideration that the gravitational field might be fundamentally classical. This is an interesting contrast, as several semiclassical theories of electrodynamical dispersion forces exist although the electromagnetic field is well known to be quantized, whereas no semiclassical theory of gravitational dispersion forces was ever developed although a full quantum theory of gravity is lacking. In the first part of this paper, we explore this evolutionary process from a historical point of view, stressing that the existence of a Casimir effect is insufficient to demonstrate that a field is quantized. In the second part of the paper, we show that the recently published results about gravitational dispersion forces can be obtained without quantizing the gravitational field. This is done first in the unretarded regime by means of Margenau’s treatment of multipole dispersion forces, also obtaining mixed potentials. These results are extended to the retarded regime by generalizing to the gravitational field the approach originally proposed by McLachlan. The paper closes with a discussion of experimental challenges and philosophical implications connected to gravitational dispersion forces.

First principles study of thermoelectric properties of β -gallium oxide

The thermoelectric effects in bulk β-gallium oxide crystals are investigated in this work using the ab initio calculated electron-phonon interactions and semi-classical Boltzmann transport theory. We have taken all major scattering mechanisms into account, namely, polar and non-polar optical phonon, acoustic phonon, and ionized impurity scattering. To accurately account for the polar phonon scattering rate, we take into account the dynamic screening at higher electron densities. An iterative solution of the Boltzmann transport equation is used in order to account for the inelastic and anisotropic nature of polar optical phonon scattering. The thermoelectric transport coefficients, Seebeck coefficient, Peltier coefficient, and electronic thermal conductivity, are calculated for a wide range of temperatures and doping densities. The calculated Seebeck coefficient is compared with the experimentally measured value and found to be in good agreement considering the mobility of the samples. The value of the Seebeck coefficient at 300 K is found to be −341 μV K−1, which is high compared to that of the other commonly studied semiconductors. The larger Seebeck coefficient is due to the higher density of states arising from comparatively high electron effective mass.

On the electrical conductivity of metals with a rough surface

ABSTRACT We discuss surface roughness effects on the conduction of electrons in metals using both the quantal Kubo–Greenwood formalism and the semi-classical Fuchs–Sondheimer method. The main purpose here is to compare these methods and clarify a few subtle and widely misunderstood conceptual issues. One of such issues is concerned with the conditions under which the broken translation symmetry along a rough surface may be restored. This symmetry has often been presumed in existing work but not always with proper justifications. Another one relates to the physical meaning of a phenomenological parameter (denoted by p) intuitively introduced in the semi-classical theory. This parameter, called the specularity parameter or sometimes the Fuchs parameter, plays an important role in the experimental studies of surface roughness but has so far lacked a rigorous microscopic definition. The third issue arises as to the domain of validity for the electrical conductivity obtained in those methods. A misplacement of the domain may have resulted in erroneous analysis of surface effects in a variety of electrodynamic phenomena including surface plasma waves.

Experimental measurement of state-selective charge exchange and test of astrophysics soft X-ray emission model

Charge exchange, or electron capture, between highly charged ions and atoms and molecules has been considered as one of important mechanisms controlling soft X-ray emissions in many astrophysical objects and environments. However, to model charge exchange soft X-ray emission, astrophysicists commonly use principal quantum number <i>n</i> and angular momentum quantum number<i>l</i> resolved state-selective capture cross section data, which are usually obtained by empirical and semi-classical theory calculations. The accuracy of the theoretical model is the key to constructing an accurate X-ray spectrum. With a newly-built cold target recoil ion momentum spectroscopy apparatus, we perform a series of precise state-selective cross section measurements on Ne<sup>8+</sup> ions’ single electron capture with He targets, with the projectile energy ranging from 1.4 to 20 keV/u. The experimentally measured Q value spectrum shows that the process of electron captured to state of Ne<sup>7+</sup> with <i>n</i> = 4 is the main reaction channel, and that with <i>n</i> = 3 and 5 are the small reaction channels. Using Gaussian curve to fit the area of each channel on the Q value spectrum and normalizing the area of all channels, we obtain the <i>n</i>-resolved relative state-selective cross section. By comparing the measured relative cross sections with the results calculated by the multichannel Landau-Zener method and molecular Coulomb over-barrier model, significant difference among the strengths of small reaction channels is found. Specifically, the multichannel Landau-Zener method overestimates the contribution of <i>n</i> = 2 channel and <i>n</i> = 3 channel, and underestimates the contribution of <i>n</i> = 5 channel. The molecular Coulomb over-barrier model overestimates the contribution of <i>n</i> = 5 channel and underestimates the contribution of <i>n</i> = 3 channel. The significant difference between the theoretical model calculation and experimental measurement is due to the limitations of semiclassical theoretical method and classical theoretical method. Furthermore, with <i>l</i> distribution models commonly used in the astrophysical literature, including the statistical model, separable model, Landau-Zener-I model, Landau-Zener-II model and even model, we calculate the soft X-ray emissions in the charge exchange between 1.6 and 2.4 keV/u Ne<sup>8+</sup> and He. It is found that the calculated intensities of X-ray spectra significantly deviate from the existing measurements, and only the separable model can partly match the laboratory simulated solar wind charge exchange X-ray measurement. Furthermore, we find that the intensity of the charge exchange X-ray emission spectrum measured experimentally is dependent on the collision energy, while the emission spectrum calculated based on the model seems to be unchanged with the increase of the collision energy. These results indicate that if the classical and semi-classical models are applied to the astrophysical plasma for studying diffusive soft X-ray background, the obtained parameters of the astrophysical plasma will be inaccurate.

Thermoelectric performance of BaBiNa and SrBiNa: A first-principle study

The high thermoelectric performance is expected to develop practical thermoelectric materials. The relationship between the dimensionless figure of merit (ZT) and the carrier concentration and the temperature is constructed to identify the best thermoelectric performance of XBiNa (X = Ba and Sr). The electronic structure and transport properties of the two semiconductors are calculated by combining the first-principle DFT with the semi-classical Boltzmann transport theory to obtain the Seebeck coefficient, electronic thermal conductivity, and electrical conductivity. The relaxation time is determined by the deformation potential theory, and the lattice thermal conductivity is calculated by the Slack model. The maximum ZTs of 1.14 and 1.16 can be achieved for the n-type BaBiNa and SrBiNa at a carrier concentration of 5.62 × 1018/3.60 × 1018 cm−3 at 800 K, respectively. The maximum thermoelectric conversion efficiency of 21.25 % is attributed to the n-type SrBiNa, implying that the compound is potential thermoelectric material. The different thermoelectric mechanisms for the n- and p-type XBiNa are elucidated through evaluating the tendency of the transport coefficients and ZT.

Microcanonical Tunneling Rates from Density-of-States Instanton Theory.

Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to the computation of thermal reaction rates in complex molecular systems including quantum tunneling effects. There have been a number of attempts to extend the theory to treat microcanonical rates. However, the previous formulations are either computationally unfeasible for large systems due to an explicit sum over states or they involve extra approximations, which make them less reliable. We propose a robust and practical microcanonical formulation called density-of-states instanton theory, which avoids the sum over states altogether. In line with the semiclassical approximations inherent to the instanton approach, we employ the stationary-phase approximation to the inverse Laplace transform to obtain the densities of states. This can be evaluated using only post-processing of the data available from a small set of instanton calculations, such that our approach remains computationally efficient. We show that the new formulation predicts results that agree well with quantum scattering theory for an atom-diatom reaction and with experiments for a photoexcited unimolecular hydrogen transfer in a Criegee intermediate. When the thermal rate is evaluated from a Boltzmann average over our new microcanonical formalism, it can overcome some problems of conventional instanton theory. In particular, it predicts a smooth transition at the crossover temperature and is able to describe bimolecular reactions with pre-reactive complexes such as CH3OH + OH.

Ab initio study of oxygen vacancy effects on structural, electronic and thermoelectric behavior of AZr1-xMxO3 (A = Ba, Ca, Sr; M= Al, Cu, x = 0.25) for application of memory devices

The structural, electronic and thermoelectric properties of AZr1-xMxO3 (A = Ba, Ca, Sr; M = Al, Cu, x = 0.25) without and with an oxygen vacancy (Vo) have been unveiled using the Perdew-Burke-Ernzerhof Generalized Gradient Approximation (PBE-GGA) functional along with Tran-Blaha modified Becke-Jonhson (TB-mBJ)approximation based on Density Functional Theory (DFT) in the framework of WIEN2k code for memristors applications. Moreover, isosurface charge density plots have been calculated by using Vienna ab initio Simulation Package (VASP) simulation code. The analysis of structural parameters reveals that substituting Zr4+ with Al3+ and Cu2+ causes the lattice distortion which tends to increase in the presence of Vo along with dopant. The study of band structure, density of states (DOS) and isosurface charge density plots predict the enhanced charge conduction and formation of conducting filaments (CFs) for all composites with dopant and/or Vo. Moreover, spin polarized density of states for Cu doped composites has also been calculated to confirm the large exchange splitting of Cu-3d states. The thermoelectric characteristics of considered composites have also been explored using the Boltztrap code to better explain the semi-classical Boltzmann transport theory. Thermoelectric parameters confirm the semiconductor nature of all composites, ensuring the compatibility for memristors and thermoelectric devices applications. In addition to this spin polarized thermoelectric behavior of Cu doped composites that ensure the contribution of spin down (↓) states of Cu for charge transport mechanism. The SrZrCuO3+Vo composite is found most promising candidate followed by BaZrCuO3 for memristors applications while, CaZrCuO3 is found most suitable amongst studied composites for thermoelectric devices.

Self-trapped atomic matter wave in a ring cavity

We studied a system of atomic Bose-Einstein condensate coupled to a ring cavity within the mean-field theory. Due to the interaction between atoms and light field, the atoms can be self-trapped. This is verified with both variational and numerical methods. We examined the stability of these self-trapped states. For a weakly pumped cavity, they spread during the evolution; while at strong pumping, they can maintain the shape for a long time. We also studied the moving dynamics of these self-trapped waves, and found out that it can be strongly affected by the cavity decay rate. For a small cavity decay rate, the self-trapped waves undergo a damped oscillation. Increasing the cavity decay rate will lead to a deceleration of the self-trapped waves. We also compared the main results with the semiclassical theory in which atoms are treated as classical particles.

Frustrated ionization of atoms in the multiphoton regime

A semiclassical analytic theory which describes the excitation of atomic Rydberg states by intense laser radiation is formulated in the multiphoton limit of ionization. The theory is based on the separation of the electron motion in fast oscillations in the laser field and slow scattering in the Coulomb field of the nucleus. It allows one to calculate classical cut-off positions in the distribution of excited atoms in principal and orbital quantum numbers, and to identify the effect of quantum interference.

Dependence of strain on the thermoelectric properties of Uranium Carbide

The present study investigates the structural, electronic and thermoelectric properties of Uranium Monocarbide using Density Functional Theory based on first principles calculation. The electronic structure of UC was calculated using the Quantum Espresso code and the Thermoelectric properties were evaluated using the BoltzTrap code based on the semiclassical Boltzmann transport theory. The dependence of strain on the thermoelectric properties such as electrical and thermal conductivity, Seebeck coefficient and thermoelectric figure of merit (ZT) is calculated. At room temperature, the Thermoelectric figure of merit (ZT) decreases under compressive strain whereas it increases over tensile strain.

Thermoelectric and Half-Metallic Behavior of the Novel Heusler Alloy RbCrC: Ab initio DFT Study

Research Highlights • Electronic, magnetic, elastic and thermoelectric properties of RbCrC alloy are investigated. • Material is half-metallic, ductile and anisotropic in nature. • The total magnetic moment (3[Formula: see text][Formula: see text]B) obeys the Slater–Pauling rule. • The HM RbCrC compound is identified as potential candidate for spintronic applications. • ZT calculated values of 0.89 and 0.94 make RbCrC a promising thermoelectric material candidate for use in future devices. The aim of this work is to investigate the half-metallicity behavior, elastic, thermodynamic and thermoelectric (TE) properties of the Heusler compound RbCrC using the generalized gradient approximation (GGA-PBE96) and the modified Becke–Johnson (mBJ) approach. The electronic band structures and density of states reveal that RbCrC is a half-metallic ferromagnet (HMF). The calculated total magnetic moment of 3[Formula: see text][Formula: see text]B follows the Slater–Pauling rule ([Formula: see text]). The half-metallicity character can be maintained in the 5.4–7.4 Å lattice constants range and the 0.8–1.2 [Formula: see text]/[Formula: see text] ratio range. Existence of half-metallic ferromagnetism in RbCrC makes it a promising material for practical applications in the spintronic field. Also, the RbCrC exhibits a ductile and anisotropic behavior. The quasi-harmonic Debye model (QHDM) is used to calculate the thermodynamic properties. The BoltzTraP code which is based on semi-classical Boltzmann theory (SCBT) is applied for calculating TE properties. According to the obtained figure of merit values (ZT between 0.89 and 0.94 from 50 K to 800 K), the RbCrC alloy remains a good candidate for thermoelectric applications.

On the Stark Broadening of Be II Spectral Lines

Calculated Stark broadening parameters of singly ionized beryllium spectral lines have been reported. Three spectral series have been studied within semiclassical perturbation theory. The plasma conditions cover temperatures from 2500 to 50,000 K and perturber densities 1011 cm−3 and 1013 cm−3. The influence of the temperature and the role of the perturbers (electrons, protons and He+ ions) on the Stark width and shift have been discussed. Results could be useful for plasma diagnostics in astrophysics, laboratory, and industrial plasmas.

The thermal and electrical transport properties of layered LaCuOSe under high pressure

In this study, first-principles calculations combined with semi-classical Boltzmann transport theory are carried out to study the thermal and electrical transport properties of LaCuOSe under high pressure. The results show that the Seebeck coefficient of LaCuOSe decreases significantly as the pressure rises, because of significant changes in crystal and electronic structures. Meanwhile, the electrical conductivity is also declined by high pressure. Additionally, the external pressure leads to decreased lattice parameters, high phonon vibrational frequency and enhanced heat transport. Therefore, the lattice thermal conductivity of LaCuOSe at 900 K increases with increasing pressure. As a result, the optimal figure of merit of LaCuOSe at 900 K is reduced from 0.99 (3.34) to 0.06 (0.35) along the a-axis (c-axis) as the pressure changes from 0 to 10 GPa. These results suggest that high hydrostatic pressure has negative effects on the thermoelectric properties of the layered LaCuOSe.

Higgs time crystal in a high- Tc superconductor

We propose to induce a time crystalline state in a high-$T_c$ superconductor, by optically driving a sum resonance of the Higgs mode and a Josephson plasma mode. The generic cubic process that couples these fundamental excitations converts driving of the sum resonance into simultaneous resonant driving of both modes, resulting in an incommensurate subharmonic motion. We use a numerical implementation of a semi-classical driven-dissipative lattice gauge theory on a three-dimensional layered lattice, which models the geometry of cuprate superconductors, to demonstrate the robustness of this motion against thermal fluctuations. We demonstrate this light-induced time crystalline phase for mono- and bilayer systems and show that this order can be detected for pulsed driving under realistic technological conditions.

Elucidating the role of lattice thermal conductivity in π‐phases of IV‐VI monochalcogenides for highly efficient thermoelectric performance

SummaryRecently, an emerging new class of cubic π‐polymorphs are being pursued as cost‐effective and relatively less toxic materials for thermoelectric, photovoltaic, and optoelectronic applications. Using density functional formalism and semiclassical Boltzmann transport theory, we have systematically studied the thermoelectric performance of π‐polymorphs. Hybrid functional (HSE03) is employed to realize accurate energy bandgaps, which helps to predict more accurate thermoelectric properties. The thermodynamic stability is observed by binding energies and phonon dispersions. It is observed that the Seebeck coefficients (S) are decreasing and electrical conductivities (σ) are increasing with carrier concentration. However, thermal conductivities are showing decreasing trends which lead to ultimately increased ZT. π‐GeSe shows a high power factor ~16.50 mW/mK2 among all π‐polymorphs. The figure of merit, ZT value, of π‐SnS, π‐SnSe, π‐GeS, and π‐GeSe are found to be 0.83, 1.20, 1.28, and 1.63 with optimal carrier concentration at 800 K. The present work highlights the potential of newly discovered cubic π‐polymorphs of chalcogenides for highly efficient thermoelectric materials.