Semiclassical Theory Research Articles

Exploring pressure induced thermoelectric properties of LiAeH3 (Ae = Ca, Sr, Ba) perovskite hydrides along with optoelectronic features

This report aims to demonstrate the plane wave pseudopotential approached ab initio computation based on density functional method integrated within semi-classical Boltzmann transport theory to investigate the pressure induced electronic, optical and thermoelectric properties of LiAeH3 (Ae = Ca, Sr, Ba) perovskite hydrides. The computed electronic structures of these compounds possess indirect band gaps with mixed covalent and ionic bonding in the whole range of studied pressure (0–50 GPa) in which the band gaps of LiCaH3 decrease while those of LiSrH3 and LiBaH3 increase as the pressure increases. The rational analyses of optical spectra devote these perovskites to optoelectronic applications. For instance, the investigated hydrides reveal plasmonic excitation owing to their unique loss spectra, which are significant in optical sensing devices. The estimated electronic and optical parameters are compared, whenever possible, to the available results and found a reasonable agreement among them. To further assess physical behavior, the pressure and temperature dependent thermoelectric properties in terms of Seebeck coefficients, thermal conductivities, electrical conductivities, power factors and figure of merits are carried out first time as implemented in the BoltzTraP code. The estimated positive Seebeck coefficients of the studied perovskites exhibit p-type semiconducting nature, and thus holes are the majority charge carriers for conduction rather than electrons. The large figure of merits and small thermal to electrical conductivity ratios disclose their suitability in thermoelectric device applications.

Exploring the structural, elastic, lattice dynamical stability and thermoelectric properties of semiconducting novel quaternary Heusler alloy LiScPdPb

Quaternary Heusler alloy LiScPdPb with an 18-valence electron count show incredible applications in photovoltaic, spintronics, and thermoelectric materials. The study related to the structural, elastic, mechanical stability, and zone center phonon frequencies of LiScPdPb quaternary Heusler alloy is not investigated so far. Therefore, in the present article, the equiatomic quaternary Heusler alloy ‘LiScPdPb’ is studied in detail for their structural stability, elastic and mechanical stability. The research work presented in this report is undertaken by implementing first-principles Density Functional Theory (DFT). The non-magnetic character of the alloy is determined by the Slater-Pauling rule. Furthermore, density functional perturbation theory is implemented to calculate the phonon dispersion curves, phonon density of states, and zone center phonon frequencies of LiScPdPb. The calculated positive phonon frequencies have established the dynamical stability of LiScPdPb in the cubic phase. Raman and infrared phonon modes are also identified for the first time for LiScPdPb by implementing density functional perturbation theory. The calculated value of the bandgap is 0.22eV using generalized gradient approximations, while the bandgap of 1.62eV is observed by using Gaussian-Perdue-Burke–Ernzerhof (Gau-PBE) hybrid functional, which ensures the semiconducting nature of the alloy. In addition to the structural, elastic, mechanical, electronic, and lattice dynamical properties, the thermoelectric response of this alloy are also evaluated by including semi-classical Boltzmann transport theory. The maximum value of the obtained figure of merit for LiScPdPb is 0.18 ​at 1200 ​K, which opens up new avenues for its applications in electronic industries. Hence, the present work will provide a fertile field for the experimental researchers to synthesis this alloy for thermoelectric applications.

A theoretical study on elastic, electronic, transport, optical and thermoelectric properties of Janus SnSO monolayer

Janus structures have superior physical properties due to their vertical asymmetric structure. Although oxygen is a chalcogen element (group VI), recent studies on Janus structures as well as monochalcogenides or dichalcogenides have usually focused on the -phase of S, Se, and Te based compounds. In this study, we systematically investigate the structural, elastic, electronic, transport, optical, and thermoelectric properties of the Janus SnSO monolayer using density functional theory. The Janus SnSO monolayer is found to be stable through phonon spectrum analysis and dynamics simulations. Obtained results demonstrate that SnSO monolayer possesses fully isotropic elastic properties and is more flexible than other two-dimensional materials. In the ground state, the SnSO monolayer is a semiconductor with a direct bandgap whose electronic properties can be easily controlled by strain engineering or the electric field. The electron mobility of the SnSO monolayer is found to be 216.460 cm2 V−1 s−1, which is favorable for applications in nanoscale electronics. The optical properties of the SnSO monolayer are accurately examined via the plus the Bethe-Salpeter equation method. Our results reveal that SnSO has a wide absorption spectrum starting in the infrared and its maximum optical absorbance is up to cm−1 in the near-ultraviolet region. Finally, we investigate the thermoelectric properties of the SnSO monolayer via the semiclassical Boltzmann transport theory. The relaxation time at room temperature is found to be s. The doping level dependence of electronic transport coefficients of the SnSO monolayer is investigated in detail.

A semi-classical theory of magnetic inelastic scattering in transmission electron energy loss spectroscopy

The feasibility of detecting magnetic excitations using monochromated electron energy loss spectroscopy in the transmission electron microscope is examined. Inelastic scattering cross-sections are derived using a semi-classical electrodynamic model, and applied to AC magnetic susceptibility measurements and magnon characterization. Consideration is given to electron probes with a magnetic moment, such as vortex beams, where additional inelastic scattering can take place due to the change in magnetic potential energy of the incident electron in a non-uniform magnetic field. This so-called ‘Stern-Gerlach’ energy loss can be used to enhance the strength of the scattering by increasing the orbital angular momentum of the vortex beam, and enables separation of magnetic from non-magnetic (i.e. dielectric) energy losses, thus providing a promising experimental route for detecting magnons. AC magnetic susceptibility measurements are however not feasible using Stern-Gerlach energy losses for a vortex beam.

High thermoelectric performance of half-Heusler ZrXPb (X = Ni, Pd, and Pt) compounds from first principle calculation

Half-Heusler compounds have distinguished themselves as outstanding thermoelectric materials on account of high temperature stability and large thermopower. However, the dimensionless figure of merit of traditional half-Heusler alloys remains low. In this study, we investigate the thermoelectric performance of novel ZrXPb (X = Ni, Pd, and Pt) ternary compounds by semi-classical Boltzmann transport theory combining with deformation potential. The n-type ZrNiPb and ZrPtPb exhibits obviously large ZT values of 1.71 around 650 K and 1.75 around 1200 K, with 1.17 × 1020 cm−3 and 3.43 × 1020 cm−3, respectively. The electron and phonon structure calculations demonstrate that for the n-type ZrXPb (X = Ni, Pd, and Pt) compounds, doping at Pb site can not only modify the carrier concentrations but also significantly decrease the lattice thermal conductivity. These investigations are expected to be beneficial to the exploration of novel high ZT thermoelectric materials.

Heavy carrier effective masses in van der Waals semiconductor Sn(SeS) revealed by high magnetic fields up to 150 T

The ${\mathrm{SnSe}}_{2(1\ensuremath{-}x)}{\mathrm{S}}_{2x}$ alloy is a van der Waals semiconductor with versatile, tunable electronic properties and prospects for future applications ranging from electronics to thermoelectrics and superconductivity. Its band structure and carrier effective masses underlie the quantum behavior of charge carriers and hold great promise in future technologies. However, experimental measurement of these properties remains a challenging task. Here magnetotransmission spectroscopy of ${\mathrm{SnSe}}_{2(1\ensuremath{-}x)}{\mathrm{S}}_{2x}$ thin films at pulsed magnetic fields $B$ of up to 150 T reveals a large electron-hole reduced cyclotron mass ${\ensuremath{\mu}}^{*}>$ 0.454 ${m}_{e}$ (${m}_{e}$ is the free electron mass). This finding is supported by first-principle calculations of the band structure and by semiclassical Boltzmann transport theory, which predict a pronounced anisotropy of the carrier effective masses and electrical conductivity over two orthogonal directions (namely in the layer plane and out-of-plane) with a different anisotropy for electrons and holes. These properties are unique and important features of this class of compounds and are critical for understanding and using the tunable band structure of ${\mathrm{SnSe}}_{2(1\ensuremath{-}x)}{\mathrm{S}}_{2x}$ in fundamental and applied research.

Lorentz symmetry violation and beyond semiclassical theory in the curved space–time of the arbitrarily dimensional Reissner–Nordström black hole

The quantum tunneling radiation of arbitrarily dimensional Reissner–Nordström black hole is corrected by beyond semiclassical theory and Lorentz symmetry violation theory, resulting in new expressions for the tunneling rate of scalar particles and the Hawking temperature at the horizon of the black hole. The physical significance of our results and the thermodynamic evolution characteristics of the black hole are also discussed.

Semiclassical theory of long time propagation in quantum chaos. Second part

We develop a semiclassical theory of wave propagation based on invariant Lagrangian manifolds existing in conservative Hamiltonian systems with chaotic dynamics. They are stable and unstable manifolds of unstable periodic orbits, and their intersections consist of homoclinic and heteroclinic orbits. For arbitrarily long times, we find matrix elements of the evolution operator between wave functions constructed in the neighbourhood of short unstable periodic orbits, in terms of canonical invariants of homoclinic and heteroclinic orbits. We verify the accuracy of these expressions by computing millions of homoclinic orbits and thousands of heteroclinic ones in the hyperbola billiard. This second part in which we describe off-diagonal matrix elements serves as complement to a previous article (first part) where we have described diagonal matrix elements.

Imaging by intensity interferometry of x-ray fluorescence at a compact x-ray free-electron laser

A semiclassical theory of incoherent diffractive imaging is given, based on the Hanbury Brown and Twiss effect when used to image inner-shell x-ray fluorescence from heavy atoms excited by the femtosecond pulses of an x-ray laser. Interference between emission from different atoms is expected when the pulse duration is shorter than the fluorescent lifetime. Simulations for atoms at the vertices of an icosahedral virus capsid are given, and reconstructions are presented based on phasing of the pair correlation function between photons emitted independently from many different atoms at two different detector pixels. The dependence of the pair-correlation function on the fluorescence lifetime relative to the pulse duration of the x-ray free-electron laser (XFEL) is computed, and a simple expression is obtained for the contrast of incoherent diffractive imaging speckles as a function of the XFEL's flux and lifetime. This indicates that compact XFELs, with reduced flux but sub-femtosecond pulses, should be ideally suited to atomic-resolution three-dimensional mapping of heavy atoms in materials science, chemistry, and biology.

High thermoelectric performance in cubic inorganic halide perovskite material AgCdX3 (X = F and Cl) from first principles

The need for high-performance thermoelectric materials is a hot topic under research to harvest the waste heat generated in the environment. In the present work, we have studied the inorganic halide perovskite AgCdX3 (X = F and Cl) in the cubic phase with the Pm − 3 m space group. We have explored the structural, electronic, elastic, and thermoelectric properties for both materials using first -principles calculations based on density functional theory. The thermoelectric transport coefficients have been calculated from band structure results with the aid of the BoltzTraP2 code based on the semiclassical Boltzmann theory under the constant relaxation time approximation. The deformation potential theory has been implemented to estimate the relaxation time for charge carriers. The Slack equation is solved to evaluate the contribution of lattice thermal conductivity. The results show that the AgCdCl3 has a high value of the figure of merit (ZT) in comparison to that of AgCdF3 at any temperature irrespective of the type of charge carriers. Our findings will provide a guide for the experimentalists to develop high-efficient thermoelectric materials.

Investigation of electronic, optical and thermoelectric properties of perovskite BaTMO3 (TM=Zr, Hf): First principles calculations

The structural, electronic, optical, and thermoelectric characteristics of crystalline oxides-perovskites BaTMO3 (TM=Zr or Hf) were investigated using the all-electron full-potential linearized augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT). The generalized gradient approximation as parameterized in Perdew, Burke, and Ernzerhof (PBE-GGA) was employed to calculate exchange-correlation potential. Also, the modified Becke Johnson exchange potential approximation as parameterized by Tarn and Blaha (TB-mBJ) was used to improve the bandgap estimation. According to our calculations, both perovskites BaZrO3 and BaHfO3 show insulator behavior and have widely indirect band-gap energy (R-Γ) 4.42 (3.39) eV for BaZrO3 and 5.25 (3.69) eV for BaHfO3 from both approaches, TB-mBJ (PBE-GGA), respectively. The optical properties such as dielectric tensor, the refractive index, the absorption coefficient, and the electron loss function have been calculated and analyzed. The optical transitions mainly take place if an electron radiate from the initial state O-2p to the final state Hf-5d or to the Zr-4d in BaHfO3 or BaZrO3 case, respectively. Furthermore, the transport characteristics calculations based on semi-classical Boltzmann theory have been discussed. The thermopower at RT of both compounds BaHfO3 and BaZrO3 are 260.47 and 208.33 μV/K, respectively. This result is good enough to consider these materials as promise thermoelectric candidates. Our results were compared with the previous ab intio calculations and experiments and showed a reasonable agreement.

Ab-initio investigation on the electronic and thermoelectric properties of new half-Heusler compounds KBiX (X = Ba and Sr)

Electronic structures and thermoelectric (TE) properties of KBiBa and KBiSr half-Heusler compounds are investigated by using the combined framework of first-principles and semi-classical Boltzmann transport theory. Elastic and phonon properties calculations reveal that these compounds are mechanically and dynamically stable. Band structures calculations, using the Tran and Blaha modified Becke–Johnson potential including spin–orbit coupling, show that KBiBa and KBiSr compounds are semiconductors with an indirect bandgap of 0.88 and 0.95 eV respectively. Performing calculations on lattice thermal conductivity, deformation potential, effective mass of charge carriers and their relaxation times allow us to deduce the dependence of the figure of merit ZT on doping concentration and temperature. At 1200 K, KBiBa and KBiSr compounds exhibit a ZT peak value of 2.68 and 1.56 at optimized n-doping values of 2.2 × 1019 and 1.7 × 1019 cm−3, respectively. Considering high ZT values, KBiBa and KBiSr are considered to be ideal TE candidates at high temperature.

Theoretical study of structural, electronic, optical and thermoelectric properties of XN (X = Sc, Y)

The structural, electronic, optical, and thermoelectric (TE) properties of XN (X=Sc, Y) were computed using density functional theory (DFT) based on the generalized gradient approximation and semi-classical Boltzmann transport theory. The present XN are found stable in rocksalt (RS) structure with nonmagnetic configuration and have shown semiconductor behavior with small indirect band gaps. Based on the analysis of the elastic constants and their derived parameters, these compounds are predicted the brittle nature and have an ionic bond and are found mechanically and thermodynamically stable. The TE properties such as Seebeck coefficient, electrical conductivity, electronic thermal conductivity, power factor and figure of merit are calculated. It is found that these properties increased with an increase in temperature for ScN and decreased for YN. At the temperature of 300K, the XN exhibits a high Seebeck coefficient, electrical conductivity and power factor. The calculated values of the figure of merit are 0.28 and 0.83 for ScN and YN at 300K, respectively. The imaginary and real parts of dielectric complex function, refractive index and absorption coefficient are calculated. The reflectivity is found less than 40% and the refractivity index about 2–3 in the visible light region. These properties make YN promising material for thermoelectric and optoelectronic applications.

Microscopic theory of magnetoconductivity at low magnetic fields in terms of Berry curvature and orbital magnetic moment

Using a microscopic theory for the magnetoconductivity at low magnetic fields we show how the Hall and longitudinal conductivity can be calculated in the low scattering rate limit. In the lowest order of the scattering rate, we recover the result of the semiclassical Boltzmann transport theory. At higher order, we get corrections containing the Berry curvature and the orbital magnetic moment. We use this formalism to study the linear longitudinal magnetoconductivity in tilted Weyl semimetals. We discuss how our result is related to the semiclassical Boltzmann approach and show the differences that arise compared to previous studies related to the orbital magnetic moment.

Random statistics of OPE coefficients and Euclidean wormholes

We propose an ansatz for OPE coefficients in chaotic conformal field theories which generalizes the eigenstate thermalization hypothesis and describes any OPE coefficient involving heavy operators as a random variable with a Gaussian distribution. In two dimensions this ansatz enables us to compute higher moments of the OPE coefficients and analyse two and four-point functions of OPE coefficients, which we relate to genus-2 partition functions and their squares. We compare the results of our ansatz to solutions of Einstein gravity in AdS3, including a Euclidean wormhole that connects two genus-2 surfaces. Our ansatz reproduces the non-perturbative correction of the wormhole, giving it a physical interpretation in terms of OPE statistics. We propose that calculations performed within the semi-classical low-energy gravitational theory are only sensitive to the random nature of OPE coefficients, which explains the apparent lack of factorization in products of partition functions.

Quantum Optical Aspects of High-Harmonic Generation

The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades.

Geometry and Greatly Enhanced Thermoelectric Performance of Monolayer MXY Transition‐Metal Dichalcogenide: MoSTe as an Example

2D thermoelectric materials with a high power factor and low lattice thermal conductivity have recently been the focus of cutting‐edge research. Herein, combining first‐principles calculations and semiclassical Boltzmann transport theory, a structural search on the monolayer transition‐metal dichalcogenide MoSTe is conducted and its electronic structure, lattice dynamics, and thermoelectric properties are carefully studied. A new tetragonal blend structure is found that is both energetically and dynamically more stable than the experimentally synthesized hexagonal Janus structure, and this blend structure possesses strong anisotropic in‐plane electron and phonon transport properties. Both structures have insulating ground states, which allow a reasonable Seebeck coefficient. Phonon dispersion reveals that several optical phonon‐branches downshift and overlap with the acoustic branches, leading to an enhanced scattering rate, greatly reduced lattice thermal conductivity, and eventually excellent thermoelectric performance with = 0.34 at 300 K and 1.0 at 600 K for the blend‐MoSTe. The results demonstrate the great potential of the monolayer MXY transition‐metal dichalcogenide in thermoelectric applications.

Criticality in the collapse of spherically symmetric massless scalar fields in semiclassical loop quantum gravity

In a recent paper we showed that the collapse to a black hole in one-parameter families of initial data for massless, minimally coupled scalar fields in spherically symmetric semi-classical loop quantum gravity exhibited a universal mass scaling similar to the one in classical general relativity. In particular, no evidence of a mass gap appeared as had been suggested by previous studies. The lack of a mass gap indicated the possible existence of a self-similar critical solution as in general relativity. Here we provide further evidence for its existence. Using an adaptive mesh refinement code, we show that "echoes" arise as a result of the discrete self-similarity in space-time. We also show the existence of "wiggles" in the mass scaling relation, as in the classical theory. The results from the semi-classical theory agree well with those of classical general relativity unless one takes unrealistically large values for the polymerization parameter.

Lifting the Optical and Thermoelectric Properties of Mg2Si as a Function of Sn Incorporation—Potential Thermoelectric Materials

By means of Density Functional Theory (DFT) study, we have performed the structural, electronic, optical and thermoelectric properties calculations of tin doped Mg2Si (Mg2Si1−xSnx, x = 0, 0.125, 0.25, 0.5, 0.75, 0.875, 1) using Full Potential Linearized Augmented Plane Wave (FP-LAPW) Method. The DFT study yields satisfactory results for electronic and thermoelectric properties of Sn doped Mg2Si compared with experimental values. With semiclassical Boltzmann transport theory, the transport properties of Mg2Si and Sn doped Mg2Si alloys has been investigated systematically. According to the calculated band structure, density of states and electron density, the parent Mg2Si/Sn materials having indirect energy gap (Γ−x) with ionic bonding; Sn doped ternary combinations Mg2Si1−xSnx, x = 0.125, 0.25, 0.5, 0.75, 0.875 having direct band gap (Γ−Γ) with a mixed covalent and ionic bonding nature. Band gap decreases linearly with the increase of Sn-concentration in each alloy system except for Mg2Si0.75Sn0.25 combination. The optical properties calculations have been performed for the energy range between 0–13.5 eV. The thermoelectric properties have been calculated for the temperature range 100 K to 800 K. Out of the five studied materials, Mg2Si0.75Sn0.25 found to be a better thermoelectric material with increased Power factor, Seebeck coefficient, electrical conductivity and corresponding thermal conductivity at high temperature range.

Effects of aluminum content on thermoelectric performance of AlxCoCrFeNi high-entropy alloys

Introducing a non-regular distribution in the mass and bonding by including distinctly different elements can reduce the phonon transport even within structurally well-ordered materials. These distributions are a quality of all high-entropy alloys (HEAs), however the inclusion of aluminum in AlxCoCrFeNi is particularly impactful due to the large mismatch in atomic mass with other components. The resultant low phonon conductivity is a requirement for high thermoelectric performance, motivating the investigation of the effects of Al content on phonon transport as well as other thermoelectric properties. This work examines the phonon and electron transport and thermoelectric conversion properties with various Al contents (0 ≤ xAl≤2) in this Cantor alloy using first-principles calculations, molecular dynamics, and semi-classical Boltzmann transport theory. The calculated phonon density of states and thermoelectric properties present reasonable agreements with experiments, including neutron scattering. A large reduction of phonon conductivity (kL) is observed even with low xAls, which we attribute to effective phonon scatterings by the large mass mismatch. However, its temperature dependence is not significant, demonstrating a minor contribution of interphonon scattering. In contrast, electrical conductivity (σ) and Seebeck coefficient (S) increase with temperature at higher xAls with body-centered cubic structures. Therefore, the thermoelectric figure of merit (ZT) of AlxCoCrFeNi HEAs is enhanced by increasing the Al content mainly due to the increase of the thermoelectric power factor (σS2) at high temperatures, while at low temperatures the phonon-scattering enhancement by mass mismatch is also important.