Phonon Contribution Research Articles

Optical conductivity of an anharmonic large polaron gas at weak coupling

In a polar solid, electrons or other charge carriers can interact with the phonons of the ionic lattice, leading to the formation of polaron quasiparticles. The optical conductivity and optical absorption spectrum of a material are affected by this electron-phonon coupling, most notably leading to an absorption peak in the midinfrared region. Recently, a model Hamiltonian for anharmonic electron-phonon coupling was derived [M. Houtput and J. Tempere, Phys. Rev. B 103, 184306 (2021)] that includes both the conventional Fr\"ohlich interaction as well as an interaction in which an electron interacts with two phonons simultaneously. In this article, we calculate and investigate the optical conductivity of the anharmonic large polaron gas, and we show that an additional characteristic absorption peak appears due to this one-electron--two-phonon interaction. We calculate a semianalytical expression for the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ at finite temperatures and weak coupling using the Kubo formula. The electronic and phononic contributions can be split and treated separately, such that the many-body effects of the electron gas may be taken into account through the well-known dynamical structure factor $S(\mathbf{k},\ensuremath{\omega})$. From the resulting optical conductivity, we calculate the polaron effective mass, an estimate for the electron-phonon scattering times, and the optical absorption spectrum of the anharmonic polaron gas. It is shown that the effects are negligible for four common III-V semiconductors (BN, AlN, BP, AlP) in the zinc-blende structure, which justifies the commonly used harmonic approximation in these materials. We show that alongside the well-known polaron absorption peak at the phonon energy $\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{LO}}$, the one-electron--two-phonon interaction leads to an additional absorption peak at $2\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{LO}}$. We propose this absorption peak as an experimentally measurable indicator for non-negligible one-electron--two-phonon interaction in a material, since the height of this peak is proportional to the strength of this anharmonic interaction.

Dynamic correlation and polaronic effects on the correlational properties of finite-temperature electron quantum wire

We study the role of dynamic correlation and polaronic effects on the correlational properties of a GaAs-based electron quantum wire at finite-temperature T. The dynamics of electron correlations is incorporated through the self-consistent mean-field approximation of Hasegawa and Shimizu (the qSTLS theory) and the polaronic effects via the Fröhlich interactions. Results are presented for the static correlation functions, dynamic structure factor and electron’s contact probability over a wide range of T and electron number density r s . We find that for a fixed wire width b and T, electrons undergo a transition from the quantum liquid to Wigner crystal state due to the dynamics of severely correlated electrons at a critical . The inclusion of polaronic effects along with the conventional electron-electron interactions tends to increase r s c significantly at each T ultimately improving the quantum phase diagram. The electron’s contact probability exhibits a non-monotonic T-dependence which remains positive over a broader range of r s owing to the inclusion of polaronic effects. Besides, we explore the effect of phonon contribution on the plasmon energy of the quantum wire at non-zero T and find that there is splitting in the energy into two branches namely, plasmonlike and phononlike with former having energy lower than the latter. Both of the energy modes show consistent blue shift with rise in T, get damp at a critical wave vector q c , and q c decreases with T. Finally, we calculate the finite-T polaronic contribution to the free energy whose magnitude increases with T as r s → 0 and it becomes almost constant at sufficiently high r s .

Effect of Sb and In additives on thermal and electrical properties of Sn–9Zn–4Bi alternative lead-free solder alloy

Due to the threats of lead to human and environmental health with Tin (Sn)- lead (Pb) solder alloys, efforts to develop lead-free solders continue. To adapt to different soldering areas, especially electronics, the search for alloys that can replace Sn–Pb has increased. The better the solders are in terms of thermal and electrical properties at the junctions, the better the performance of the circuit. In this study, changes in thermal conductivity, electrical conductivity, and melting behavior of 0.5–2 mass percent (wt.%) antimony (Sb) and 0.5–1.5 mass percent (wt.%) indium (In) addition to Sn–9Zn–4Bi alloy were investigated. Measurements of thermal and electrical conductivity with temperature were made by linear heat flow and four-point probe methods, respectively. The melting temperatures (peak temperature) of the alloys produced vary between 477.70 and 484 K (K). When the transition temperature, which is important in solders, is compared to Sn–9Zn–4Bi-[x]Sb (x = 0.5–2 wt%) and Sn–9Zn–4Bi-yIn (y = 0.5–1.5 wt%) alloys, it is the alloy with the lowest value with 13.80 K and the addition of 1 wt% Sb. The thermal and electrical conductivity values increased with the contribution of Sb and In. In addition, temperature coefficients for thermal and electrical conductivity were calculated. Electron and phonon contributions to the thermal conductivity were determined from the Wiedemann-Franz law. It was determined that electron contribution was higher for each alloy.

Electronic and phonon contributions to the Thermoelectric properties of newly discovered half-Heusler alloys XHfPb (X= Ni, Pd, and Pt)

In this work we calculate the thermoelectric figure of merit of XHfPb (X= Ni, Pd, and Pt) by computing the both the power factor and the lattice thermal conductivity by first principles. We make reasonable approximations: we use the Constant Relaxation Time Approximation (CRTA) to compute the electron transport contribution and the modified Debye–Callaway model to calculate the thermal lattice conductivity. We also report the dielectric properties of these semiconductors and the mode Grüneisen parameters. Not surprisingly we find that the average Grüneisen coefficient correlates with the thermal conductivity. Next, we consider a realistic relaxation time τ and carrier concentration n from experimental data on ZrHfPb and obtain the figure of merit ZT as a function of temperature. Our main finding is that despite the Pt is isoelectronic with Ni and Pd, the ZT of PtHfPb is larger and behaves differently from the other two materials, suggesting that PtHfPb is better suited for high temperature thermoelectric generators.

On the contribution of phonons to electrochemical potential of Li-ion metal-organic frameworks

According to Nernst equation, the prediction of equilibrium voltage in electrochemical cells involve the calculation of all contributions of the free energy, corresponding to electronic, vibrational and translational degrees of freedom. Most simulations are restricted to the electronic energy computed in the frame of DFT, mainly because accurate ab-initio investigations of electronic structure usually provides a useful approximation, while the calculations of properties for periodic structures typically involve massive computational resources. In this paper we propose a methodology that allows for the calculation of vibrational contributions to Nernst equation and show that in the case of organic materials (i.e. Li2-Mn-DOBDC electrodes) they represent an important contribution to the total electrode potential that cannot be neglected for the correct understanding of the redox mechanism.

Improved wear resistance and low thermal radiative conductivity of a middle‐entropy tantalate Y0.5Gd0.5Ta0.5Nb0.5O4

AbstractFerroelastic YTaO4 is a promising material for thermal barrier coatings (TBCs), and its thermal and mechanical properties can be further optimized by various methods. In this study, a ferroelastic middle‐entropy ceramic Y0.5Gd0.5Ta0.5Nb0.5O4 was synthesized by solid‐phase sintering, and its microstructures and thermophysical properties were key points. We determined the contributions of phonons and photons to total thermal conductivity, and a low thermal conductivity was obtained by inhibiting high‐temperature thermal radiation. The thermal expansion coefficients were improved by introducing of Nb atom into the lattice of the prepared middle‐entropy ceramic, which meets the requirements of TBCs. The improved wear resistance originated from relatively high Young's modulus and the hardness of Y0.5Gd0.5Ta0.5Nb0.5O4, and it would contribute to the service performance of the corresponding coatings. This work motivates the engineering applications of ferroelastic RETaO4 and RENbO4 (RE is rare‐earth element) as high‐temperature TBCs.

Temperature-resilient anapole modes associated with TE polarization in semiconductor nanowires

Polarization-dependent scattering anisotropy of cylindrical nanowires has numerous potential applications in, for example, nanoantennas, photothermal therapy, thermophotovoltaics, catalysis, sensing, optical filters and switches. In all these applications, temperature-dependent material properties play an important role and often adversely impact performance depending on the dominance of either radiative or dissipative damping. Here, we employ numerical modeling based on Mie scattering theory to investigate and compare the temperature and polarization-dependent optical anisotropy of metallic (gold, Au) nanowires with indirect (silicon, Si) and direct (gallium arsenide, GaAs) bandgap semiconducting nanowires. Results indicate that plasmonic scattering resonances in semiconductors, within the absorption band, deteriorate with an increase in temperature whereas those occurring away from the absorption band strengthen as a result of the increase in phononic contribution. Indirect-bandgap thin ([Formula: see text]) Si nanowires present low absorption efficiencies for both the transverse electric (TE, [Formula: see text]) and magnetic (TM, [Formula: see text]) modes, and high scattering efficiencies for the TM mode at shorter wavelengths making them suitable as highly efficient scatterers. Temperature-resilient higher-order anapole modes with their characteristic high absorption and low scattering efficiencies are also observed in the semiconductor nanowires ([Formula: see text] nm) for the TE polarization. Herein, the GaAs nanowires present [Formula: see text] times greater absorption efficiencies compared to the Si nanowires making them especially suitable for temperature-resilient applications such as scanning near-field optical microscopy (SNOM), localized heating, non-invasive sensing or detection that require strong localization of energy in the near field.

Heat capacity and thermal conductivity of CdCr2Se4 ferromagnet: Magnetic field dependence, experiment and calculations

The low-temperature specific heat capacity and thermal conductivity under magnetic field 0–13 T is investigated on polycrystalline sample of the ferromagnetic insulator CdCr2Se4, possessing spinel structure with magnetic Cr3+ ions in the octahedrally coordinated sites. The phonon (lattice) and magnon contributions are separated by their characteristic temperature dependencies and by quenching of the magnon component under high magnetic fields in the isothermal measurements. The results are analyzed with respect to formulas for model systems and confronted with ab-initio calculations of phonon and magnon spectra. The theoretical formula for the field-induced quenching of magnon heat capacity is well reproduced, but there are two kinds of deviations from expected behavior deserving attention: (1) Heat capacity at low fields is by several percent lower than expected and approaches the theoretical curve only above ∼0.5 T. We propose that the zero-field magnon heat capacity is diminished by a presence of magnetic domain walls and the expected field dependence is restored when magnetic field converts the sample into a single domain state. (2) The suppression of magnon heat capacity under high magnetic field is incomplete. While the data follow well the theoretical line for given temperature as regards the curvature, the final saturation seems to tend several percent above the expected value for lattice heat capacity. We propose that this behavior is related to the phonon-magnon coupling arising due to Zeeman gap in the magnon spectra and subsequent formation of intersection points with the phonon spectra. The thermal conductivity has shown substantial deviations with respect to model predictions as concerns temperature dependence of the phonon contribution and suppression of the magnon contribution in markedly lower magnetic fields than predicted by the model. We ascribe this discrepancy to a complex character of the intergrain heat transfer.

Beta-borophene under the circularly polarized radiation: polaritonic and polaronic dynamic band structure

We study the effect of circularly polarized electromagnetic radiation on the optical polarons in a monolayer \({\beta}\)-borophene. We focus our attention on the off-resonant regime of large driving frequencies, which allows us to set up an effectively time-independent Hamiltonian describing the radiation field up to the second perturbational order. The contributions of optical surface phonons are incorporated according to the Lee–Low–Pines theory, via a sequence of appropriate unitary transformations. A central object in our investigation is the electronic band gap, which is shown to be widely controllable via the variation of light irradiation and substrate properties. We also show that the polaron self-energy contribution gives more contribution than the combination of the polaronic and polaritonic effects.

First-principles calculations of the dynamical and thermodynamic properties of lead chalcogenides PbX (X = S, Se, Te)

We perform first-principles calculations of the dynamical and thermodynamic properties of lead chalcogenides PbX (X = S, Se, Te ). Using density functional perturbation theory, we obtain the phonon frequencies and the phonon dispersion curves, as well as corresponding density of states. The calculated phonon frequencies at the Γ, X, and L points of the Brillouin zone show good agreement with the experimental values for most vibration modes. The thermodynamics properties including the phonon contribution to the Helmholtz free energy ΔF, the phonon contribution to the internal energy ΔE, the entropy S, and the constant-volume specific heat Cv are determined within the harmonic approximation based on the calculated phonon dispersion relations. The difference values of H-H298 have been also calculated and compared with the available experimental data.

Thermal properties of the metallic delafossite PdCoO2 : A combined experimental and first-principles study

Metallic delafossite materials (e.g., $\mathrm{PdCo}{\mathrm{O}}_{2}, \mathrm{PtCo}{\mathrm{O}}_{2}$), have attracted much recent attention due to record-high oxide conductivities, the origins of which remain unclear. Relatively little attention has been paid to their related thermal properties, however. We address this here via wide temperature range experimental studies of the crystal structure, thermal expansion, and specific heat of single-crystal $\mathrm{PdCo}{\mathrm{O}}_{2}$, combined with density-functional theory (DFT) calculations of the electronic and phononic densities of states, and thus thermal properties. $\mathrm{PdCo}{\mathrm{O}}_{2}$ is shown to retain the $R\overline{3}m$ space group from 12 to 1000 K, exhibiting a- and c-axis thermal expansion in good quantitative agreement with DFT-based lattice dynamics calculations. The Co-O bond lengths additionally elucidate the stability of the low-spin state of the nominally ${\mathrm{Co}}^{3+}$ ions, which is a notable difference between the edge-shared Co-O octahedra in $\mathrm{PdCo}{\mathrm{O}}_{2}$ and the corner-shared octahedra in Co-based perovskites. Measurements of specific heat from 1.9 to 400 K provide accurate values for the Debye temperature and Sommerfeld coefficient, the phononic part being describable via a combined Debye-Einstein approach (accounting for high-frequency oxygen-related optical phonons), with excess intermediate-temperature specific heat due to a prominent low-energy peak in the phonon density of states. Most significantly, all electronic and phononic contributions to the specific heat are shown to be remarkably closely reproduced by DFT-based calculations, establishing quantitative understanding of key thermal properties of the metallic delafossite $\mathrm{PdCo}{\mathrm{O}}_{2}$.

Electron removal spectral function of a polaron coupled to dispersive optical phonons

We explore the ground state and thermodynamic properties of the polaron coupled to quantum dispersive optical phonons in one spatial dimension. Calculations are performed using the finite--temperature Lanczos method augmented by a highly efficient construction of the variational Hilbert space. We focus on the electron removal spectral function as relevant for the angle-resolved photoemission experiments. We show that photoemission spectroscopy can be used to measure the phonon dispersion relation in a dilute system of polarons. The spectral weight of observed phonon bands is proportional to the phonon contribution to the wavefunction at finite phonon momentum. In addition, we demonstrate that when removing an electron from a polaron ground state, the polaron band does not appear in the spectral function. The latter becomes observable only at elevated temperatures.

The role of phonon anharmonicity on the structural stability and phonon heat transport of CrFeCoNiCux high-entropy alloys at finite temperatures

Chemical disorder and lattice distortion make high-entropy alloys (HEAs) promising to become a new generation of thermoelectric materials. However, the large parameter space of HEAs makes it still a great challenge to study their anharmonic unfolded phonon properties, and the role of anharmonicity in their structural stability and phonon heat transport is still unclear. Here we provide a new scheme to achieve a breakthrough in obtaining the unfolded anharmonic phonon properties from the dynamic trajectories. Through careful analysis of the unfolded phonon dispersions, we found that CrFeCoNiCu HEA has a special anharmonic phonon scattering distribution, which makes the contribution of short-wavelength and long-wavelength phonons to lattice thermal conductivity significantly different. In addition, we have developed a model for estimating the formation energy of HEAs based on the formation energy of binary alloy from first-principles calculation. Our results also show that anharmonic phonon scattering plays an important role in the stability of CrFeCoNiCux HEAs solid-solution phase, which also complements the dynamic mechanism of the formation and stability of dual-FCC phase. CrFeCoNiCu HEA has very low lattice thermal conductivity even at extremely low temperatures. The contribution of long-wavelength phonons to lattice thermal conductivity is more than ten times that of short-wavelength phonons, and they are the main contributors of phonon heat transport of CrFeCoNiCu HEA. This study makes it possible to study the unfolded phonon properties of HEAs at finite temperature and provides important theoretical support and information for the stability of solid-solution structure and phonon engineering for HEAs.

Tuning phononic and electronic contributions of thermoelectric in defected S-shape graphene nanoribbons

Thermoelectrics as a way to use waste heat, is essential in electronic industries, but its low performance at operational temperatures makes it inappropriate in practical applications. Tailoring graphene can change its properties. In this work, we are interested in studying the transport properties of S-shape graphene structures with the single vacancy (SV) and double vacancy (DV) models. The structures are composed of a chiral part, which is an armchair graphene nanoribbon, and two zigzag graphene ribbons. We investigate the changes in the figure of merit by means of the Seebeck coefficient, electronic conductance, and electronic and phononic conductances with the vacancies in different device sizes. The transport properties of the system are studied by using the non-equilibrium Green’s function method, so that the related Hamiltonians (dynamical matrices) are obtained from the tight-binding (force constant) model. The maximum figure of merit (ZT) obtains for the DVs in all lengths. Physical properties of such a system can be tuned by controlling various parameters such as the location and the type of the defects, and the device size. Our findings show that lengthening the structure can reduce phononic contribution, and single vacancies than double vacancies can better distinguish between electronic thermal conductance behavior and electronic conductance one. Namely, vacancy engineering can significantly increase thermoelectric performance. In the large devices, the SVs can increase the ZT up to 2.5 times.

Phononic heat conductance of gold atomic contacts: Coherent versus incoherent transport

We present here a theoretical method to determine the phononic contribution to the thermal conductance of nanoscale systems in the phase-coherent regime. Our approach makes use of classical molecular dynamics (MD) simulations to calculate the temperature-dependent dynamical matrix, and the phononic heat conductance is subsequently computed within the Landauer-B\"uttiker formalism with the help of nonequilibrium Green's function techniques. Tailored to nanostructures, crucial steps of force constant and heat transport calculations are performed directly in real space. As compared to conventional density functional theory (DFT) approaches, the advantage of our method is two-fold. First, interatomic interactions can be described with the method of choice. Semiempirical potentials may lead to large computational speedups, enabling the study of much larger systems. Second, the method naturally takes into account the temperature dependence of atomic force constants, an aspect that is ignored in typical static DFT-based calculations. We illustrate our method by analyzing the temperature dependence of the phononic thermal conductance of gold (Au) chains with lengths ranging from 1 to 12 atoms. Moreover, in order to evaluate the importance of anharmonic effects in these atomic-scale wires, we compare the phase-coherent approach with nonequilibrium MD (NEMD) simulations. We find that the predictions of the phase-coherent method and the classical NEMD approach largely agree above the Debye temperature for all studied chain lengths, which shows that heat transport is coherent and that our phase-coherent approach is well suited for such nanostructures.

Significant regulation of stress on the contribution of optical phonons to thermal conductivity in layered Li2ZrCl6: First-principles calculations combined with the machine-learning potential approach

The layered solid electrolyte Li2ZrCl6 and Li metal electrodes have a very good contact stability, but the thermal transport properties of Li2ZrCl6 are still unclear. Here, we systematically study the intrinsic lattice thermal conductivity (κp) of Li2ZrCl6 using the machine-learning potential approach based on first-principles calculations combined with the Boltzmann transport theory. The results show that the κp of Li2ZrCl6 at room temperature is 3.94 W/mK along the in-plane (IP) direction and 1.05 W/mK along the out-plane (OP) direction, which means that the κp is significantly anisotropic. In addition, under the compressive stress in the OP direction, the κp evolution along the IP and OP directions exhibits completely different trends, because the stress has a significant regulatory effect on the contribution of optical phonons to κp. With the increase in stress, the κp in the IP direction monotonically decreases, while the κp in the OP direction increases by a factor of 2.2 under a compressive strain of 13%. This is because the contribution of low-frequency optical phonons to κp in the IP direction is as high as 58% when no stress is applied, and this contribution is significantly suppressed with increasing compressive strain. However, the contribution of optical phonons in the OP direction to the κp increases with the increase in stress. Our results reveal the thermal transport properties of Li2ZrCl6 and the effect of the compressive strain on the κp of Li2ZrCl6, thereby providing a reference for the use of Li2ZrCl6 in Li-metal batteries.

Exploring the Spondias mombin (Hog plum) mediated ZnWO4– CuWO4 nanocomposite for photocatalysis and electrochemical nitrite sensing

A new fuel of Spondias mombin (hog plum) assisted, simple, environment friendly, cost-effective combustion synthesised ZnWO4–CuWO4 composite has been adopted for the photocatalytic dye degradation and nitrite sensing. The elemental, structural and morphological analysis of the composite has been carried out using wide range of techniques. Band gap energy and surface area are calculated with the help of UV-DRS and BET results. The photocatalytic study of binary tungstate ZnWO4–CuWO4 has showed better enhanced results compared to individual tungstates towards methylene blue (MB) dye degradation in the presence of visible light interactions. It is more suitable in the acidic environment for the effluent's removal. Despite of the phonon's contribution, higher mobility could be achievable due to more excited electrons and holes in a catalytic reaction. The detection limit of 26.09 μM for the detection of 5 mM nitrite possible with the ZnWO4– CuWO4 nanocomposite modified glassy carbon electrode (GCE).

Photoinduced band renormalization effects in the topological nodal-line semimetal ZrSiS

Out-of-equilibrium effects provide an elegant pathway for probing and understanding the underlying physics of topological materials. In particular, controlling electronic band structure properties using ultrafast optical pulses has shown promise for creating exotic states of matter. Of recent interest is band renormalization in Dirac and Weyl semimetals as it leads to direct physical observables through the enhancement of the effective mass or in the shift of resonant energies. Here we provide experimental and theoretical signatures of photoinduced renormalization of the electronic band structure in the topological nodal-line semimetal ZrSiS. Specifically, we show how the change in the transient reflectivity spectra under femtosecond optical excitations is induced by out-of-equilibrium effects that renormalize the kinetic energy of electrons. We associate the observed spectral features with an enhancement of the effective mass and to a redshift of the resonant frequency as a function of pump field strength. Finally, we show that the transient relaxation dynamics of the reflectivity is primarily an electronic effect with a negligible phononic contribution. Our study presents conclusive modifications of electronic properties in ZrSiS using ultrashort pulses and demonstrates the potential of this approach in creating photoinduced phases in topological quantum matter through an all-optical route.

Tailored light emission from color centers in nanodiamond using self-assembled photonic crystals

The defect centers in solid-state materials especially the nitrogen-vacancy (NV) centers in diamond have shown a tremendous potential for their utilization in quantum technology applications. However, they exhibit certain drawbacks such as the feeble zero phonon line with huge phonon contribution and the higher lifetime values. Here, we present a novel approach to control the spontaneous emission from NV centers in nanodiamond using engineered self-assembled photonic crystals. Using two complimentary emission measuring geometries at room temperature, we show a 63% suppression and 17% enhancement of NV center emission intensity using photonic stopgap, supported with simulations. The emission rates are modified in a broad spectral range of NV center emission and are consistent with the Barnett–Loudon sum rule. The results are crucial for emerging quantum technologies using NV centers in diamond.

Heat transfer in granular media with weakly interacting particles

We study the heat transfer in weakly interacting particle systems in vacuum. The particles have surface roughness with self-affine fractal properties, as expected for mineral particles produced by fracture, e.g., by crunching brittle materials in a mortar, or from thermal fatigue or the impact of micrometeorites on asteroids. We show that the propagating electromagnetic (EM) waves give the dominant heat transfer for large particles, while for small particles both the evanescent EM-waves and the phononic contribution from the area of real contact are important. As an application, we discuss the heat transfer in rubble pile asteroids.