Electronic thermal conductivity in suspended and supported bilayer graphene

Electronic thermal conductivity κ_e is investigated, using Boltzmann transport equation approach, in a suspended and supported bilayer graphene (BLG) as a function of temperature and electron concentration. The electron scattering due to screened charged impurity, short-range disorder and acoustic phonon via deformation potential are considered for both suspended and supported BLG. Additionally, scattering due to surface polar phonons, is considered in supported BLG. In suspended BLG, calculated κ_e is compared with the experimental data leaving the phonon thermal conductivity. It is emphasized that κ_e is important in samples with very high electron concentration and reduced phonon thermal conductivity. κ_e is found to be about two times smaller in supported BLG compared to that in suspended BLG. With the reduced extrinsic disorders, in principle, the intrinsic scattering by acoustic phonons can set a fundamental limit on possible intrinsic κ_e.     

Dynamical properties of the Peierls-Fröhlich state on the many-phonon-coupling model

The amplitude and phase phonons and the frequency dependent conductivity below the mean-field Peierls-Fröhlich transition temperature T_c, and the Kohn anomaly and fluctuation induced charge-density-wave conductivity above T_c, are discussed on the basis of the many-phonon-coupling model recently introduced by Rice, Duke and Lipari. For dominant intramolecular phonon coupling an isotope effect in T_c is related to the isotopic shift in the small polaron binding energy.     

Effect of magnon-phonon interaction on phonon damping of two-dimensional Heisenberg ferromagnetic system at finite temperature

A magnon-phonon interaction model is developed on the basis of a two-dimensional square Heisenberg ferromagnetic system. By using Matsubara Green function theory we studied the transverse and longitudinal acoustic phonon dampings and calculated the transverse and longitudinal acoustic phonon damping curves on the main symmetric point and line in the first Brillouin zone. It is found that on the line Δ there is no damping for transverse acoustic phonon and on the line Z there is no damping for longitudinal acoustic phonon. In the first Brillouin zone the damping of transverse acoustic phonons is at least one order larger than that of longitudinal acoustic phonons. The influences of various parameters on transverse and longitudinal acoustic phonon dampings are discussed and the lifetime and the density of state of transverse and longitudinal acoustic phonons are explored as well according to the relation of the phonon damping and its lifetime and the relation of the phonon damping and its density of state.     

Raman spectroscopy of ZnS nanostructures

We report Raman scattering results of wurtzite ZnS nanowires, nanocombs, and nanobelts. The Raman spectrum obtained from ZnS nanowires exhibits first‐order phonon modes at 272, 284, and 350 cm⁻¹, corresponding to A₁/E₁ transverse optical, E₂ transverse optical, and A₁/E₁ longitudinal optical phonons, respectively. Several multiphonon modes are also observed. The longitudinal optical phonon mode varies in wavenumber for nanocombs and nanobelts, indicating that the residual strain varies during the morphological change from ZnS nanowires to nanocombs and ultimately to nanobelts. Interestingly, a surface optical (SO) phonon mode varies in wavenumber depending on the shape and surface roughness of the ZnS nanostructures. The surface modulation wavelengths of the ZnS nanowires, nanocombs, and nanobelts are estimated using the SO phonon dispersion relations and the observed SO phonon wavenumbers. Copyright © 2012 John Wiley & Sons, Ltd.     

Phonon focusing effect on thermal conductivity of hexagonal group III-nitrides and silicon carbide crystals

Thermal conductivity κ of 4H-, 6H-SiC and wurtzite GaN, InN, AlN crystals is calculated accounting phonon focusing effect at low temperatures with only diffusive phonon boundary scattering. The orientation dependence of thermal conductivity is similar in these materials. Thermal conductivity is enhanced in the direction of approximately 45^∘ to the c axis up to 27% for GaN, 24% for 6H-SiC, 32% for InN, and 9% for AlN compared to the isotropic case for the circular cross-section and finite-length samples. Contributions of transverse T1 and T2 modes are nearly the same, about 40–45%, while the focusing of T2 mode contributes essentially to the angular dependence of κ. We find that the phonon focusing does not change κ value (within 5%) in the direction of 60^∘ to the c axis in all hexagonal crystals studied so far.     

Mode dependent scattering of phonons by domain walls in ferroelectric KDP

Thermal conductivity and ballistic phonon imaging measurements in KH₂PO₄ (KDP) at low temperature (T<3K) indicate that scattering from domain walls has a large effect on phonon transport. kDP has a ferroelectric phase transition from tetragonal to orthorhombic structure atT _c =122 K. BelowT _c domains of opposite electric polarization and crystal orientation form unless the sample is colled in an electric field. Thermal conductivity measured along the [100] (tetragonal) axis drops 30% when domain walls are present, which is independent of sample size and temperature. We attribute this decrease to phonon polarization-dependent scattering at the domain boundaries. This is verified by measurements of ballistic transport, using phonon imaging techniques, which reveal the phonon polarization and mode dependence of the scattering. The scattering is successfully modelled using continuum acoustics with simple acoustic mismatch at the domainwall. The interface scattering is found to be mode dependent: Caustic structures in the phonon images due to slow transverse phonons are most affected by the domain wall scattering, which channels these phonons along parallel planes by multiple reflections without mode conversion. Mode conversion scattering, though possible for a number of phonons, has little effect on the overall phonon transmission.     

Phonon linewidths in YNi<Subscript>2</Subscript>B<Subscript>2</Subscript>C

Phonons in a metal interact with conduction electrons which give rise to a finite linewidth. In the normal state, this leads to a Lorentzian shape of the phonon line. Density functional theory is able to predict the phonon linewidths as a function of wave vector for each branch of the phonon dispersion. An experimental verification of such predictions is feasible only for compounds with very strong electron-phonon coupling. YN₂B₂C was chosen as a test example because it is a conventional superconductor with a fairly high T _c (15.2 K). Inelastic neutron scattering experiments did largely confirm the theoretical predictions. Moreover, they revealed a strong temperature dependence of the linewidths of some phonons with particularly strong electron-phonon coupling which can as yet only qualitatively be accounted for by theory. For such phonons, marked changes of the phonon frequencies and linewidths were observed from room temperature down to 15 K. Further changes were observed on entering into the superconducting state. These changes can, however, not be described simply by a change of the phonon linewidth.      

Interpretation of temperature dependence of the in-plane electrical resistivity in YBa2Cu4O8: Electron–phonon approach

In this paper, we undertake a quantitative analysis of observed temperature-dependent in-plane normal state electrical resistivity of single crystal YBa₂Cu₄O₈. The analysis is within the framework of classical electron–phonon i.e., Bloch-Gruneisen model of resistivity. It is based on the inherent acoustic (low frequency) phonons (ω_ac) as well as high frequency optical phonons (ω_op), the contributions to the phonon resistivity were first estimated. The optical phonons of the oxygen breathing mode yields a relatively larger contribution to the resistivity compared to the contribution of acoustic phonons. Estimated contribution to in-plane electrical resistivity by considering both phonons i.e., ω_ac and ω_op, along with the zero-limited resistivity, when subtracted from single crystal data infers a quadratic temperature dependence over most of the temperature range [80 ? T ? 300]. Quadratic temperature dependence of ρ_diff. = [ρ_exp − {ρ₀ + ρ_e−ph (=ρ_ac + ρ_op)}] is understood in terms of electron–electron inelastic scattering. The relevant energy gap expressions within the Nambu-Eliashberg approach are solved imposing experimental constraints on their solution (critical temperature T_c). It is found that the indirect-exchange formalism provides a unique set of electronic parameters [electron–phonon (λ_ph), electron-charge fluctuations (λ_pl), electron–electron (μ) and Coulomb screening parameter (μ^*)] which, in particular, reproduce the reported value of T_c.     

Spin-phonon interactions near the one-dimensional antiferromagnetic ordering in CsNiCl3

The velocity of 10 MHz and 27 GHz longitudinal phonons propagating along the c-axis in the one-dimensional antiferromagnet CsNiCl₃ has been measured using ultrasonic and Brillouin light scattering techniques, respectively. An anomalous change in phonon velocity near the one-dimensional magnetic ordering temperature due to the spin-phonon interaction has been observed in both cases.     

Phonons in the organic conductor TEA(TCNQ)2 studied by neutron inelastic scattering

The lattice dynamics of the one-dimensional organic conductor TEA(TCNQ)₂ is studied by inelastic neutron scattering at temperatures 77, 175 and 295 K. Special attention is paid to the phonons propagating along c¹ which is approximately along the conducting axis. These phonons show a well defined Kohn anomaly at 2k_F as well as gaps which we attribute to both the tetrametic structure of the crystals and to the electron- phonon coupling. The temperature variation of the phonons along c¹ is found to be typical for a system where electron-phonon coupling dominates.     

Spin-state transition, magnetic, electrical and thermal transport properties of the perovskite cobalt oxide Gd0.7Sr0.3CoO3

The magnetization, resistivity ρ, thermoelectric power (TEP) S, and thermal conductivity κ in perovskite cobalt oxide Gd_0.7Sr_0.3CoO₃ have been investigated systematically. Based on the temperature dependence of susceptibility χ_g(T) and Seebeck coefficient S(T), a combination of the intermediate-spin (IS) state for Co³⁺ and the low-spin (LS) state for Co⁴⁺ can be suggested. A metal-insulator transition (MIT) caused by the hopping of σ* electrons (localized or delocalized e_g electrons) from the IS Co³⁺ to the LS Co⁴⁺ is observed. Meanwhile, S(T) curve also displays an obvious phonon drag effect. In addition, based on the analysis of the temperature dependence of S(T) and ρ(T), the high-temperature small polaron conduction and the low-temperature variable-range-hopping conduction are suggested, respectively. As to thermal conduction κ(T), rather low κ values in the whole measured temperature range is attributed to unusually large local Jahn-Teller (JT) distortion of Co³⁺O₆ octahedra with IS state.     

Thermal transport properties in the normal state of CaAlxSi2−x superconductors

Normal state electrical and thermal properties, including electrical resistivity (ρ), Seebeck coefficient (S), and thermal conductivity (κ) of the CaAl_xSi_2−x (x=0.9-1.2) system were investigated. It is found that the electrical resistivity and Seebeck coefficient exhibit a typical metallic character throughout the temperature range investigated, and the metallicity of this series is enhanced with increase in Al/Si ratio. On the other hand, the thermal conductivity shows a weak temperature variation at low temperatures, whereas κ follows a T²-dependence for T>150 K. Analysis of the electronic thermal resistivity based on Klemen’s model reveals that the scattering of electrons from the defects and static imperfections becomes dominant as the temperature approaches T_c. These results are discussed in the light of simultaneous existence of various crystal structures and development of ultra-soft phonon mode recently observed in the CaAlSi system.     

Strongly anisotropic thermal conductivity in planar hexagonal borophene oxide sheet

The flat hexagonal borophene oxide (B₂O) has the highest Li storage capacity among existing two-dimensional materials. Thermal conductivity is an important parameter for the safety of Li-ion batteries. We investigate the lattice thermal conductivity of B₂O by solving phonon Boltzmann transport equation combined with the first-principles calculations. We found that the relaxation time approximation remarkably underestimate the thermal conductivity (κ) of monolayer B₂O, revealing phonon hydrodynamics characteristic. The κ of B₂O from the exact solution of Boltzmann transport equation is 53 W m⁻¹ K⁻¹ and 130 W m⁻¹ K⁻¹ along armchair-direction and zigzag-direction at 300 K, respectively. B₂O exhibits strong thermal transport anisotropy due to anisotropic phonon group velocity, obviously larger than that of other borophene allotropes. At room temperature, the phonon mean free path of B₂O is about 231 nm and 49 nm along armchair-direction and zigzag-direction, respectively. The highly anisotropic thermal conductivity of B₂O offers new possibilities for its applications in thermal management.     

Wärmeleitung abschreckend kondensierter Bleischichten

The thermal conductivity of lead containing a large number of structural lattice defects is measured in the temperature range of about 2 to 20 °K. For the first time it is made possible by means of a special technique to investigate quenched films, which have been evaporated on to a cooled substrate in a high vacuum. The thermal conductivity of these films, which is much smaller than that of the bulk material, increases either by annealing or by increasing condensation temperature and film thickness, respectively. For most of the films the heat conduction is shown to be due only to the electrons. Therefore it can be discussed with respect to the validity of Wiedemann-Franz' Law and to deviations from Matthiessen's Rule in the temperature range of small angle scattering between electrons and phonons. The data of the superconducting state can be fitted to the BRT-expression for electronic conduction limited by defect scattering, if an energy gap of 2? ₀=(4.20±0.15)kT _c is chosen. The very small values of the phonon conductivity, estimated for the films with the lowest condensation temperatures, could result from the high concentrations of non-zero dimensional lattice defects, which have been observed earlier in such films.     

Observation of the quasidiffusive propagation of phonons in Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript>:Ho<Superscript>3+</Superscript> using time-resolved photo-phonon spectroscopy

The energy flux of phonons produced due to the nonradiative laser-induced transitions of Ho³⁺ impurity ions in forsterite from the ⁵F₅ states has been measured using a superconductor bolometer at a temperature of 2 K. The dependence of the flux on the laser wavelength, the time elapsed after the action of a laser pulse, and the phonon propagation path length is analyzed. It is found that the excitation of Ho³⁺ to some states leads to the diffusive propagation of emitted phonons in the spontaneous frequency decay mode (quasidiffusive mode of propagation): the time of arrival of a phonon pulse is almost a linear function of the path length, but it is several times longer than the longest ballistic time of flight (for transverse phonons). The diffusion coefficient and the nonradiative relaxation time are determined from the best fit to the experiment.     

Temperature variation of phonon frequency distribution in the fast ion conductor lead fluoride

A weighted phonon frequency distribution has been measured in PbF₂ at temperatures 10, 302, 660 and 910 K, using a neutron scattering technique. At 10 K good agreement is found between the measured distribution and the phonon density-of-states calculated from the low temperature dispersion relation of PbF₂. At the higher temperatures, near the ionic conductivity transition temperature, T_c ～ 700 K, the optic modes are observed to broaden into a high energy tail consistent with strong anharmonicity or extensive disorder. A low energy peak arising from transverse acoustic modes remains well defined even at temperatures above T_c.     

A method to calculate thermal conductivity of a nonperiodic system,bamboo Si<Subscript>1−x</Subscript>Ge<Subscript>x</Subscript> nanowire with axially degraded components

For a nonperiodic system, a bamboo Si_1?x Ge _x nanowire with axially degraded components, it is impossible to obtain its phonon dispersion relations through lattice dynamic or the first principle calculation. Therefore, we present a simple and available method to solve this problem. At first, the Si_1?x Ge _x nanowire with axially degraded component is divided into several sections according to its component distribution like bamboos’ sections formed in the growth process. For each section with a given x value, we constructed a pseudo-cell to calculate its phonon dispersion relations. Thermal conductances of junctions and of each section are then calculated by the phonon mismatch model and the phonon transmission probability with diffusive and ballistic portions. The dependences of thermal conductivity on the length of each section and the gradient of degraded component between sections are presented. We studied thermal conductivity dependence on temperature, length and diameter of the Si_1?x Ge _x nanowire with axially degraded component. And we found κ ~ l ^0.8, in which the exponent 0.8 is ascribed to the competition between phonons ballistic and diffusive transport. Furthermore, thermal conductivities along axial (100), (110), and (111) directions are discussed in detail. The method provides a simple and available tool to study thermal conductivity of a non-period system, such as a quasiperiodic superlattice or a nanowire with axially degraded component.     

Heat transport in the insulating phases of Sm1+x Ba2-x Cu3Oy high temperature superconductors

Thermal conductivity (κ) of two series of high-temperature superconductors with general formula Sm_1+x Ba_2-x Cu₃O_y have been measured. Both series begin with the same sample of T _c = 90.4 K and extend to nonsuperconducting phases. The first series is of 123 cation stoichiometry and variable oxygen content y, the second is a series of solid solutions with variable x. The temperature dependences of κ are very similar for superconducting partner samples from both series (i.e. with the same T _c), whereas the nonsuperconducting samples reveal dramatic differences. We propose to attribute the huge increase of κ and the change of its temperature characteristics of insulating oxygen deficient sample to some additional heat carriers, supposedly of magnetic origin. Absence of this additional heat transport mechanism for insulating solid solution allows to treat it as a proper reference for estimation of phonon contribution in the superconducting 123 compounds.     

The effect of normal phonon-phonon scattering processes on the maximum thermal conductivity of isotopically pure silicon crystals

The effect of normal phonon-phonon scattering processes on the thermal conductivity of silicon crystals with various degrees of isotope disorder is considered. The redistribution of phonon momentum in normal scattering processes is taken into account within each oscillation branch (the Callaway generalized model), as well as between different oscillation branches of the phonon spectrum (the Herring mechanism). The values of the parameters are obtained that determine the phonon momentum relaxation in anharmonic scattering processes. The contributions of the drift motion of longitudinal and transverse phonons to the thermal conductivity are analyzed. It is shown that the momentum redistribution between longitudinal and transverse phonons in the Herring relaxation model represents an efficient mechanism that limits the maximum thermal conductivity in isotopically pure silicon crystals. The dependence of the maximum thermal conductivity on the degree of isotope disorder is calculated. The maximum thermal conductivity of isotopically pure silicon crystals is estimated for two variants of phonon momentum relaxation in normal phonon-phonon scattering processes.     

Interpretation of thermoelectric power behaviour of Zinc nanowire composites: Phonon-scattering mechanism

We develop a theoretical model for quantitative analysis of temperature-dependent thermoelectric power (S) of Zn nanowires. In doing so, we first use the Mott expression to compute the electron diffusive thermoelectric power (S_c^diff.) using Fermi energy as electron-free parameter, S_c^diff. shows linear temperature dependence. Further, the S_c^diff. contribution is subtracted from the experimental data and the difference (S_experimental-S_c^dif) is characterized as phonon drag thermoelectric power (S_ph^drag) which is obtained within the relaxation time approximation where the thermoelectric power is limited by the scattering of phonons with impurities, grain boundaries, charge careers and phonons in the nanowires. The S_ph^drag shows anomalous temperature-dependent behaviour, which is an artifact of various operating scattering mechanisms. The observed anomalies are well accounted in terms of interaction among the phonons-impurity, phonon-grain boundaries, phonon-electron and the umklapp scattering. It is also shown that for phonons the scattering and transport cross-sections are proportional to ω⁴ in the Rayleigh regime where ω is the frequency of the phonons. Numerical analysis of thermoelectric power from the present model shows similar results as those revealed from experiments.