Nernst-Ettingshausen Coefficient Research Articles

Нернстовская подвижность дырок в Bi2Te3

This paper presents the results of a study of the electrical conductivity coefficient, the Hall coefficient, the Seebeck coefficient, the transverse Nernst-Ettingshausen coefficient and their anisotropy in a Bi2Te3 single crystal with a hole concentration p =1 × 1019 cm–3 at temperatures 77–350 К. It is established that hole scattering occurs mainly on long-wave acoustic phonons. Despite the fact thatthe chemical potential level is located near the top of the additional extreme of the valence band, no interband scattering was detected. The complex structure of the valence band is confirmed.

Comparative Study of the Nernst–Ettingshausen Coefficient in the Normal Phase in the Y1 – xPrxBa2Cu3Oy and Y0.85 – xPrxCa0.15Ba2Cu3Oy Systems

The results of the comparative study of the modification of the temperature dependences of the Nernst–Ettingshausen coefficient Q in the normal phase of two series of the samples of the Y1 – xPrxBa2Cu3Oy and Y0.85 – xPrxCa0.15Ba2Cu3Oy compositions due to praseodymium doping are presented. The specific features of dependences Q(T) and Q300 K(T) appeared as additional calcium ions exist in the YBa2Cu3Oy lattice have been revealed and analyzed. It is shown that dependences Q(T) and the temperature dependences of the thermopower coefficient obtained for the same samples previously are completely described in terms of the narrow-band model for both systems under study. The charge carrier mobilities and the degrees of asymmetry of the dispersion law are determined using a quantitative analysis of the experimental data. It is shown that the existence of additional calcium ions in the lattice does not influence a change in the asymmetry of the dispersion law with an increase in the praseodymium content, but strongly influences the character of changing the mobility. The found dependence of the mobility on the level of doping in the two systems and the observed difference in the characters of the changes in the absolute values of the thermopower coefficient and the Nernst–Ettingshausen coefficient in the Y0.85 – xPrxCa0.15Ba2Cu3Oy system are explained on the basis of the analysis of the mechanisms of influence of the energy spectrum parameters on the charge carrier mobility in the YBa2Cu3Oy system.

On the Band Structure of Bi2Te3

For p-Bi2Te3 crystals grown by the Czochralski method, the temperature dependences of the conductivity, Hall coefficient, thermoelectric power (α), and transverse Nernst–Ettingshausen coefficient are obtained experimentally in the temperature range 77–450 K. The transmittance spectrum in the range 400–5250 cm–1 is recorded at room temperature. It is shown that, to interpret the temperature dependences of the scattering parameter r and the ratio of the thermoelectric power to temperature (α/T), it is essential to take into account the complex valence-band structure and the contribution of heavy holes to transport phenomena. Estimations of the energy band parameters in the context of the two-band model give a hole effective mass close to the free electron mass and the energy gap between nonequivalent extrema at a level of several hundredths of eV. In the absorption spectrum derived from the transmittance spectrum, a sharp increase in absorption defined by indirect interband transitions with the band gap Eg ≈ 0.14 eV is observed in the region of frequencies ν ≥ 1000 cm–1. The absorption spectrum calculated from the reflectance data using the Kramers–Kronig relations is in agreement with the experimental absorption spectrum.

О зонной структуре Bi-=SUB=-2-=/SUB=-Te-=SUB=-3-=/SUB=-

AbstractFor p -Bi_2Te_3 crystals grown by the Czochralski method, the temperature dependences of the conductivity, Hall coefficient, thermoelectric power (α), and transverse Nernst–Ettingshausen coefficient are obtained experimentally in the temperature range 77–450 K. The transmittance spectrum in the range 400–5250 cm^–1 is recorded at room temperature. It is shown that, to interpret the temperature dependences of the scattering parameter r and the ratio of the thermoelectric power to temperature (α/ T ), it is essential to take into account the complex valence-band structure and the contribution of heavy holes to transport phenomena. Estimations of the energy band parameters in the context of the two-band model give a hole effective mass close to the free electron mass and the energy gap between nonequivalent extrema at a level of several hundredths of eV. In the absorption spectrum derived from the transmittance spectrum, a sharp increase in absorption defined by indirect interband transitions with the band gap E _ g ≈ 0.14 eV is observed in the region of frequencies ν ≥ 1000 cm^–1. The absorption spectrum calculated from the reflectance data using the Kramers–Kronig relations is in agreement with the experimental absorption spectrum.

Transverse Nernst–Ettingshausen Effect in Superlattices Upon Electron-Phonon Scattering

The Nernst–Ettingshausen coefficient is calculated in superlattices with the cosine dispersion law in the case of the scattering of charge carriers at acoustic and polar optical phonons in a magnetic field in the layer plane. A significant increase in the Nernst–Ettingshausen coefficient of a degenerate quasi-three-dimensional electron gas in a weak magnetic field is shown. For polar optical-phonon scattering, the Nernst–Ettingshausen coefficient changes sign in a strong magnetic field.

Anisotropy of Nernst–Ettingshausen Effect in Superlattices During Scattering on Phonons

The paper focuses on anisotropy of the transverse Nernst–Ettingshausen effect in superlattices depending on the degree of mini-band filling and magnetic field direction during scattering on acoustic and polar optical phonons. The authors demonstrate that in the case of scattering on polar optical phonons one observes considerable anisotropy and, depending on the magnetic field direction, the Nernst–Ettingshausen coefficient may change its sign.

Поперечный эффект Нернста-Эттингсгаузена в сверхрешетках при электрон-фононном рассеянии

AbstractThe Nernst–Ettingshausen coefficient is calculated in superlattices with the cosine dispersion law in the case of the scattering of charge carriers at acoustic and polar optical phonons in a magnetic field in the layer plane. A significant increase in the Nernst–Ettingshausen coefficient of a degenerate quasi-three-dimensional electron gas in a weak magnetic field is shown. For polar optical-phonon scattering, the Nernst–Ettingshausen coefficient changes sign in a strong magnetic field.

Determination of parameters of a system of charge carriers in Y1–2x Ca x Pr x Ba2Cu3O y within a combined analysis of temperature dependences of thermoelectric power and Nernst–Ettingshausen coefficients

The temperature dependences of thermoelectric power S and transverse Nernst–Ettingshausen effect Q in high-temperature superconductors of the Y1–2xCaxPrxBa2Cu3Oy system with different concentrations of dopants have been investigated experimentally. It has been shown that all the specific features revealed in the behavior of the two kinetic coefficients under investigation can be described using the narrowband model with a single concept of the structure of an energy spectrum and a common set of model parameters that characterize the structure of the spectrum and properties of a system of charge carriers. Based on the quantitative analysis of the dependences S(T) and Q(T), the values of these parameters for samples of the studied composition have been determined and the character of their changes with an increase in the impurity content has been analyzed. It has been demonstrated that, for the explanation of the obtained results, it is necessary to take into account the interaction of calcium and praseodymium ions upon their simultaneous introduction into the lattice. It has been found that the mobility of charge carriers has extremely low values and almost does not depend on the level of doping, which is associated with the character of changes in the structure of the energy spectrum of Y1–2xCaxPrxBa2Cu3Oy upon doping. It has been concluded that the structure of the energy spectrum of high-temperature superconductors in the yttrium system is characterized by an asymmetry of the dispersion curve.

Magnetization currents of fluctuating Cooper pairs

Recent experiments show that the Nernst-Ettingshausen effect is orders of magnitude stronger than the thermoelectric Seebeck effect in superconductors above the critical temperature. We explain different magnitudes of the two effects accounting for the magnetization current of virtual Cooper pairs. The method allows for detailed understanding of the surprising non-monotonic dependence of the Nernst-Ettingshausen coefficient on the magnetic field.

Quantum oscillations as the tool for study of new functional materials (Review Article)

We present an overview of our recent results on quantum magnetic oscillations in new functional materials. We begin with the Lifshitz and Kosevich approach for quasi-2D layered materials and obtain general formulas for the oscillatory parts of the grand thermodynamic potential and magnetization. Then we consider the oscillations of the Nernst–Ettingshausen coefficient which consists of thermal and magnetization parts. The difference between normal and Dirac carriers is also discussed. To conclude we consider a model for multilayer grapheme which allows to calculate exactly the Berry phase which remains undetermined in the Lifshitz–Kosevich approach. The magnetic oscillations of the density of states and capacitance for different number of the carbon layers are described.

Transport phenomena in the anisotropic layered compounds MeBi4Te7 (Me = Ge, Pb, Sn)

The transport coefficients (the Nernst-Ettingshausen coefficient Q123, electrical conductivity σ11, thermal conductivity κii, the Seebeck coefficients S11 and S33, and the Hall coefficient R213) in samples of layered compounds of the homologous series AIVBVI-A2VB3VI (AIV = Ge, Sn, Pb; AV = Bi, Sb; BVI = Te), specifically, SnBi4Te7 and PbBi4Te7 (of n-type conductivity), have been experimentally studied in the temperature range of 77–400 K. The crystals were grown by the Czochralski method. Analysis showed that the obtained data on the transport phenomena in SnBi4Te7 and PbBi4Te7 can be considered in the one-band energy spectrum model. Comparison of the parameters found for the stoichiometric samples demonstrated that the electron density of states and the fraction of electrons scattered at impurity ions increase when passing from GeBi4Te7 to SnBi4Te7 and PbBi4Te7. It is found that additional doping of PbBi4Te7 with cadmium and silver significantly affects its electronic and phonon systems, just as doping with copper affects the electric and thermal properties of GeBi4Te7.

Simple apparatus for the multipurpose measurements of different thermoelectric parameters

A simple apparatus for the simultaneous measurement of Seebeck coefficient ( α) and electrical resistivity ( ρ) in the temperature range 100–600 K, Hall coefficient ( R H) and transverse Nernst–Ettingshausen coefficient ( N) in the temperature range 300–600 K of the bar shaped samples has been fabricated. The instrument has been designed so simply that the sample can be easily mounted for the fast measurements of different thermoelectric parameters. The sample holder assembly of the apparatus has been designed so cleverly that any part of that section can be replaced in case of any damage; and so it can be regarded as a modular based system. The apparatus is relatively cheaper in cost and also portable.

Doping of the Bi1.9Sb0.1Te3 solid solution with Sn impurity

In (Bi1.9Sb0.1)1 − x Sn x Te3 solid solution with different contents of Sn, the electrical conductivity (σ11) and the Hall (R 123 and R 321), Seebeck (S 11 and S 33), and Nernst-Ettingshausen (Q 123 and Q 321) coefficients have been measured. It is shown that doping with tin strongly modifies temperature dependences of the kinetic coefficients. The effect of tin on electrical homogeneity of the samples has been studied: with increasing number of Sn atoms embedded, crystals become more homogeneous. These features indicate the presence of the quasi-local states of Sn in the valence band of Bi1.9Sb0.1Te3. Within a one-band model, we estimated the effective mass of the density of hole states (m d ), the energy gap extrapolated to 0 K (E g0 = 0.20–0.25 eV), the energy of impurity states (E Sn ≈ 40–45 meV), and the scattering parameter (r ≈ 0.1–0.4). Numerical values of the scattering parameter indicate a mixed mechanism of scattering in the samples under investigation with dominant scattering at acoustic phonons. With increasing content of tin in the samples, the contribution of impurity scattering increases.

Influence of impurities on the thermoelectric properties of layered anisotropic PbBi4Te7 compound: Experiment and calculations

The kinetic coefficients of high-quality single crystals of ternary layered n-PbBi4Te7 compounds have been measured in the temperature range of 77–400 K. These crystals, doped with electroactive Cd and Ag impurities, were grown by Czochralski pulling with melt supply through a floating crucible. A significant anisotropy of the thermoelectric properties is found. The means of incorporation of electroactive impurities into the ternary compound lattice is established. The experimental values of the Nernst—Ettingshausen coefficient have been analyzed together with the Seebeck, Hall, and conductivity data. The features of transport phenomena in PbBi4Te7 can be explained within the single-band model of nonparabolic energy spectrum and mixed mechanism of electron scattering from acoustic phonons and the Coulomb potential of impurities. It is suggested that acoustic phonon scattering is dominant along the cleavage plane, whereas the impurity scattering dominates along the trigonal axis.

Magneto-thermoelectric effects in two-dimensional quantum well: role of short-range potential

We have studied transverse thermomagnetic effects in a quantum well (QW) with parabolic potential in the presence of a magnetic field parallel to the two-dimensional electron gas layer. The calculation was carried out for the case of elastic electron scattering on short-range potential for degenerate and non-degenerate electron gas. It is shown that the reviewed mechanism of charge carriers' relaxation is essential for the electroconductivity at low temperatures. In the quantum limit, the dependencies of the transverse Nernst–Ettingshausen coefficient and the thermopower on the magnetic field strength, the temperature and the carrier density are determined and analyzed. We have showed that the magnetothermopower is not determined by the entropy only, as is the case for bulk specimens.

On the hole scattering anisotropy in the PbSb2Te4 layered compound from data on the Nernst-Ettingshausen coefficient

Three independent components of the Nernst-Ettingshausen coefficient tensor Q ikl are experimentally measured for an anisotropic single crystal of the p-PbSb2Te4 layered compound. The components Q 123 and Q 132 are found to be negative, whereas the component Q 321 is positive. The experimental data on the anisotropy of the Nernst-Ettingshausen coefficient are discussed together with the available data on the thermopower, the Hall effect, and the electrical conductivity. The analysis demonstrates that the experimental data on the transport effects in p-PbSb2Te4 can be explained within a one-band model of the band spectrum and a mixed mechanism of hole scattering under the assumption that scattering from acoustic phonons and scattering from impurity ions are dominant in the cleavage plane and along the c 3 trigonal axis, respectively.

Effect of copper doping on kinetic phenomena in n-Bi2Te2.85Se0.15

In single crystals of copper-doped and undoped Bi2Te2.85Se0.15 solid solutions with an electron concentration close to 1 × 1019 cm−3, the temperature dependences are investigated for the Hall (R 123, R 321) and Seebeck (S 11) kinetic coefficients, the electrical-conductivity (σ 11), Nernst-Ettingshausen (Q 123), and thermalconductivity (k 11) coefficients in the temperature range of 77–400 K. The absence of noticeable anomalies in the temperature dependences of the kinetic coefficients makes it possible to use the one-band model when analyzing the experimental results. Within the framework of the one-band model, the effective mass of density of states (m d ≈ 0.8m 0), the energy gap (eg ≈ 0.2 eV), and the effective scattering parameter (r eff ≈ 0.2) are estimated. The obtained value of the parameter r eff is indicative of the mixed electron-scattering mechanism with the dominant scattering by acoustic phonons. Data on the thermal conductivity and the lattice resistivity obtained by subtracting the electron contribution according to the Wiedemann-Franz law are presented.

The Nernst-Ettingshausen coefficient in hole-doped manganites

A systematic study of the Nernst-Ettingshausen coefficient (NEC) in hole-doped manganites of the LaMnO3 and SmMnO3 systems was carried out at temperatures both above and below the point of transition to the magnetically ordered state (Tc). The results obtained for T > Tc suggest that conduction is mediated here by small-radius polarons. For all the compositions studied, the Nernst mobilities at T = 300 K are small (of the order of 0.1–2 cm2/V s) and the carrier relaxation time at T > Tc increases with carrier energy. At temperatures below Tc, the NEC exhibits an anomalous behavior. The giant NEC effect was observed, which consists in a strong dependence of the NEC on applied magnetic field and the presence of a peak in the temperature dependence of the NEC at T ≈ Tc. Near the transition to the magnetically ordered state, the NEC follows a behavior similar to that of colossal magnetoresistance and giant magnetothermoelectric power. A possible origin of the anomalous NEC behavior at T < Tc is discussed.

The Nernst–Ettingshausen Coefficient in the Normal Phase of Doped HTSCs of the YBa[sub 2]Cu[sub 3]O[sub y] System

The temperature dependence of the Nernst-Ettingshausen coefficient Q(T) in the normal phase of doped HTSCs of the yttrium system was studied. The main features characterizing the behavior of this coefficient were revealed, and the character and mechanism of the effect that various nonisovalent substituents exert on the Q(T) dependence were analyzed. It is shown that the narrow-band model permits one not only to describe all the specific features observed in the Q(T) curves but also to perform a simultaneous quantitative analysis of the temperature dependences of four kinetic coefficients (the electrical resistivity and the Seebeck, Hall, and Nernst-Ettingshausen coefficients) with the use of a common set of model parameters characterizing the band structure and carrier system in the normal phase of an HTSC. This approach was employed to determine the carrier mobilities and the asymmetry of the dispersion curve in the systems studied (YBa2Cu3Oy, y = 6.37–6.91; YBa2Cu3−xCoxOy, x = 0–0.3; Y1−xCaxBa2Cu3Oy, x = 0–0.25; Y1−xCaxBa2−xLaxCu3Oy, x = 0–0.5) and to analyze the effect of the substitutions involved on the variation of these parameters.

Thermoelectric and Thermomagnetic Transport in PbTe with Nanoscale Structures

ABSTRACTQuantum-dot superlattices (QDSLs) have demonstrated thermoelectric figure of merit (ZT) values double those of classical bulk materials, providing the proof that nanoscale materials can address this age-old limitation on thermoelectric technology. Since QDSL materials can only be obtained in thin-film form, the development of bulk materials with nanoscale inclusions would be useful for many large-scale applications. Nanometer-scale inclusions in lead chalcogenides are known to improve the thermoelectric figure of merit through a combination of two factors: a strong decrease in lattice thermal conductivity, and an increase in the Seebeck coefficient over that of bulk PbTe for a given carrier concentration. This paper focuses on experimental results obtained on two types of PbTe nanocomposites, namely samples prepared by sintering powders with nanometer-sized grains, and samples prepared with nanoprecipitates of metallic Pb. The results are analyzed using the “method of four coefficients.” At each measurement temperature there are four unknowns. These are the carrier concentration, the mobility, the carrier effective mass, and the energy dependence of the relaxation time Tau, which is modeled by a power law: Tau proportional to energy to power Lamda. Therefore, at each temperature, four measurements are taken: the electrical conductivity, and the Hall, Seebeck and transverse Nernst-Ettingshausen coefficients. This analysis concludes that the effect of the nanoscale inclusions on the power factor is due to an increase in the scattering parameter λ, and that the nanoscale inclusions affect the electron scattering in such a way as to increase the Seebeck coefficient.