Ettingshausen Coefficient Research Articles

Magnetothermoelectric transport properties of multiterminal graphene nanoribbons

The Peltier effect and the Ettingshausen effect are investigated in graphene nanoribbons, where charge current produces heat current along the longitudinal direction in the former case, and longitudinal charge current generates transverse heat current in the latter case. With the aid of the nonequilibrium Green's function and the Landauer-B\"uttiker formalism, the Peltier coefficient ${\mathrm{\ensuremath{\Pi}}}_{c}$ and the Ettingshausen coefficient ${\mathrm{E}}_{c}$ are obtained. We found that the Kelvin relation is always valid for the longitudinal thermoelectric transport, i.e., ${\mathrm{\ensuremath{\Pi}}}_{c}=\mathcal{T}{S}_{c}$, with $\mathcal{T}$ the temperature and ${S}_{c}$ the Seebeck coefficient. In contrast, for transverse magnetothermoelectric transport, the Kelvin relation breaks down and ${\mathrm{E}}_{c}\ensuremath{\ne}\mathcal{T}{N}_{c}$ usually, with ${N}_{c}$ the Nernst coefficient. In the region of weak magnetic field, the Ettingshausen effect depends strongly on device parameters. When the Fermi energy ${E}_{F}$ is close to the Dirac point, the Ettingshausen effect of the semiconducting armchair graphene nanoribbon is much stronger than that of the metallic one. When ${E}_{F}$ is far away from the Dirac point, the Ettingshausen coefficient ${\mathrm{E}}_{c}$ oscillates around zero. When under a strong magnetic field, ${\mathrm{E}}_{c}$ is independent of the device parameters and swells only near the Dirac point. Further, the dependence of ${\mathrm{E}}_{c}$ on ${E}_{F}$ can be scaled by ${E}_{F}/{k}_{B}\mathcal{T}$, with a peak value of $(2ln2){k}_{B}\mathcal{T}/e$ for the three-terminal system and $(\frac{4}{3}ln2){k}_{B}\mathcal{T}/e$ for the four-terminal system. We also study the impact of disorder on the Ettingshausen effect. Regardless of the magnetic field strength, ${\mathrm{E}}_{c}$ is robust against moderate disorder scattering. In addition, in the strong magnetic field, ${\mathrm{E}}_{c}$ with additional regular oscillating structure can be caused by disorder.

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.

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.

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.

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.

Thermomagnetic properties of the overdoped La 1.7Sr 0.3CuO 4 superconductor

We have studied the normal-state transport phenomena of the La 1.7Sr 0.3CuO 4 overdoped high- T c superconductor. The Ettingshausen ( P E), Hall ( R H) and Seebeck ( S) coefficients as well as the thermal ( κ) and electrical ( σ) conductivities have been measured. The temperature dependence of the isothermal Nernst ( Q i) coefficient has been estimated on the basis of the Bridgman relation. The results have been interpreted in terms of a rigid, single-band model, with an assumption that both doping and temperature change the band filling resulting in the variation of the Fermi surface curvature. The latter quantity appeared to be a key feature driving the temperature dependences of P E and R H. In opposition to the usual interpretation, the temperature dependence of the R H for La 1.7Sr 0.3CuO 4 is dominated by variations of the Fermi surface shape, and not by the changes in the charge carrier concentration. The consistency of this physical picture was controlled by an estimation of P E using measured values of σ, R H, S and κ and comparison with measured value of the Ettingshausen coefficient.

Thermo-magnetic effects in La 2− xSr xCuO 4

The room temperature values of the Ettingshausen ( P), Hall ( R H) and Seebeck ( S) coefficients have been measured for La 2− x Sr x CuO 4 superconductor ( x=0.03–0.35). It was found that in the whole composition range P is of the order of 10 −7 m 3 K/ J , which is characteristic of typical metals. The Ettingshausen coefficient is positive for x<0.07 and negative for higher Sr content. The Hall coefficient changes sign for much higher Sr concentration of x≈0.32, whereas the thermopower remains positive for all samples. The compositional dependences of the measured transport coefficients have been described in terms of simple tight-binding model with smooth variation of the Fermi surface curvature from positive to negative.

Normal-state Ettingshausen, Seebeck, and Hall effects inLa2−xSrxCuO4

The room temperature values of the Ettingshausen ${(P}_{E}),$ Hall ${(R}_{H}),$ and Seebeck (S) coefficients as well as of the electrical conductivity $(\ensuremath{\sigma})$ have been measured for a ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ high-${T}_{c}$ superconductor $(x=0.03\char21{}0.35).$ It was found that in the whole composition range ${P}_{E}$ is of the order of ${10}^{\ensuremath{-}7} {\mathrm{m}}^{3}\mathrm{K}/\mathrm{J},$ which is characteristic of typical metals. The Ettingshausen coefficient is positive for $x\ensuremath{\lesssim}0.07$ and negative for higher Sr content. Both the Hall coefficient and thermopower decrease logarithmically, with increasing x, down to $x\ensuremath{\approx}0.3,$ then ${R}_{H}$ changes sign but S remains positive, exhibiting a minimum. A short review of the interpretations of the Ettingshausen effect is presented. The behavior of the measured transport coefficients have been described by a simple tight-binding-like model with a smooth variation of the Fermi surface curvature from positive to negative, which explains the sign change in ${R}_{H}$ and the minimum in S. The sign inversion of the Ettingshausen coefficient was interpreted as a result of a competition between two processes generating this effect, called ``scattering'' and ``curvature'' mechanisms.

Normal-state Ettingshausen effect in La2-xSrxCuO4

A method for measurements of small (metallic) Ettingshausen coefficient (P) was developed. The influence of the dominating thermal effects, the Joule and Thomson heats, was eliminated by making use of the odd symmetry of the Ettingshausen temperature gradient with respect to reversal of the direction of the magnetic field and electrical current. The method was applied to La2-xSrxCuO4 (x = 0.03-0.35) high-Tc superconductor in the normal state. We have found that in the whole composition range the Ettingshausen coefficient is of the order of 10-7 m3 K J-1 which is characteristic of typical metals. The coefficient changes sign from positive to negative near x0.07. Weak variation of P is in contrast to the behaviour of other transport coefficients for La2-xSrxCuO4, such as the thermoelectric power or the Hall coefficient, which have been reported in the literature to change their values by more than two orders of magnitude with Sr doping.

Fluctuational Ettingshausen effect in single crystals of YBa 2Cu 3O 7−δ

We have studied the Ettingshausen effect in single crystals of YBa 2Cu 3O 7−δ near the superconducting transition temperature T c . Two distinct regimes were found in the field dependence of the Ettingshausen coefficient — a low-field regime where flux-flow dominates and a high-field regime where fluctuation dominates. The result is in agreement with Ullah and Dorsey's scaling theory for fluctuational Ettingshausen effect, and seems also consistent with Maki's mean-field theory when the temperature of the sample is several Kelvins away from T c .

Relation between thermoelectric power and Hall coefficient with application to the normal state of high Tc superconductors

Arguments going back to Bridgman relate longitudinal and transverse transport coefficients. In particular, Ettingshausen, Thomson and Hall coefficients are thereby interconnected. By exploiting both one- and two-band models, the Ettingshausen coefficient is microscopically connected to the Hall coefficient. This leads to a formula which relates thermoelectric power linearly to the Hall coefficient. Data for high T c superconductors in the normal state supports such a direct correlation between these properties.

Effect of fluctuations on the transport properties of type-II superconductors in a magnetic field.

The time-dependent Ginzburg-Landau theory is used to study both transverse and longitudinal transport properties of a layered superconductor in a magnetic field near the mean-field transition temperature ${\mathit{T}}_{\mathit{c}2}$(H). We evaluate the transport coefficients in the self-consistent Hartree approximation which interpolates smoothly between the high-temperature regime, dominated by Gaussian fluctuations, and the low-temperature flux-flow regime, with no intervening divergence. This behavior is in agreement with the experimental results for the Ettingshausen coefficient, Nernst coefficient, longitudinal conductivity, and Hall conductivity in high-temperature superconductors.

Critical fluctuations in high-temperature superconductors and the Ettingshausen effect.

We study the fluctuation Ettingshausen effect in a type-II superconductor using the time-dependent Ginzburg-Landau equation. The free-fluctuation theory predicts a divergence in the Ettingshausen coefficient at T=${\mathit{T}}_{\mathit{c}2}$(H), in conflict with the recent data of Palstra et al. [Phys. Rev. Lett. 64, 3090 (1990)]. Including interactions through a self-consistent Hartree approximation eliminates the divergence and provides a quantitative explanation of the experiments.

A study of the quantum oscillations in the thermopower of molybdenum

This paper is concerned with quantum oscillations in the thermoelectric coefficients of metals which do not undergo magnetic breakdown, and in particular focuses on the compensated metal Mo. An expression for the amplitude of the oscillations in the thermopower has been developed and is tested using a detailed set of experimental results on Mo taken with [Formula: see text] over the range 1.5–8 T at liquid helium temperatures. Good agreement is obtained for the temperature and field dependence, and absolute amplitudes are predicted to within a factor near unity. Oscillations of appreciable amplitude arc neither expected nor observed in the Nernst–Ettingshausen (N.E.) coefficient of Mo. Available thermopower data on In have also been analysed; it is concluded that, contrary to a previous speculation. In does not undergo magnetic breakdown at fields of the order of 2 T. It is suggested that, contrary to the thermopower. the N.E. coefficient will provide an unambiguous test for the occurrence of breakdown in metals since it is expected to exhibit large amplitude quantum oscillations only under breakdown conditions.

Drift-diffusion contributions to the thermopower and Nernst–Ettingshausen coefficient of graphite

Abstract Drift-diffusion contributions to the thermoelectric power and Nernst–Ettingshausen effect have been calculated for graphite, using simplified models for the dispersion relationship ∊(k) and carrier relaxation time τ(∊). A comparison of the results with those derived from experiment on single-crystal and highly oriented pyrolytic graphite allows phonon-drag contributions to be estimated. The calculations suggest that differences in the temperature dependence of the thermoelectric power for these types of graphite are due to differences in scattering mechanisms at low temperature. Several experiments are suggested to check the predictions of the models.

Electron transport properties of InP

Measurements of electrical conductivity σ and Hall coefficient RH have been made as a function of temperature in the range room temperature to 250 °C and as a function of magnetic field up to 3.2 T on single crystal n-type samples of InP with carrier concentrations in the range 3.5 × 1021 to 1.2 × 1024 m−3. Theoretical calculations of σ and RH have been made using the method of Fletcher and Butcher and the resulting values fitted to the experimental data by using various scattering parameters as adjustable. The parameters so obtained have then been used to predict further magnetoresistance values and values of thermoelectric power and Nernst–Ettingshausen coefficient. The predicted values of magnetoresistance and thermoelectric power show good agreement with experimental values but not those of the Nernst–Ettingshausen coefficient, possibly due to experimental problems.

The transverse magnetothermoelectric properties of an indium single crystal

Recently published results show that, at temperatures of the order of very-much-less-than/sub D//10, Al and In exhibit large changes in the thermopower when a high magnetic field is applied transverse to the samples. To improve our understanding of this effect, we have experimentally determined six independent transport coefficients of an In single crystal with a magnetic field (up to 2 T) along (001) at temperatures between 2.5 and 8 K. This procedure enables us to ascertain which quantities make the major contribution to the observed thermopower change; it is found that the Hall resistivity rho/sub yx/ and the Nernst--Ettingshausen coefficient epsilon''/sub yx/ play the major role. We are able to prove that phonon drag is mainly responsible for the effects.

Galvano- and Thermomagnetic phenomena in thin films with nonidentical surfaces

A theory of galvano- and thermomagnetic phenomena in thin films with nonidentical surfaces is presented. The kinetic equation is solved with consideration of boundary conditions in films with nonidentical surfaces in the presence of a magnetic field perpendicular to the film plane, and an electric field and temperature gradient within the film plane. General expressions are found for the components of the galvano- and thermomagnetic tensorsδik,βik,κik which are oscillating functions of film thickness and magnetic field. A detailed analysis is performed of the dependence of magnetic resistanceρ(d, H), the Nernst — Ettingshausen(N-E) coefficient Q(d, H), the electron component of thermal conductivityκ(d, H), and the thermo-emfα(d, H) on film thickness and magnetic field.

Thermal conductivity and ettingshausen coefficient in rare-earth metals

Values of thermal conductivity in polycrystalline samples of Y, Gd, Tb, Dy and Yb at 300°K are presented together with their Ettingshausen coefficients. The results are interpreted of the basis of a qualitative multi-band model.