Phonon-drag Thermopower Research Articles

Screening effect on the phonon drag induced seebeck coefficient in bilayer graphene/quasi-two-dimensional electron gas structures

In this work, we investigate the impacts of the temperature-dependent screening effect on the Seebeck coefficient originating from the phonon drag, namely phonon—drag thermopower S g , of a double layer system consisting of bilayer graphene (BLG) separated from a quasi-two-dimensional electron gas (q2DEG) by an air medium (hereafter referred to as BLG-q2DEG). For such a system, we can assume that the two-dimensional (2D) electrons in BLG only interact internally with acoustic phonons. We consider the effects of screening induced by the 2D electrons in q2DEG on the electron–phonon interactions in BLG by comparing with the results obtained when only using the monolayer screening function in BLG. The monolayer screening functions in BLG (q2DEG) do not depend on the distance d between the two layers, and the screening function of the double layer system approaches the respective monolayer screening functions for large d. When taking into account of the screening effect caused by charged carriers in both layers, S g of a BLG-q2DEG decreases compared to the case of only considering the monolayer screening effect, especially in the low-T regime. With different carrier densities in the two layers NsBLG≠NsGaAs, it has shown that S g strongly depends on BLG. Besides, when changing the width L of the q2DEG such as GaAs quantum well, the double layer screening function makes S g increase for small L and negligibly affects S g for large L. On the contrary, the monolayer screening functions make S g decrease for large L. The monolayer screening functions cause S g to increase for NsBLG<NsGaAs.

Flexural and acoustic phonon-drag thermopower and electron energy loss rate in silicene

We have performed a comprehensive numerical and analytical examination of two crucial transport aspects in silicene: the phonon-drag thermopower, Sp , and the electron’s energy loss rate, Fe . Specifically, our investigation is centered on their responses to out-of-plane flexural phonons and in-plane acoustic phonons in silicene, a two-dimensional allotrope of silicon as a function of electron temperature, T, and electron concentration, n, upto the room temperature. It is found that the calculated quantities have a non-monotonic dependence for the phonon modes for both parameters (T and n) considered while analytical results predict definite dependencies up to the complete low-temperature Bloch–Gruneisen (BG) regime. To provide a more comprehensive picture, we contrast the complete numerical outcomes with the approximated analytical BG results, revealing a convergence within a specific range of temperature and carrier concentration. In light of this convergence, we put forth suggestions to elucidate the underlying factors responsible for this behavior. A comparison based on the magnitude of the calculated quantities can be made from the figures between the two considered phonon modes, which clearly shows that the out-of-plane flexural phonons are effective throughout the considered temperature range. This observation leads us to posit that the dominating contribution of the out-of-plane flexural phonon modes hinges upon the deformation potential constant and phonon energy associated with the phonon mode. Our study carries significant implications for estimating the electrical and thermal properties of silicene and provides valuable insights for the development of devices based on silicene-based technologies.

High-frequency phonons drive large phonon-drag thermopower in semiconductors at high carrier density

It has been well established that (i) the thermopower of semiconductors can be enhanced through a phenomenon known as the drag effect, and (ii) the drag enhancement involves only low-frequency acoustic phonons and benefits from low electron densities and low temperatures. Using first-principles calculations we show that large drag enhancements to the thermopower are possible at high carrier density even at room temperature and arise from high-frequency acoustic phonons. A fascinating example is cubic boron arsenide (BAs) for which the calculated room temperature drag enhancement of the thermopower exceeds an order of magnitude at a high hole density of ${10}^{21}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$. This remarkable behavior stems from the simultaneously weak phonon-phonon and phonon-hole scattering of the high-frequency phonons in BAs that become drag active at high carrier densities through electron-phonon interactions. This work advances our understanding of coupled electron-phonon nanoscale transport and introduces an unexpected paradigm for achieving large thermopowers.

Study the effects on the phonon drag Seebeck coefficient of bilayer graphene and bilayer graphene−bilayer graphene double layers

This paper presented the investigation of the influence of the temperature−dependent screening effect on the Seebeck phonon drag coefficient Sg of a monolayer of bilayer graphene (BLG) and a BLG−BLG double layer placed in an air environment. For a system in an air environment, the two-dimensional electrons of the BLG was assumed to interact only with the intralayer deformation acoustic potential phonons in the BLG. After reviewing the results published by Kubakaddi and Bhargavi, “Enhancement of phonon-drag thermopower in bilayer graphene” in Phys. Rev. B 82, 155410 (2010), this paper expanded the mentioned-results to encompass the screening and double layers and found that the phonon drag coefficient in the BLG monolayer system was strongly reduced by the screening effect, even up to several orders of magnitude compared to the zero temperature screening function, as shown in some recent publications. When comparing the effect of electron screening in the second layer on electron-phonon interaction in the remaining layer, or on the intralayer screening function, the distance between the two layers was small. The screening effect of the second layer significantly reduced the magnitude of the phonon drag Seebeck coefficient Sg in the BLG-BLG double layer. The effect of temperature, layer spacing and particle density on Sg for symmetric and asymmetric systems with varying layer densities were also investigated.

Phonon-drag thermopower and thermoelectric performance of MoS2 monolayer in quantizing magnetic field

We present a theory of phonon-drag thermopower, , in MoS2 monolayer at a low-temperature regime in the presence of a quantizing magnetic field B. Our calculations for consider the electron–acoustic phonon interaction via deformation potential (DP) and piezoelectric (PE) couplings for longitudinal (LA) and transverse (TA) phonon modes. The unscreened TA-DP is found to dominate over other mechanisms. The is found to oscillate with the magnetic field where the lifting effect of the valley and spin degeneracies in MoS2 monolayer has been clearly observed. An enhanced with a peak value of mV K−1 at about T = 10 K is predicted, which is closer to the zero field experimental observation. In the Bloch–Grüneisen regime the temperature dependence of gives the power-law , where δ e varies marginally around 3 and 5 for unscreened and screened couplings, respectively. In addition, is smaller for larger electron density n e . The power factor PF is found to increase with temperature T, decrease with n e , and oscillate with B. The prediction of an increase of thermal conductivity with temperature and the magnetic field is responsible for the limit of the figure of merit (ZT). At a particular magnetic field and temperature, ZT can be maximized by optimizing electron density. By fixing cm−2, the highest ZT is found to be 0.57 at T = 5.8 K and B = 12.1 T. Our findings are compared with those in graphene and MoS2 for the zero-magnetic field.

Thermoelectric Properties of Zn Nanowires: Phonon Scattering Effect

The temperature-dependent thermoelectric power (S) of Zn nanostructures is numerically estimated using a theoretical model. The electron diffusive and phonon drag contributions to thermoelectric power are calculated within the relaxation time approximation. The phonon drag thermopower is an artifact of various operating scattering mechanisms. The anomalous behavior of (S) is successfully estimated in accordance with interaction of heat carrying phonons with impurity, grain boundaries, electrons and phonons. The scattering and transport cross sections are function of phonon frequency  in the present model and produce similar results.

Phonon Drag Thermopower in Silicene in Equipartition Regime at Room Temperature

Abstract: Similar to graphene, zero band gap limits the application of Silicene in nanoelectronics despite of its high carrier mobility. In this article we calculate the contribution of electron-phonon interaction to thermoelectric effects in silicene. One considers the case of free standing silicene taking into account interaction with intrinsic acoustic phonons. The temperature considered here is at room temperature. We noticed that the contribution to thermoelectromotive force due to electron drag by phonons is determined by the Fermi energy. The explicit temperature dependence of the contribution to thermoelectromotive force deriving from by phonons is weak in contrast to that due to diffusion, which is directly proportional to temperature. Thus a theoretical limit has been established for a possible increase of the thermoelectromotive force through electron drag by the intrinsic phonons of silicene. Keywords: Phonon-drag thermopower, electron-diffusion thermopower, silicene, fermi energy, zero band gap

Large phonon drag thermopower boosted by massive electrons and phonon leaking in LaAlO3/LaNiO3/LaAlO3 heterostructure.

An unusually large thermopower (S) enhancement is induced by heterostructuring thin films of the strongly correlated electron oxide LaNiO3. The phonon-drag effect, which is not observed in bulk LaNiO3, enhances S for thin films compressively strained by LaAlO3 substrates. By a reduction in the layer thickness down to three unit cells and subsequent LaAlO3 surface termination, a 10 times S enhancement over the bulk value is observed due to large phonon drag S (Sg), and the Sg contribution to the total S occurs over a much wider temperature range up to 220 K. The Sg enhancement originates from the coupling of lattice vibration to the d electrons with large effective mass in the compressively strained ultrathin LaNiO3, and the electron–phonon interaction is largely enhanced by the phonon leakage from the LaAlO3 substrate and the capping layer. The transition-metal oxide heterostructures emerge as a new playground to manipulate electronic and phononic properties in the quest for high-performance thermoelectrics.

Giant thermopower and power factor in magic angle twisted bilayer graphene at low temperature

The in-plane phonon-drag thermopower S g, diffusion thermopower S d and the power factor PF are theoretically investigated in a twisted bilayer graphene (tBLG) as a function of twist angle θ, temperature T and electron density n s in the region of low T (1–20 K). As θ approaches magic angle θ m, the S g and S d are found to be strongly enhanced, which is manifestation of great suppression of effective Fermi velocity v F * of electrons in moiré flat band near θ m. This enhancement decreases with increasing θ and T. In the Bloch–Grüneisen (BG) regime, it is found that S g ∼ v F *−2, T 3 and n s −1/2. As T increases, the exponent δ in S g ∼ T δ , changes from 3 to nearly zero and a maximum S g value of ∼10 mV K−1 at ∼20 K is estimated. S g is found to be larger (smaller) for smaller n s in low (high) temperature region. On the other hand, S d, taken to be governed by Mott formula with S d ∼ v F *−1, T and n s −1/2 and S d ≪ S g for T > ∼2 K. The power factor PF is also shown to be strongly θ dependent and is very much enhanced. Consequently, possibility of a giant figure of merit is discussed. In tBLG, θ acts as a strong tuning parameter of both S g and S d and PF in addition to T and n s. Our results are qualitatively compared with the measured out-of-plane thermopower in tBLG.

Phonon drag thermopower and energy loss rate in single and bilayer graphene due to piezoelectric surface acoustic phonons in Bloch-Gruneisen regime

In this report, we have both numerically and analytically calculated the phonon drag thermopower, Spz and, energy loss rate, Fpz due to piezoelectric surface acoustic phonons present in the underlying piezoelectric substrate at a distance, d apart from single and bilayer graphene as a function of carrier's temperature, concentration and phonon mean free path. The numerical results are then reduced to analytical results in the Bloch-Gruneisen regime and the corresponding power dependency of the quantities described above are obtained. We have also included the effect of Thomas-Fermi and Random Phase Approximation screening into account in these calculations. The obtained unscreened results are further reduced in much simpler form for a particular case having no distance between the graphene samples and the underlying substrate or at larger values of distances. The temperature dependency in Spz and Fpz for both SLG and BLG systems is found to be one order less than the in-plane acoustic phonons dependency, which is directly related to the matrix element of electron-in plane acoustic phonon interaction having a linear dependence on the phonon wave vector, q. Furthermore, a comparison of these calculations is made between the in-plane and piezoelectric surface acoustic phonon modes. One finds a crossover between these phonons modes depicting these are important in providing effective scattering channels for energy relaxation in typical experimental situations at different temperatures.

Solid solubility of Mg and enhanced electrical conduction in the C-axis orientation of CuCr1-xMgxO2 polycrystals

ABSTRACT The c-axis orientation of CuCr1-xMgxO2 (0 ≤ x ≤ 0.08) ceramics was prepared through solid-state reactions. The effects of a Mg solid solution in CuCrO2 have been investigated in terms of electrical conductivity, thermopower, and microstructure. While x = 0–0.03, the polycrystalline grains in a single-phase delafossite grew along the ab-plane with increasing (00 l) Lotgering factors of up to 0.53. It exhibited semiconducting electrical transport. The room temperature conductivity increased by 3–4 orders of magnitude, even up to 12.03 S·cm−1, because of a reduction in Arrhenius activation energy. The Seebeck coefficient decreased from 828 to 257.8 μV·K−1 at 330 K. For the doped samples, due to the contribution of the phonon drag thermopower overmatching the variation of the carrier concentration to the thermopower, it increased with increasing temperature, which was the opposite to that observed in the undoped samples. While x = 0.04–0.08, the second-phase MgCr2O4 spinel appeared and the properties and microstructure hardly changed. The layered structure of the c-axis orientation led to dominant electrical transport along the ab-plane and reduced the grain boundary, leading to weakened defect scattering, which caused an enhancement in conductivity.

Chirality effect on electron phonon relaxation, energy loss, and thermopower in single and bilayer graphene in BG regime

We investigate the energy dependent electron-phonon relaxation rate, energy loss rate, and phonon drag thermopower in single layer graphene (SLG) and bilayer graphene (BLG) under the Bloch-Gruneisen (BG) regime through coupling to acoustic phonons interacting via the Deformation potential in the Boltzmann transport equation approach. We find that the consideration of the chiral nature of electrons alters the temperature dependencies in two-dimensional structures of SLG and BLG from that shown by other conventional 2DEG system. Our investigations indicate that the BG analytical results are valid for temperatures far below the BG limit (∼TBG/4) which is in conformity with a recent experimental investigation for SLG [C. B. McKitterick et al., Phys. Rev. B 93, 075410 (2016)]. For temperatures above this renewed limit (∼TBG/4), there is observed a suppression in energy loss rate and thermo power in SLG, but enhancement is observed in relaxation rate and thermopower in BLG, while a suppression in the energy loss rate is observed in BLG. This strong nonmonotonic temperature dependence in SLG has also been experimentally observed within the BG limit [Q. Ma et al., Phys. Rev. Lett. 112, 247401 (2014)].

Effects of a piezoelectric substrate on phonon-drag thermopower in monolayer graphene

The phonon-drag thermopower is studied in a monolayer graphene on a piezoelectric substrate. The phonon-drag contribution from the extrinsic potential of piezoelectric surface acoustic (PA) phonons of a piezoelectric substrate (GaAs) is calculated as a function of temperature T and electron concentration ns. At a very low temperature, is found to be much greater than of the intrinsic deformation potential of acoustic (DA) phonons of the graphene. There is a crossover of and at around ~5 K. In graphene samples of about >10 µm size, we predict Sg ~ 20 µV at 10 K, which is much greater than the diffusion component of the thermopower and can be experimentally observed. In the Bloch–Gruneisen (BG) regime T and ns dependence are, respectively, given by the power laws () ~ T2(T3) and , ~ . The T(ns) dependence is the manifestation of the 2D phonons (Dirac phase of the electrons). The effect of the screening is discussed. Analogous to Herring’s law (Sgμp ~ T−1), we predict a new relation Sgμp ~ , where μp is the phonon-limited mobility. We suggest that the ns dependent measurements will play a more significant role in identifying the Dirac phase and the effect of screening.

Effect of Phonon Drag on the Thermopower in a Parabolic Quantum Well

The theory of phonon-drag thermopower resulting from a temperature gradient in the plane of a two-dimensional electron gas layer in a parabolic quantum well is developed. The interaction mechanisms between electrons and acoustic phonons are considered, taking into account potential screening of the interaction. It is found that the effect of electron drag by phonons makes a significant contribution to the thermopower of the two-dimensional electron gas. It is shown that the consideration of screening has a significant effect on the drag thermopower. For the temperature dependence of the thermopower in a parabolic GaAs/AlGaAs quantum well in the temperature range of 1–10 K, good agreement between the obtained theoretical results and experiments is shown.

Phonon-drag thermopower in 3D Dirac semimetals

A theory of low-temperature phonon-drag thermopower Sg in three-dimensional (3D) Dirac semimetals has been developed considering screened electron–phonon deformation potential coupling. Numerical investigations of Sg, in the boundary scattering regime for phonons, are made in 3D Dirac semimetal Cd3As2, as a function of temperature T and electron concentration ne. Sg is found to increase rapidly for about T < 1 K and nearly levels off for higher T. It is also seen that Sg increases (decreases) with decreasing ne at lower (higher) T (<2 K). A screening effect is found to be very significant, strongly affecting T and ne dependence for about <1 K and becoming negligible at higher temperature. In the Bloch–Gruneisen (BG) regime the power laws Sg ~ T8 (T4) and Sg ~ with (without) screening are obtained. These laws with respect to T and ne are, respectively, characteristics of 3D phonons and Dirac 3D electrons. Comparison with diffusion thermopower Sd shows that Sg dominates (and is much greater than) Sd for about T > 0.2 K. Herring’s law Sgμp ~ T −1, relating phonon limited mobility μp and Sg in the BG regime, is shown to be valid in 3D Dirac semimetals. The results obtained here are compared with those in 3D semiconductors, low-dimensional semiconductor heterojunctions and graphene. We conclude that ne-dependent measurements, rather than T-dependent ones, provide a clearer signature of the 3D Dirac semimetal phase.

Geometry Effects on the Phonon-Drag Contribution to Thermopower in a Coupled-Quantum-Well System at Low Temperature

The effects of geometry on the phonon-drag contribution to thermopower in a coupled-quantum-well system at low temperature are theoretically investigated. It is shown that increasing the separation between two quantum wells up to a certain limit enhances the phonon-drag thermopower over the whole temperature range of interest. Moreover, calculations suggest that the effect of layers’ thickness on the phonon drag is temperature dependent. The effect of spatial asymmetry, which turns out to be a very small one, is studied as well. Calculations based on the Fang–Howard model for the quantum wells are presented and compared with both experiment and results obtained from the infinitely deep quantum well model.

Theory of magnetothermoelectric phenomena in high-mobility two-dimensional electron systems under microwave irradiation

The response of two-dimensional electron gas to a temperature gradient in perpendicular magnetic field under steady-state microwave irradiation is studied theoretically. The electric currents induced by the temperature gradient and the thermopower coefficients are calculated taking into account both diffusive and phonon-drag mechanisms. The modification of thermopower by microwaves takes place because of Landau quantization of the electron energy spectrum and is governed by the microscopic mechanisms which are similar to those responsible for microwave-induced oscillations of electrical resistivity. The magnetic-field dependence of microwave-induced corrections to phonon-drag thermopower is determined by mixing of phonon resonance frequencies with radiation frequency, which leads to interference oscillations. The transverse thermopower is modified by microwave irradiation much stronger than the longitudinal one. Apart from showing prominent microwave-induced oscillations as a function of magnetic field, the transverse thermopower appears to be highly sensitive to the direction of linear polarization of microwave radiation.

Electron–phonon interaction in a spin–orbit coupled quantum wire with a gap

Interaction between electron and acoustic phonon in an in-plane magnetic field induced gapped quantum wire with Rashba spin–orbit interaction is studied. We calculate acoustic phonon limited resistivity (ρ) and phonon-drag thermopower (Sg) due to two well-known mechanisms of electron–phonon interaction, namely, deformation potential (DP) and piezoelectric (PE) scattering. In the so-called Bloch–Gruneisen temperature limit, both ρ and Sg depend on temperature (T) in a power law fashion, i.e., ρ or . For resistivity, takes the value 5 and 3 due to DP and PE scattering, respectively. On the other hand, is 4 and 2 due to DP and PE scattering, respectively, for phonon-drag thermopower. Additionally, we find numerically that depends on Rashba parameter (α) and electron density (n). The dependence of on α becomes more prominent at lower density. We also study the variations of ρ and Sg with carrier density in the Bloch–Gruneisen regime. Through a numerical analysis, a similar power law dependence ρ or is established in which the effective exponent undergoes a smooth transition from a low density behavior to a high density behavior. At a higher density regime, matches excellently with the value obtained from theoretical arguments. Approximate analytical expressions for both resistivity and phonon-drag thermopower in the Bloch–Gruneisen regime are given.

Phonon-drag thermopower in a monolayer MoS2

The theory of phonon-drag thermopower Sg is developed in a monolayer MoS2, considering the electron–acoustic phonon interaction via deformation potential (DP) and piezoelectric (PE) coupling, as a function of temperature T and electron concentration ns. DP coupling of TA (LA) phonons is taken to be unscreened (screened) and PE coupling of LA and TA phonons is taken to be screened. Sg due to DP coupling of TA phonons is found to be dominant over all other mechanisms and in the Bloch–Grüneisen regime it gives power law Sg ∼ T3. All other mechanisms give Sg ∼ T5. These power laws are characteristic of two-dimensional (2D) phonons with linear dispersion. Screening enhances the exponent of T by 2 and strongly suppresses Sg due to the large effective mass of the electrons. We find that Sg, due to screened DP and PE couplings is nearly the same in contrast to the results in GaAs heterojunctions. Also, we predict that , a characteristic of 2D electrons with parabolic relation. With the increasing (decreasing) T(ns) its exponent decreases. For comparison, we give diffusion thermopower Sd. At very low T and high ns, Sd ∼ T and . Sd is found to be greater than Sg for about T < 2–3 K. The results are compared with those in conventional 2D electron gas and graphene.

Linear temperature behavior of thermopower and strong electron-electron scattering in thick F-doped SnO2 films

Both the semi-classical and quantum transport properties of F-doped SnO2 thick films (∼1 μm) were investigated experimentally. We found that the resistivity caused by the thermal phonons obeys Bloch-Grüneisen law from ∼90 to 300 K, while only the diffusive thermopower, which varies linearly with temperature from 300 down to 10 K, can be observed. The phonon-drag thermopower is completely suppressed due to the long electron-phonon relaxation time in the compound. These observations, together with the fact that the carrier concentration has negligible temperature dependence, indicate that the conduction electrons in F-doped SnO2 films possess free-electron-like characteristics. At low temperatures, the electron-electron scattering dominates over the electron-phonon scattering and governs the inelastic scattering process. The theoretical predications of scattering rates of large- and small-energy-transfer electron-electron scattering processes, which are negligibly weak in three-dimensional disordered conventional conductors, are quantitatively tested in this lower carrier concentration and free-electron-like highly degenerate semiconductor.