Thermoelectric effects in a double-dot Aharonov-Bohm interferometer with Rashba spin-orbit interaction

We investigate the thermoelectric effects in a double-dot Aharonov-Bohm interferometer coupled to ferromagnetic leads held at different temperatures. The interplay of Rashba spin-orbit interaction (RSOI) and magnetic flux ϕ induces various interesting spin-dependent interference phenomena. The thermoelectric transport oscillates with ϕ. The peak of the thermopower S and figure of merit ZT splits into two new peaks and its splitting increases with the Rashba induced phase factor φ _R . With increasing φ _R S and ZT at ϕ = ± 2nπ (n = 0,1,2,...) exhibit a conversion from a peak to a valley. In the presence of the interplay of RSOI and ϕ by increasing spin polarization the splitting peaks of S (ZT) become asymmetric and ZT is greatly enhanced. The influence of the quantum dot levels on thermoelectric effects is also analyzed.     

Heat transport and thermoelectric efficiency of two-level quantum dot attached to ferromagnetic electrodes

Energy transport, in the linear response regime, through a two-level quantum dot/molecule attached to ferromagnetic leads is studied in the Coulomb blockade region with use of the Green function formalism. Thermal conductance and figure of merit ZT are calculated and discussed for two configurations of magnetic moments and different polarization factor in the leads. A strong dependence of ZT on polarization is found. A substantial enhancement of efficiency can be observed in molecular junctions with one of energy levels weakly coupled to the leads. Moreover, in systems, in which spin accumulation in electrodes is important, a quite considerable spin efficiency can be expected.     

Thermoelectric properties of a single quantum dot in mixed-valence regime

We study thermoelectric effects in correlated quantum dot coupled to ferromagnetic electrodes by calculating thermal conductance κ, thermopower S and Figure of merit ZT in the mixed-valence regime as function of on-dot energy level and temperature. The system is represented by the Anderson model and the results agree well with those recently experimental measured for a quantum dot coupled to two leads.     

Thermoelectric figure of merit in a quantum wire coupled to a graphene sheet between ferromagnetic leads

We theoretically investigate the figure of merit ZT for a quantum wireside-coupled by a graphene sheet and sandwiched between two ferromagnetic electrodes withnoncollinear magnetic moments. By using the nonequilibrium Green’s function combining withthe tight-binding Hamiltonian, we demonstrate that the ZT for the system developsan oscillating behavior and weakly depends on the wire-graphene coupling strength as wellas magnetic configuration of the leads. On the contrary, it is strongly dependent ontemperature and the polarization strength of the leads. Importantly, the maximum value ofZT for thesystem without the polarization strength (p = 0) is about 1.1 at temperature k _B T =0.015Γ ₀, which is in agreement with theexperimental measurements for silicon nanowires.     

Colossal enhancement in thermoelectric effect in a laterally coupled double-quantum-dot chain by the Coulomb interactions

Thermoelectric effects, including Seebeck coefficient (S), thermal conductance (κ), and figure of merit (ZT), in a laterally coupled double-quantum-dot (DQD) chain with two external nonmagnetic contacts are investigated theoretically by the nonequilibrium Green's function formalism. In this system, the DQD chain between two contacts forms a main channel for thermal electrons transporting, and each QD in the main chain couples laterally to a dangling one. The numerical calculations show that the Coulomb interactions not only lead to the splitting of the asymmetrical double-peak structure of the Seebeck coefficient, but also make the thermal spectrum show a strong violation of the Wiedemann–Franz law, leading to a colossal enhancement in ZT. These results indicate that the coupled DQD chain has potential applications in the thermoelectric devices with high thermal efficiency.     

Enhanced Spin Seebeck Efficiency in Closed Triple Quantum Dots Ring with Spin-Dependent Interdot Couplings

Spin Seebeck effect (SSE) in triple quantum dots coupled to ferromagnetic leads is studied by using the Keldysh nonequilibrium Green’s function technique. In low temperature regimes, the Fano effect arising from the interferences between the isolated states and the continuum plays an dominant role in the electronic and thermoelectric transport processes. The Seebeck coefficient depends on spin degree of freedom when the leads’ magnetic moments are in parallel configuration. When the leads’ polarization is varied, the charge Seebeck coefficients are less influenced, whereas those of the spin counterparts are obviously changed. The magnitudes of both the SSE coefficient and the spin figure of merit (FOM) will be enhanced by increasing the asymmetry of the leads’ spin polarization. In the presence of the spin-dependent interdot couplings, the strengths of the charge and spin thermoelectric quantities are individually suppressed and enhanced, and then the magnitudes of the SSE coefficient and the spin FOM are comparable to those of the charge counterparts. Interestingly, by the joint effects of the ferromagnetism on the leads and the spin-dependent interdot couplings, the spin thermopower can even changes its sign around the antiresonance states.

     

Thermoelectric power of magnetic metals: II. Anisotropic metals

We present a theory of the thermoelectric power tensor of anisotropic ferromagnetic metals with localized magnetic moments starting from the Boltzmann equation and incorporating anisotropy effects due to the lattice structure through a parameter measuring the anisotropy in the sound velocity. Elastic and inelastic phonon and spin scattering contributions are taken into account through a linear superposition of scattering cross sections. A mean field approximation is used to describe the ordered magnetic phase. Spin wave and impurity scattering, phonon and magnon drag are not included. In a range encompassing the Curie temperature, i.e. at “moderate temperatures”, the theory quantitatively reproduces observed features except for specific details (e.g. rounding near T_c) needing other physical input. We compare our theory to data on single crystals of Gd and Tb₇₅Gd₂₅. The c-axis thermoelectric power is well recovered for very reasonable values of anisotropy and scattering strength parameters. A conjecture is given to explain the basal plane thermoelectric power positive slope at high temperature.     

Electronic structure and magnetic phase transition in MnSi

Temperature variations of the amplitude of zero-point and thermal spin fluctuations in a helicoidal ferromagnetic (MnSi) are characterized using the electronic structure model that follows from ab initio LDA + U + SO calculations. It is found that a drastic reduction in the amplitude of zero-point spin fluctuations at temperature T _S (in the vicinity of the magnetic phase transition) leads to ferromagnetic solution instability (a change in the sign of the intermode interaction parameter). The observed magnetovolume effect and a sharp change in the radius of spin correlations have the same underlying cause. The results of calculation of the volumetric coefficient of thermal expansion agree well with the observed anomaly in the region of the magnetic phase transition.     

Thermoelectric efficiency enhanced in a quantum dot with polarization leads,spin-flip and external magnetic field

We theoretically study the thermoelectric transport properties in a quantum dot system with two ferromagnetic leads, the spin-flip scattering and the external magnetic field. The results show that the spin polarization of the leads strongly influences thermoelectric coefficients of the device. For the parallel configuration the peak of figure of merit increases with the increase of polarization strength and non-collinear configuration trends to destroy the improvement of figure of merit induced by lead polarization. While the modulation of the spin-flip scattering on the figure of merit is effective only in the absence of external magnetic field or small magnetic field. In terms of improving the thermoelectric efficiency, the external magnetic field plays a more important role than spin-flip scattering. The thermoelectric efficiency can be significantly enhanced by the magnetic field for a given spin-flip scattering strength.     

Phase transitions in the 2D J 1-J 2 Heisenberg model with arbitrary signs of exchange interactions

The ground state of the J ₁-J ₂ Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.     

Spin-dependent thermoelectric transport through double quantum dots

We study the thermoelectric transport through a double-quantum-dot system with spin-dependent interdot coupling and ferromagnetic electrodes by means of the non-equilibrium Green’s function in the linear response regime.It is found that the thermoelectric coefficients are strongly dependent on the splitting of the interdot coupling,the relative magnetic configurations,and the spin polarization of leads.In particular,the thermoelectric efficiency can reach a considerable value in the parallel configuration when the effective interdot coupling and the tunnel coupling between the quantum dots and the leads for the spin-down electrons are small.Moreover,the thermoelectric efficiency increases with the intradot Coulomb interaction increasing and can reach very high values at appropriate temperatures.In the presence of the magnetic field,the spin accumulation in the leads strongly suppresses the thermoelectric efficiency,and a pure spin thermopower can be obtained.     

Skyrmion burst and multiple quantum walk in thin ferromagnetic films

We propose a new type of quantum walk in thin ferromagnetic films. A giant Skyrmion collapses to a singular point in a thin ferromagnetic film, emitting spin waves, when external magnetic field is increased beyond the critical one. After the collapse the remnant is a quantum walker carrying spin S. We determine its time evolution and show the diffusion process is a continuous-time quantum walk. We also analyze an interference of two quantum walkers after two Skyrmion bursts. The system presents a new type of quantum walk for S>1/2, where a quantum walker breaks into 2S quantum walkers.     

Large spin figure of merit in a double quantum dot coupled to noncollinear ferromagnetic electrodes

The spin thermoelectric effects are studied in a Rashba double quantum dot (QD) attached to ferromagnetic leads with noncollinear magnetic moments. The spin conductance G(s), spin thermopower S(s), electron thermal conductance κ(el) and spin thermoelectric figure of merit Z(s)T are calculated by using Green's function method. We find that the magnitude of the spin figure of merit can be remarkably enhanced by the coexistence of the Rashba spin-orbit interaction in the QDs and the leads' spin polarization, and can reach even as high as 3 by optimizing the parameters of the structure. The angle between the leads' magnetic moments can act as a powerful means to manipulate the properties of the spin figure of merit.     

Thermoelectric properties of one-dimensional graphene antidot arrays

We investigate the thermoelectric properties of one-dimensional (1D) graphene antidot arrays by nonequilibrium Green?s function method. We show that by introducing antidots to the pristine graphene nanoribbon the thermal conductance can be reduced greatly while keeping the power factor still high, thus leading to an enhanced thermoelectric figure of merit (ZT). Our numerical results indicate that ZT values of 1D antidot graphene arrays can be up to unity, which means the 1D graphene antidot arrays may be promising for thermoelectric applications.     

Magnetic and electrical properties of the ZnGeAs<Subscript>2</Subscript>: Mn chalcopyrite

Doping of the ZnGeAs₂ semiconductor with manganese has produced compositions with spontaneous magnetization and high Curie temperatures of up to 367 K for the composition 3.5 wt% Mn. Their magnetic properties are characteristic of spin glasses at temperatures T < T _S and magnetic fields H < 11 kOe. In stronger fields, the spin glass state transforms into a phase with a spontaneous magnetization 4–5 times weaker than that to be expected under ferromagnetic ordering of all Mn ions. This is obviously a singly-connected ferromagnetic phase containing regions with frustrated bonds. The frustrated regions and the spin glass phase have inclusions of noninteracting ferromagnetic clusters, because these regions and the spin glass phase at low temperatures exhibit a strong increase in the magnetization M, with the dependence M(T) being described by the Langevin function. Measurements of the electrical resistivity ρ and the Hall effect have revealed that, for T < 30 K, the resistivity ρ of compositions with 1.5 and 3.5 wt % Mn is higher that at 30 K, which makes superexchange dominant and gives rise to the onset of the spin glass state. The nonuniform distribution of Mn ions in the spin glass phase accounts for the existence of isolated ferromagnetic clusters, their ferromagnetism being generated by carrier-mediated exchange. As the temperature increases still more, the increase in the mobility occurs faster than the decrease in the concentration, thus promoting an enhancement of the carrier-mediated exchange and growth of the ferromagnetic clusters in size, which at T = T _S come in contact. This signifies a transition from a multiply-to a singly-connected ferromagnetic phase, which contains microregions with frustrated bonds.     

Investigation of the possibilities for increasing the thermoelectric figure of merit of nanostructured materials based on Bi2Te3-Sb2Te3 solid solutions

The transport coefficients and thermoelectric figure of merit ZT for bulk nanostructured materials based on Bi₂Te₃-Sb₂Te₃ solid solutions have been investigated theoretically. Similar materials prepared by rapid quenching of the melt with the subsequent grinding and sintering contain amorphous and nanocrystalline regions with different sizes of particles. According to the performed estimations, the thermoelectric figure of merit of the amorphous phase can exceed the value of ZT for the initial solid solution by a factor of 2?C3 primarily due to the significant decrease in the thermal conductivity. The effective transport coefficients of the medium as a whole have also been investigated as a function of the parameters of each phase, and the concentration range of the amorphous phase, which corresponds to the effective values ZT > 1, has been determined.     

Thermoelectric properties of nano-bulk bismuth telluride prepared with spark plasma sintered nano-plates

The pursuit for a high-performance thermoelectric n-type bismuth telluride-based material is significant because n-type materials are inferior to their corresponding p-type materials in highly efficient thermoelectric modules. Herein, to improve the thermoelectric performance of an n-type Bi₂Te₃, we prepared Bi₂Te₃ nano-plates with a homogeneous sub-micron size distribution and thickness range of about a few tens of nanometers. This was achieved using a typical nano-chemical synthetic method, and the prepared materials were then spark plasma sintered to fabricate n-type nano-bulk Bi₂Te₃ samples. We observed a significant enhancement of the anisotropic electrical transport properties for the nano-bulk sample with a higher power factor along the in-plane direction (24.3?μW?cm^?1?K^?2 at 300?K) than that along the out-of-plane direction (8.1?μW?cm^?1?K^?2 at 300?K). However, thermal transport properties were insensitive along the measured direction for the nano-bulk sample. We used a dimensionless figure of merit ZT to calculate the thermoelectric performance. The results showed that the maximum ZT value of 0.69 was achieved along the in-plane direction at 440?K for the nano-bulk n-type Bi₂Te₃ sample, which was however smaller than that of the previously reported n-type samples (ZT of 1.1). We believe that a further enhancement of the ZT value in the fabricated nano-bulk sample could be accomplished by effectively removing the surface organic ligand of the Bi₂Te₃ nano-plate particles and optimizing the spark plasma sintering conditions, maintaining the nano-plate morphology intact.     

Enhancement of the thermoelectric figure of merit in a quantum dot due to external ac field

We investigate the figure of merit of a quantum dot (QD) system irradiated with an external microwave filed by nonequilibrium Green?s function (NGF) technique. Results show that the frequency of microwave field influence the figure of merit ZT significantly. At low temperature, a sharp peak can be observed in the figure of merit ZT as the frequency of ac field increases. As the frequency varies, several zero points and resonant peaks emerge in the figure of merit ZT. By adjusting the frequency of the microwave field, we can obtain high ZT. The figure of merit ZT increases with the decreasing of linewidth function Γ. In addition, Wiedemann–Franz law does not hold, particularly in the low frequency region due to multi-photon emission and absorption. Some novel thermoelectric properties are also found in two-level QD system.     

Advances in thermoelectrics

Thermoelectric generators, capable of directly converting heat into electricity, hold great promise for tackling the ever-increasing energy sustainability issue. The thermoelectric energy conversion efficiency is heavily dependent upon the materials’ performance that is quantified by the dimensionless figure-of-merit (ZT). Therefore, the central issue in the research of thermoelectric materials lies in continuously boosting the ZT value. Although thermoelectric effects were discovered in the nineteenth century, it was only until the 1950s when classic materials like Bi₂Te₃ and PbTe were developed and basic science of thermoelectrics was established. However, the research of thermoelectrics did not take a smooth path but a rather tortuous one with ups and downs. After hiatus in the 1970s and 1980s, relentless efforts starting from the 1990s were devoted to understanding the transport and coupling of electrons and phonons, identifying strategies for improving the thermoelectric performance of existing materials, and discovering new promising compounds. Rewardingly, substantial improvements in materials’ performance have been achieved that broke the ZT limit of unity. Meanwhile, advancements in fundamental understanding related to thermoelectrics have also been made. In this Review, recent advances in the research of thermoelectric materials are overviewed. Herein, strategies for improving and decoupling the individual thermoelectric parameters are first reviewed, together with a discussion on open questions and distinctly different opinions. Recent advancements on a number of good thermoelectric materials are highlighted and several newly discovered promising compounds are discussed. Existing challenges in the research of thermoelectric materials are outlined and an outlook for the future thermoelectrics research is presented. The paper concludes with a discussion of topics in other fields but related to thermoelectricity.