In this work we present a detailed study and derivation of the thermopower and thermoelectric coefficient of nano-granular metals at large tunneling conductance between the grains, g_T>> 1. An important criterion for the performance of a thermoelectric device is the thermodynamic figure of merit which is derived using the kinetic coefficients of granular metals. All results are valid at intermediate temperatures, E_c>>T/g_T>δ, where δis the mean energy level spacing for a single grain and E_c its charging energy. We show that the electron-electron interaction leads to an increase of the thermopower with decreasing grain size and discuss our results in the light of future generation thermoelectric materials for low temperature applications. The behavior of the figure of merit depending on system parameters like grain size, tunneling conductance, and temperature is presented.
We investigate thermoelectric transport through interfaces with inelastic scatterings by developing a quantum theory, which has been extensively validated by existing theories. We find that under temperature bias, while a two-terminal conductor-insulator interface behaves only as a thermal resistor, a three-terminal conductor-insulator-conductor interface can function as an electricity generator caused by phonon-mediated electron scatterings with heat-charge current separation. Unlike conventional thermoelectrics which is a property of a bulk caused by the Seebeck effect, this thermoelectric b…
We theoretically consider the spin Seebeck effect, the charge Seebeck coefficient, and the thermoelectric figure of merit in superconducting hybrid structures including either magnetic textures or intrinsic spin-orbit coupling. We demonstrate that large magnitudes for all these quantities are obtainable in Josephson-based systems with either zero or a small externally applied magnetic field. This provides an alternative to the thermoelectric effects generated in high-field ($\sim 1$ T) superconducting hybrid systems, which were recently experimentally demonstrated. The systems studied contain …
A first-principles approach is presented for the thermoelectricity in molecular junctions formed by a single molecule contact. The study investigates the Seebeck coefficient considering the source-drain electrodes with distinct temperatures and chemical potentials in a three-terminal geometry junction. We compare the Seebeck coefficient in the amino-substituted and unsubstituted butanethiol junction and observe interesting thermoelectric properties in the amino-substituted junction. Due to the novel states around the Fermi levels introduced by the amino-substitution, the Seebeck coefficient co…
Improving the thermoelectric figure of merit zT is one of the greatest challenges in material science. Recent discovery of topological insulators (TIs) offers new promise in this prospect. In this work, we demonstrate theoretically that zT is strongly size dependent in TI, and the size parameter can be tuned to enhance zT to be significantly greater than 1. Furthermore, we show that the life time of the edge states in TI is strongly energy dependent, leading to large and anomalous Seebeck effects with an opposite sign to the Hall effect. These striking properties make TIs the promising materia…
Thermoelectric phenomena in photoexcited graphene have been the topic of several theoretical and experimental studies because of their potential usefulness in optoelectronic applications. However, available theoretical descriptions of the thermoelectric effect in terms of the Seebeck coefficient do not take into account the role of the photoexcited electron density. In this work, we adopt the concept of effective Seebeck coefficient [G.D. Mahan, J. Appl. Phys. 87, 7326 (2000)] and extend it to the case of a photoexcited two-dimensional (2D) electron gas. We calculate the effective Seebeck coef…
The spin Seebeck effect (SSE) refers to the generation of a spin current as a result of a temperature gradient in magnetic materials including insulators. The SSE is applicable to thermoelectric generation because the thermally generated spin current can be converted into a charge current via spin-orbit interaction in conductive materials adjacent to the magnets. The insulator-based SSE device exhibits unconventional characteristics potentially useful for thermoelectric applications, such as simple structure, device-design flexibility, and convenient scaling capability. In this article, we rev…
Considering screeening of electron scattering interactions in terms of the finite-temperature STLS theory and solving the linearized Boltzmann equation (with no appeal to a relaxation time approximation), we present a theoretical analysis of the low-temperature Seebeck effect in two-dimensional semiconductors with dilute electron densities. We find that the temperature ($T$) dependencies of the diffusion and phonon-drag thermoelectric powers ($S_d$ and $S_g$) can no longer be described by the conventional simple power-laws. As temperature increases, $|S_d|/T$ decreases when $T\gtrsim 0.1 ε_F$ …
We studied the thermoelectric coefficients (Seebeck and thermal conductance)of FeCo|MgO|FeCo(001) magnetic tunnel junctions (MTJs) from first principles using a generalized Landauer-Büttiker formalism. FeCo|MgO|FeCo(001) MTJs usually yield smaller thermoelectric effects compared with epitaxial Fe|MgO|Fe(001) MTJs. The (magneto-) Seebeck effect is sensitive to the details of the FeCo$|$MgO interfaces. Interfacial oxygen vacancies (OVs) can enhance the thermoelectric effects in MTJs greatly. We also compute angular dependent Seebeck coefficients that provide more information about the transport …
We theoretically study the nonequilibrium thermoelectric transport properties of a strongly-correlated molecule (or quantum dot) embedded in a tunnel junction. Assuming that the coupling of the molecule to the contacts is asymmetric, we determine the nonlinear current driven by the voltage and temperature gradients by using the perturbation theory. However, the subsystem consisting of the molecule strongly coupled to one of the contacts is solved by using the numerical renormalization group method, which allows for accurate description of Kondo correlations. We study the temperature gradient a…
Nanoscale structuring holds promise to improve thermoelectric properties of materials for energy conversion and photodetection. We report a study of the spatial distribution of the photothermoelectric voltage in thin-film nanowire devices fabricated from single metal. A focused laser beam is used to locally heat the metal nanostructure via a combination of direct absorption and excitation of a plasmon resonance in Au devices. As seen previously, in nanowires shorter than the spot size of the laser, we observe a thermoelectric voltage distribution that is consistent with the local Seebeck coeff…
The atomic variations of electronic wavefunctions at the surface and electron scattering near a defect have been detected unprecedentedly by tracing thermoelectric voltages given a temperature bias [Cho et al., Nature Mater. 12, 913 (2013)]. Because thermoelectricity, or Seebeck effect, is associated with heat-induced electron diffusion, how the thermoelectric signal is related to the atomic-scale wavefunctions and what the role of the temperature is at such a length scale remain very unclear. Here we show that coherent electron and heat transport through a point-like contact produces an atomi…
A model of charge hopping transport that accounts for anisotropy of localized states and Coulomb interaction between charges is proposed. For the anisotropic localized states the degree of orientation relates exponentially to the ratio of conductivities in parallel and perpendicular directions, while the ratio of Seebeck coefficients stays nearly unaffected. However, the ratio of Seebeck coefficients increases if Coulomb interaction is screened stronger in a direction parallel to the predominant orientation of the localized states. This implies two different physical mechanisms responsible for…
The electronic thermoelectric coefficients are analyzed in the vicinity of one and two Anderson localization thresholds in three dimensions. For a single mobility edge, we correct and extend previous studies, and find universal approximants which allow to deduce the critical exponent for the zero-temperature conductivity from thermoelectric measurements. In particular, we find that at non-zero low temperatures the Seebeck coefficient and the thermoelectric efficiency can be very large on the "insulating" side, for chemical potentials below the (zero-temperature) localization threshold. Correct…
Local variations in the Seebeck coefficient in low-dimensional materials-based nanostructures and devices play a major role in their thermoelectric performance. Unfortunately, currently most thermoelectric measurements probe the aggregate characteristics of the device as a whole, failing to observe the effects of the local variations and internal structure. Such variations can be caused by local defects, geometry, electrical contacts or interfaces and often substantially influence thermoelectric properties, most profoundly in two-dimensional (2D) materials. Here, we use Scanning Thermal Gate M…
We have fabricated bilayer-graphene double layers separated by a thin ($\sim$20 nm) boron nitride layer and performed Coulomb drag and counterflow thermoelectric transport measurements. The measured Coulomb drag resistivity is nearly three orders smaller in magnitude than the intralayer resistivities. The counterflow Seebeck coefficient is found to be well approximated by the difference between Seebeck coefficients of individual layers and exhibit a peak in the regime where two layers have opposite sign of charge carriers. The measured maximum counterflow power factor is $\sim$ 700 $μ$W/K$^2$c…
Fano and hybrid resonances of bilayer graphene could be attractive for thermoelectric devices. The special profile presented by such resonances could significantly enhance the Seebeck coefficient and the power factor. In this work, we study the thermoelectric properties of bilayer graphene single and double barrier structures. The charge carriers are described as massive chiral particles through an effective Dirac-like Hamiltonian. The Hybrid matrix method, the Landauer-Büttiker formalism and the Cutler-Mott formula are implemented to obtain the transmission, transport and thermoelectric prope…
We have experimentally studied the role of thermoelectric effects in nanoscale nonlocal spin valve devices. A finite element thermoelectric model is developed to calculate the generated Seebeck voltages due to Peltier and Joule heating in the devices. By measuring the first, second and third harmonic voltage response non locally, the model is experimentally examined. The results indicate that the combination of Peltier and Seebeck effects contributes significantly to the nonlocal baseline resistance. Moreover, we found that the second and third harmonic response signals can be attributed to Jo…
We develop a theoretical framework to study the influences of coupling asymmetry on the thermoelectrics of a strongly coupled SU($N$) Kondo impurity based on a local Fermi liquid theory. Applying non-equilibrium Keldysh formalism, we investigate charge current driven by the voltage bias and temperature gradient in the strong coupling regime of an asymmetrically coupled SU($N$) quantum impurity. The thermoelectric characterizations are made via non-linear Seebeck effects. We demonstrate that the beyond particle-hole (PH) symmetric SU($N$) Kondo variants are highly desirable with respect to the …
The Seebeck effect describes the generation of an electric potential in a conducting solid exposed to a temperature gradient. Besides fundamental relevance in solid state physics, it serves as a key quantity to determine the performance of functional thermoelectric materials. In most cases, it is dominated by an energy-dependent electronic density of states at the Fermi level, in line with the prevalent efforts toward superior thermoelectrics through the engineering of electronic structure. Here, we demonstrate an alternative source for the Seebeck effect based on charge-carrier relaxation: A …
The spin-Seebeck effect mediated thermoelectric energy conversion can provide efficient alternative to traditional thermoelectrics for waste heat recovery. To achieve this goal, efficient spin to charge conversion using earth-abundant materials is essential. Proximity induced Rashba effect arises from the charge potential mediated by structural inversion asymmetry, which has been reported in Si thin films and can be manipulated by controlling the thickness of Rashba layer. We demonstrate a giant Rashba spin-Seebeck effect in NiFe/p-Si (polycrystalline) bilayer thin films. The bilayer thin film…
We study features of the thermoelectric transport through a Kitaev chain hosting Majorana bound states (MBS) at its ends. We describe the behavior of the Seebeck coefficient and the ZT figure of merit for two different configurations between MBS and normal current leads. We find an important violation of the Wiedemann-Franz law in one of these geometries, leading to sizeable values of the thermoelectric efficiency over a narrow window in chemical potential away from neutrality. These findings could lead to interesting thermoelectric-based MBSs detection devices, via measurements of the Seebeck…
We theoretically investigate the thermoelectric and spin thermoelectric properties of a T-shaped double quantum dot strongly coupled to two ferromagnetic leads, focusing on transport regime where the system exhibits the two-stage Kondo effect. We study the dependence of the (spin) Seebeck coefficient, the corresponding power factor and the figure of merit on temperature, leads' spin polarization and dot level position. We show that the thermal conductance fulfills a modified Wiedemann-Franz law. We also demonstrate that the spin thermopower is enhanced at temperatures corresponding to the seco…
We found a giant Seebeck effect in semiconducting single-wall carbon nanotube (SWCNT) films, which exhibited a performance comparable to that of commercial Bi2Te3 alloys. Carrier doping of semiconducting SWCNT films further improved the thermoelectric performance. These results were reproduced well by first-principles transport simulations based on a simple SWCNT junction model. These findings suggest strategies that pave the way for emerging printed, all-carbon, flexible thermoelectric devices.
Transverse magneto-thermoelectric effects are studied in permalloy thin films grown on MgO substrates. We find that small parasitic magnetic fields below 1 Oe can produce artifacts of the order of 1 % of the amplitude of the anisotropic magneto-thermopower which is also detected in the experiments. The measured artifacts reveal a new source of uncertainties for the detection of the transverse spin Seebeck effect. Taking these results into account we conclude that the contribution of the transverse spin Seebeck effect to the detected voltages is below the noise level of 20 nV.
In this article, we show fundamentals and recent advances on the transverse thermoelectric generation, in which a thermopower is generated in the direction perpendicular to an applied temperature gradient. Transverse thermoelectric generation is one of the central topics in condensed matter physics, and can be a breakthrough approach to solve long-standing technological problems with contact resistances in thermoelectric generators. We review here the six currently known driving mechanisms: the ordinary Nernst effect, the anomalous Nernst effect, goniopolar materials, the spin Seebeck effect, …
In this work, we study the conductance and the thermoelectric properties of a quantum dot embedded between two metallic leads with a side-coupled triple quantum dot molecule under a magnetic field. We focus on the spin polarization and thermoelectric quantities. Our results show the possibility of design an efficient spin filter device besides a noticeable enhancement of the Seebeck coefficient driven by the asymmetry in the quantum dots energy levels and a tunable pure spin Seebeck effect is obtained. This behavior also holds in the interacting case, where a pure spin Seebeck effect can be ob…
Using first-principles approaches, we have investigated the thermoelectric properties and the energy conversion efficiency of the paired metal-Br-Al junction. Owing to the narrow states in the vicinity of the chemical potential, the nanojunction has large Seebeck coefficients such that it can be considered an efficient thermoelectric power generator. We also consider the nanojunction in a three-terminal geometry, where the current, voltage, power, and efficiency can be efficiently modulated by the gate voltages. Such current-voltage characteristics could be useful in the design of nano-scale e…
The thermoelectric effects in semiconducting single-walled carbon nanotubes (SWCNTs) are investigated based on the linear response theory combined with the thermal Green's function method. It is shown that the electronic states near the lowest conduction band minimum and the highest valence band maximum can be effectively described in terms of one-dimensional (1D) Dirac electrons to which a theoretical scheme is developed to describe the thermoelectric responses making it possible to study the effects of inter-band impurity scattering and in-gap states. Using the proposed scheme, the bipolar t…
Spin caloritronics is the science and technology to control spin, charge, and heat currents in magnetic nanostructures. The spin degree of freedom provides new strategies for thermolelectric power generation that have not yet been fully explored. After an elementary introduction into conventional thermoelectrics and spintronics, we give a brief review of the physics of spin caloritronics. We discuss spin-dependent thermoelectrics based on the the two-current model in metallic magnets as well as the spin Seebeck and Peltier effects that are based on spin wave excitations in ferromagnets. We der…
We examine how the photo-induced carriers contribute the thermoelectric transport, i.e. the nature of the photo-Seebeck effect, in the wide-gap oxide semiconductor ZnO for the first time. We measure the electrical conductivity and the Seebeck coefficient with illuminating light. The light illumination considerably changes the Seebeck coefficient as well as the conductivity, which is sensitive to the photon energy of the illuminated light. By using a simple parallel-circuit model, we evaluate the contributions of the photo-induced carriers to the conductivity and the Seebeck coefficient, whose …
This is a numerical study of thermoelectric properties of ballistic bilayer graphene in the presence of trigonal warping term in the effective Hamiltonian. We find, in the mesoscopic samples of the length $L>10\,μ$m at sub-Kelvin temperatures, that both the Seebeck coefficient and the Lorentz number show anomalies (the additional maximum and minimum, respectively) when the electrochemical potential is close to the Lifshitz energy, which can be attributed to the presence of the van Hove singularity in a bulk density of states. At higher temperatures the anomalies vanish, but measurable quantiti…
Within the semiclassical Boltzmann transport theory, the formula for Seebeck coefficient $S$ is derived for an isotropic two-dimensional electron gas (2DEG) system that exhibits anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) originating from Berry curvature on their bands. Deviation of $S$ from the value $S_0$ estimated neglecting Berry curvarture is computed for a special case of 2DEG with Zeeman and Rashba terms. The result shows that, under certain conditions the contribution of Berry curvature to Seebeck effect could be non-negligible. Further study is needed to clarify the …
Thermoelectric effect generating electricity from thermal gradient and vice versa appears in numerous generic applications. Recently, an original prospect of thermoelectricity arising from the nonlocal Cooper pair splitting (CPS) and the elastic co-tunneling (EC) in hybrid normal metal-superconductor-normal metal (NSN) structures was foreseen. Here we demonstrate experimentally the existence of non-local Seebeck effect in a graphene-based CPS device comprising two quantum dots connected to an aluminum superconductor and theoretically validate the observations. This non-local Seebeck effect off…
We investigate hot carrier propagation across graphene using an electrical nonlocal injection/detection method. The device consists of a monolayer graphene flake contacted by multiple metal leads. Using two remote leads for electrical heating, we generate a carrier temperature gradient that results in a measurable thermoelectric voltage VNL across the remaining (detector) leads. Due to the nonlocal character of the measurement, VNL is exclusively due to the Seebeck effect. Remarkably, a departure from the ordinary relationship between Joule power P and VNL, VNL ~ P, becomes readily apparent at…
The influence of nanostructuring and quantum confinement on the thermoelectric properties of materials has been extensively studied. While this has made possible multiple breakthroughs in the achievable figure of merit, classical confinement, and its effect on the local Seebeck coefficient has mostly been neglected, as has the Peltier effect in general due to the complexity of measuring small temperature gradients locally. Here we report that reducing the width of a graphene channel to 100 nm changes the Seebeck coefficient by orders of magnitude. Using a scanning thermal microscope allows us …
The increase of a thermoelectric material's figure of merit (ZT value) is limited by the interplay of the transport coefficients. Here we report the greatly enhanced thermoelectric performance of a ZrS2 monolayer by the biaxial tensile strain, due to the simultaneous increase of the Seebeck coefficient and decrease of the thermal conductivity. Based on the first-principles calculations combined with the Boltzmann transport theory, we predict the band gap of the ZrS2 monolayer can be effectively engineered by the strain and the Seebeck coefficient is significantly increased. The thermal conduct…
We investigate the spin-dependent thermoelectric effects in magnetic graphene in both diffusive and ballistic regimes. Employing the Boltzmann and Landauer formalisms we calculate the spin and charge Seebeck coefficients (thermopower) in magnetic graphene varying the spin splitting, temperature, and doping of the junction. It is found that while in normal graphene the temperature gradient drive a charge current, in the case of magnetic graphene a significant spin current is also established. In particular we show that in the undoped magnetic graphene in which different spin carriers belong to …
We propose a highly efficient thermoelectric diode device built from the coupling of a quantum dot with a normal or ferromagnetic electrode and a superconducting reservoir. The current shows a strongly nonlinear behavior in the forward direction (positive thermal gradients) while it almost vanishes in the backward direction (negative thermal gradients). Our discussion is supported by a gauge-invariant current-conserving transport theory accounting for electron-electron interactions inside the dot. We find that the diode behavior is greatly tuned with external gate potentials, Zeeman splittings…
A thermoelectric effect of the noncentrosymmetric electron-phonon coupled system is proposed, in which a temperature difference between electrons and phonons, instead of a spatial temperature gradient, induces an electric current. This is a realization of Seebeck ratchet in solids with the asymmetric energy dispersion of electrons, and the dynamical phonons act as the fluctuation of the scalar potential and induce the dc current. Possible realizations of this mechanism are also discussed.
The tunnel magneto-Seebeck effect is the dependence of the thermopower of magnetic tunnel junctions on the magnetic configuration. It is conventionally interpreted in terms of a thermoelectric generalization of the tunnel magnetoresistance. Here, we investigate the heat-driven electron transport in these junctions associated with electron-magnon scattering, using stochastic Landau-Lifshitz phenomenology and quantum kinetic theory. Our findings challenge the widely accepted single-electron picture of the tunneling thermopower in magnetic junctions.
We express the link between conductivity and coefficients of Seebeck, Nernst-Ettingshausen, Peltier, and Thompson and Reghi-Leduc via the temperature derivative of the chemical potential of a system. These general expressions are applied to three-, two- and one-dimensional systems of charge carriers having a parabolic or Dirac spectrum. The method allows for predicting thermoelectric and thermomagnetic properties of novel materials and structures.
We study the photoresponse of single-layer MoS2 field-effect transistors by scanning photocurrent microscopy. We find that, unlike in many other semiconductors, the photocurrent generation in single-layer MoS2 is dominated by the photo-thermoelectric effect and not by the separation of photoexcited electron-hole pairs across the Schottky barriers at the MoS2/electrode interfaces. We observe a large value for the Seebeck coefficient for single-layer MoS2 that, by an external electric field, can be tuned between -4x10^2 uV/K and -1x10^5 uV/K. This large and tunable Seebeck coefficient of the sin…
When two planar atomic membranes are placed within the van der Waals distance, the charge and heat transport across the interface are coupled by the rules of momentum conservation and structural commensurability, leading to outstanding thermoelectric properties. Here we show that an effective "interlayer phonon drag" determines the Seebeck coefficient (S) across the van der Waals gap formed in twisted bilayer graphene (tBLG). The cross-plane thermovoltage, which is non-monotonic in both temperature and density, is generated through scattering of electrons by the out-of-plane layer breathing (Z…
We investigate the thermoelectric properties of a quantum dot coupled to ferromagnetic and superconducting electrodes. The combination of spin polarized tunneling at the ferromagnetic-quantum dot interface and the application of an external magnetic field that Zeeman splits the dot energy level leads to large values of the thermopower (Seebeck coefficient). Importantly, the thermopower can be tuned with an external gate voltage connected to the dot. We compute the figure of merit that measures the efficiency of thermoelectric conversion and find that it attains high values. We discuss the diff…
We report on the electrical and thermal transport properties of nickel nanoparticles with crystallite size from 23.1 to 1.3 nm. These nanoparticles show a systematic metal to insulator transition with the change in the conduction type from n to p type, colossal Seebeck coefficient, and ultralow thermal conductivity at 300 K as the crystallite size drops. The electrical resistivity analysis reveals a dramatic change in the electronic excitation spectrum indicating the opening of an energy gap, and cotunneling and Coulomb blockade of the charge carriers. Seebeck coefficient shows transport energ…
Stannous selenide is a layered semiconductor that is a polar analogue of black phosphorus, and of great interest as a thermoelectric material. Unusually, hole doped SnSe supports a large Seebeck coefficient at high conductivity, which has not been explained to date. Angle resolved photo-emission spectroscopy, optical reflection spectroscopy and magnetotransport measurements reveal a multiple-valley valence band structure and a quasi two-dimensional dispersion, realizing a Hicks-Dresselhaus thermoelectric contributing to the high Seebeck coefficient at high carrier density. We further demonstra…
We calculate the charge and heat current associate with electrons, generated by a temperature gradient and chemical potential difference between two ends of a tubular nanowire of 30 nm radius in the presence of an external magnetic field perpendicular to its axis. We consider a nanowire based on a semiconductor material, and use the Landauer-Bttiker approach to calculate the transport quantities. We obtain the variation of the Seebeck coefficient ($S$), thermal conductivity kappa, and the figure of merit ($ZT$), with respect to the temperature up to 20\,K, and with the magnetic field up to 3 T…
We investigate the thermoelectric properties of Fe/MgO/Fe(001) magnetic tunnel junctions (MTJs) by means of the linear-response theory combined with a first-principles-based Landauer-Büttiker approach. We find that the Seebeck coefficient of Fe/MgO/Fe(001) MTJs strongly depends on the barrier thickness and the tetragonal distortion. A compressive tetragonal distortion of the in-plane lattice parameter in the MTJs provides interface resonant states just above the Fermi energy. This causes resonant tunneling in the MTJs and significantly enhances the Seebeck coefficient when the thickness of the…
We evaluated the thermoelectric properties of longitudinal spin Seebeck devices by using ten different transition metals (TMs). Both the intensity and sign of spin Seebeck coefficients were noticeably dependent on the degree of the inverse spin Hall effect and the resistivity of each TM film. Spin dependent behaviors were also observed under ferromagnetic resonance. These results indicate that the output of the spin Seebeck devices originates in the spin current.
We investigate dissipationless magneto-Seebeck effect in three-dimensional Dirac/Weyl semimetal. The Hall resistivity $ρ_{yx}$ and thermoelectric Hall coefficient $α_{xy}$ exhibit plateaus at the quantum limit, where electrons occupy only the zeroth Landau level. In this condition, quantum oscillation in the Seebeck coefficient $S_{xx}\approx ρ_{yx}α_{xy} $ is suppressed, and the massless fermions are transformed into a Fermi liquid system. We show that the Seebeck coefficient at the quantum limit is expressed by the harmonic sum of Fermi wavelength and thermal de Broglie wavelength scaled by …
We study thermoelectric properties of granular semiconductors with weak tunneling conductance between the grains, g_t < 1. We calculate the thermopower and figure of merit taking into account the shift of the chemical potential and the asymmetry of the density of states in the vicinity of the Fermi surface due to n- or p-type doping in the Efros-Shklovskii regime for temperatures less than the charging energy. We show that for weakly coupled semiconducting grains the figure of merit is optimized for grain sizes of order 5nm for typical materials and its values can be larger than one. We also s…
