Unconventional four-terminal thermoelectric transport due to inelastic transport: cooling by transverse current, transverse thermoelectric effect and Maxwell demon
We show that in mesoscopic four-terminal thermoelectric devices with two electrodes (the source and the drain) and two heat baths, inelastic scattering processes can lead to unconventional thermoelectric transport. The source (or the drain) can be cooled by passing a thermal current between the two heat baths, with no net heat exchange between the heat baths and the electrodes. This effect, termed as cooling by heat current, is a mesoscopic heat drag effect. In addition, there is a transverse thermoelectric effect where electrical current and power can be generated by a transverse temperature bias (i.e., the temperature bias between the two heat baths). This transverse thermoelectric effect, originates from inelastic scattering processes, may have advantages for improved figures of merit and power factor due to spatial separation of charge and heat transport. We study the Onsager current-affinity relations, the linear-response transport properties, and the transverse thermoelectric figure of merit of the four-terminal thermoelectric devices for various system parameters. In addition, we investigate the efficiency and power of the cooling by transverse current effect in both linear and nonlinear transport regimes. We also demonstrate that by exploiting the inelastic transport in the quantum-dot four-terminal systems, a type of Maxwell's demon can be realized using nonequilibrium heat baths.
We theoretically describe a thermoelectric effect that is entirely due to Andreev processes involving the formation of Cooper pairs through the coupling of electrons and holes. The Andreev thermoelectric effect can occur in ballistic ferromagnet-superconductor junctions with a dominant superconducting proximity effect on the ferromagnet, and it is very sensitive to surface states emerging in unconventional superconductors. We consider hybrid junctions in two and three dimensions to demonstrate that the thermoelectric current is always reversed in the presence of low-energy Andreev bound states…
Thermoelectric transport in strongly spin-orbit coupled two-dimensional Rashba system is studied using the exact solution of the linearized Boltzmann equation. Some unusual transport behaviors are revealed. We show that the electrical conductivity takes a Drude form when the Fermi energy $E_{F}$ is above the band crossing point, but a non-Drude form which is a quadratic function of $E_{F}$ when $E_{F}$ lies below the band crossing point. The Mott relation breaks down when $E_{F}$ lies in the vicinity of the band crossing point. It is shown that the thermopower and thermoelectric figure of meri…
We analyze the effect of the tilt on the transverse thermoelectric coefficient of Weyl semimetals in the \emph{conformal} limit, i.e., zero temperature and zero chemical potential. Using the Kubo formalism, we find a nonmonotonic behavior of the thermoelectric conductivity as a function of the tilt perpendicular to the magnetic field, and a linear behavior when the tilt is aligned to the magnetic field. An ``axial Nernst" current (chiral currents counter propagating perpendicularly to the magnetic field and the temperature gradient) is generated in inversion symmetric Weyl materials when the t…
In the past decade, a new research frontier emerges at the interface between physics and renewable energy, termed as the inelastic thermoelectric effects where inelastic transport processes play a key role. The study of inelastic thermoelectric effects broadens our understanding of thermoelectric phenomena and provides new routes towards high-performance thermoelectric energy conversion. Here, we review the main progress in this field, with a particular focus on inelastic thermoelectric effects induced by the electron-phonon and electron-photon interactions. We introduce the motivations, the b…
In an unconventional superconductor, the interplay of scattering off impurities and Andreev processes may lead to different scattering times for electronlike and holelike quasiparticles. Such electron-hole asymmetry appears when the impurity scattering phase shift is intermediate between the Born and unitary limits and leads to an expectation for large thermoelectric effects. Here, we examine the thermoelectric response of a $d$-wave superconductor connected to normal-metal reservoirs under a temperature bias using a fully self-consistent quasiclassical theory. The thermoelectrically induced q…
We report the discovery of two-dimensional electron gas (2DEG) at the surface of thermoelectric material In$_4$Se$_3$ by angle-resolved photoemission spectroscopy. The observed 2DEG exhibits a nearly isotropic band dispersion with a considerably small effective mass of m* = 0.16 m_0, and its carrier density shows a significant temperature dependence, leading to unconventional metal-semiconductor transition at the surface. The observed wide-range thermal tunability of 2DEG in In$_4$Se$_3$ gives rise to additional degrees of freedom to better control the surface carriers of semiconductors.
We show that the Coulomb interaction between two circuits separated by an insulating layer leads to unconventional thermoelectric effects, such as the cooling by thermal current effect, the transverse thermoelectric effect and Maxwell's demon effect. The first refers to cooling in one circuit induced by the thermal current in the other circuit. The middle represents electric power generation in one circuit by the temperature gradient in the other circuit. The physical picture of Coulomb drag between the two circuits is first demonstrated for the case with one quantum dot in each circuits and t…
We investigate the thermoelectric current and heat conductance in a chiral Josephson contact on a surface of a 3D topological insulator, covered with superconducting and magnetic insulator films. The contact consists of two junctions of Majorana and Dirac channels next to two superconductors. Geometric asymmetry results in a supercurrent without a phase bias. The interference of Dirac fermions causes oscillations of the electric and heat currents with an unconventional period $2Φ_0=h/e$ as functions of the Aharonov-Bohm flux. Due to the gapless character of Majorana modes, there is no threshol…
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…
These compounds have long been known as promising thermoelectric materials. Recently it was revealed, that they also have unconventional electronic topology. This renewed interest to the investigation of their transport properties. In order to improve theoretical description of thermoelectric transport in these compounds, we take into account electron scattering beyond commonly used constant relaxation time approximation. Using first principle calculations, we investigate the scattering of charge carriers by phonons and point defects. The dependence of the scattering rate on the energy correla…
Recently, a thermodynamic uncertainty relation (TUR) has been formulated for classical Markovian systems demonstrating trade-off between precision (current fluctuation) and cost (dissipation). Systems that violate the TUR are interesting as they overcome another trade-off relation concerning the efficiency of a heat engine, its power, and its stability (power fluctuations). Here, we analyze the root, extent, and impact on performance of TUR violations in quantum thermoelectric junctions at steady state. Considering noninteracting electrons, first we show that only the "classical" component of …
We study charge and energy transfer in two-site molecular electronic junctions in which electron transport is assisted by a vibrational mode. To understand the role of mode harmonicity/anharmonicity on transport behavior, we consider two limiting situations: (i) the mode is assumed harmonic, (ii) we truncate the mode spectrum to include only two vibrational levels, to represent an anharmonic molecular mode. Based on the models' cumulant generating functions, we analyze the linear-response and nonlinear performance of these junctions and demonstrate that while the electrical and thermal conduct…
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 …
We present a microscopic theory of the magnetic quadrupole moment density $\mathcal{Q}_{ij}$ in periodic crystals with combined time reversal ($\mathcal{T}$) and inversion ($\mathcal{I}$) symmetry. We obtain a gauge-invariant expression with clear physical interpretation and demonstrate the typical behaviour of $\mathcal{Q}_{ij}$ in a minimal two-band model that hosts a tilted Dirac cone. We then show that $\mathcal{Q}_{ij}$ leads to an intrinsic nonlinear anomalous thermoelectric current. As an example, we calculate the nonlinear Nernst and Hall current in the loop-current model for cuprate s…
Entropy is a fundamental thermodynamic quantity indicative of the accessible degrees of freedom in a system. While it has been suggested that the entropy of a mesoscopic system can yield nontrivial information on emergence of exotic states, its measurement in such small electron-number system is a daunting task. Here we propose a method to extract the entropy of a Coulomb-blockaded mesoscopic system from transport measurements. We prove analytically and demonstrate numerically the applicability of the method to such a mesoscopic system of arbitrary spectrum and degeneracies. We then apply our …
We propose a scheme of multilayer thermoelectric engine where {\em one} electric current is coupled to {\em two} temperature gradients in three-terminal geometry. This is realized by resonant tunneling through quantum dots embedded in two thermal and electrical resisting polymer matrix layers between highly conducting semiconductor layers. There are two thermoelectric effects, one of which is pertaining to inelastic transport processes (if energies of quantum dots in the two layers are different) while the other exists also for elastic transport processes. {These two correspond to the transver…
We investigate the thermoelectric properties of a T-shaped double quantum dot system described by a generalized Anderson Hamiltonian. The system's electrical conduction (G) and the fundamental thermoelectric parameters such as the Seebeck coefficient ($S$) and the thermal conductivity ($κ$), along with the system's thermoelectric figure of merit (ZT) are numerically estimated based on a Green's function formalism that includes contributions up to the Hartree-Fock level. Our results account for finite onsite Coulomb interaction terms in both component quantum dots and discuss various ways leadi…
We study thermoelectric effects in Coulomb-coupled quantum-dot (CCQD) systems beyond lowest-order tunneling processes and the often applied wide-band approximation. To this end, we present a master-equation (ME) approach based on a perturbative $T$-matrix calculation of the charge and heat tunneling rates and transport currents. Applying the method to transport through a non-interacting single-level QD, we demonstrate excellent agreement with the Landauer-B{ü}ttiker theory when higher-order (cotunneling) processes are included in the ME. Next, we study the effect of cotunneling and energy-depe…
We numerically study the thermoelectric transports of Dirac fermions in graphene in the presence of a strong magnetic field and disorder. We find that the thermoelectric transport coefficients demonstrate universal behavior depending on the ratio between the temperature and the width of the disorder-broadened Landau levels(LLs). The transverse thermoelectric conductivity $α_{xy}$ reaches a universal quantum value at the center of each LL in the high temperature regime, and it has a linear temperature dependence at low temperatures. The calculated Nernst signal has a peak at the central LL with…
The power factor of a thermoelectric device is a measure of the heat-to-energy conversion efficiency in nanoscopic devices. Yet, even as interest in low-dimensional thermoelectric materials has increased, experimental research on what influences the power factor in these systems is scarce. Here, we present a detailed thermoelectric study of graphene quantum dot devices. We show that spin-degeneracy of the quantum dot states has a significant impact on the zero-bias conductance of the device and leads to an increase of the power factor. Conversely, we demonstrate that non-ideal heat exchange wi…
We show theoretically that a thermoelectric heat engine, operating exclusively due to quantum-mechanical interference, can reach optimal linear-response performance. A chiral edge state implementation of a close-to-optimal heat engine is proposed in an electronic Mach-Zehnder interferometer with a mesoscopic capacitor coupled to one arm. We demonstrate that the maximum power and corresponding efficiency can reach 90\% and 83\%, respectively, of the theoretical maximum. The proposed heat engine can be realized with existing experimental techniques and has a performance robust against moderate d…
We experimentally investigate thermoelectric response of a 100~nm thick SnSe single crystal flake under the current-induced dc electric field. Thermoelectric response appears as a second-harmonic transverse voltage $V_{xy}^{2ω}$, which reflects temperature gradient across the sample due to the Joule heating by harmonic ac excitation current $I_{ac}$. In addition to strongly non-monotonous dependence $V_{xy}^{2ω}$, we observe that dc field direction controls the sign of the temperature gradient in the SnSe flake. We provide arguments, that electrocaloric effect is the mostly probable reason for…
A new thermoelectric effect mechanism inspired by an autonomous Maxwell's demon [P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Phys. Rev. Lett. 110, 040601 (2013)] is proposed. In contrast to the former work where a model for microscopic systems is proposed, a specific model for the thermoelectric effect in solid is formulated and its response to the electric field and temperature gradient is calculated in the framework of stochastic thermodynamics. The results show that relatively high $ZT$, which represents efficiency of the thermoelectric material, can be achieved within a range o…
We investigate the finite-frequency thermal transport through a quantum dot subject to strong interactions, by providing an exact, nonperturbative formalism that allows us to carry out a systematic analysis of the thermopower at any frequency. Special emphasis is put on the dc and high-frequency limits. We demonstrate that, in the Kondo regime, the ac thermopower is characterized by a universal function that we determine numerically.
The high-magnetic-field thermoelectric effect in nodal-line semimetals with straight nodal lines was investigated. Three-dimensional (3D) Dirac/Weyl semimetals exhibit constant thermoelectric Hall conductivity at the high-magnetic-field quantum limit, resulting in a boundless linear increase of Seebeck coefficient. This is known as the quantized thermoelectric Hall effect (QTHE), and is expected to lead to high-performance thermoelectricity at low temperatures. Here, in addition to Dirac/Weyl semimetals, we demonstrated that 3D semimetals with straight nodal lines can also exhibit the QTHE und…
Using a first principles approach to electron transport, we calculate the electrical and thermoelectrical transport properties of a series of molecular wires containing benzo-difuran subunits. We demonstrate that the side groups introduce Fano resonances, the energy of which is changing with the electronegativity of selected atoms in it. We also study the relative effect of single, double or triple bonds along the molecular backbone and find that single bonds yield the highest thermopower, approximately 22$μ$V/K at room temperature, which is comparable with the highest measured values for sing…
Molecular junctions are a versatile test bed for investigating thermoelectricity on the nanoscale1-10 and contribute to the design of new cost-effective environmentally-friendly organic thermoelectric materials11. It has been suggested that transport resonances associated with the discrete molecular levels would play a key role in the thermoelectric performance12,13, but no direct experimental evidence has been reported. Here we study single-molecule junctions of the endohedral fullerene Sc3N@C80 connected to gold electrodes using a scanning tunnelling microscope (STM). We find that the magnit…
We consider thermoelectric transport properties of the edge states of a two dimensional topological insulator in a double quantum point contact geometry coupled to two thermally biased reservoirs. Both spin-preserving and spin-flipping tunneling processes between opposite edges are analyzed in the presence of electron-electron interactions. We demonstrate that the simultaneous presence of spin-flipping processes and interactions gives rise to a finite longitudinal spin current. Moreover, its sign and amplitude can be tuned by means of gate voltages with the possibility to generate a pure spin …
We demonstrate high-temperature thermoelectric conversion in InAs/InP nanowire quantum dots by taking advantage of their strong electronic confinement. The electrical conductance G and the thermopower S are obtained from charge transport measurements and accurately reproduced with a theoretical model accounting for the multi-level structure of the quantum dot. Notably, our analysis does not rely on the estimate of co-tunnelling contributions since electronic thermal transport is dominated by multi-level heat transport. By taking into account two spin-degenerate energy levels we are able to eva…
Thermoelectric properties of finite graphene nanoribbons (GNRs) coupled to metallic electrodes are theoretically studied in the framework of tight-binding model and Green's function approach. When the zigzag sides are coupled to the electrodes, the electron transport through the localized edge states can occur only if the channel length between electrodes is smaller than the decay length of these localized zigzag edge states. When the armchair edges are coupled to the electrodes, there is an interesting thermoelectric behavior associated with the mid-gap states when the GNR is in the semicondu…
We review some of our recent experimental studies on low-carrier concentration, mesoscopic two-dimensional electron gases (m2DEGs). The m2DEGs show a range of striking characteristics including a complete avoidance of the strongly localised regime even when the electrical resistivity $ρ>> h/e^2$, giant thermoelectric response, and an apparent decoupling of charge and thermoelectric transport. We analyse the results and demonstrate that these observations can be explained based on the assumption that the charge carriers retain phase coherence over the m2DEG dimensions. Intriguingly, this would …
We demonstrate that thermoelectric signal as well as dc Josephson current may be severely enhanced in multi-terminal superconducting hybrid nanostructures exposed to a temperature gradient. At temperatures $T$ strongly exceeding the Thouless energy of our device both the supercurrent and the thermo-induced voltage are dominated by the contribution from non-equilibrium low energy quasiparticles and are predicted to decay slowly (algebraically rather than exponentially) with increasing $T$. We also predict a non-trivial current-phase relation and a transition to a $π$-junction state controlled b…
Thermoelectric power (TEP) is measured in bilayer graphene for various temperatures and charge-carrier densities. At low temperatures, measured TEP well follows the semiclassical Mott formula with a hyperbolic dispersion relation. TEP for a high carrier density shows a linear temperature dependence, which demonstrates a weak electron-phonon interaction in the bilayer graphene. For a low carrier density, a deviation from the Mott relation is observed at high temperatures and is attributed to the low Fermi temperature in the bilayer graphene. Oscillating TEP and the Nernst effect for varying car…
Quantum dots are useful model systems for studying quantum thermoelectric behavior because of their highly energy-dependent electron transport properties, which are tunable by electrostatic gating. As a result of this strong energy dependence, the thermoelectric response of quantum dots is expected to be nonlinear with respect to an applied thermal bias. However, until now this effect has been challenging to observe because, first, it is experimentally difficult to apply a sufficiently large thermal bias at the nanoscale and, second, it is difficult to distinguish thermal bias effects from pur…
Although it was demonstrated that discrete molecular levels determine the sign and magnitude of the thermoelectric effect in single-molecule junctions, full electrostatic control of these levels has not been achieved to date. Here, we show that graphene nanogaps combined with gold microheaters serve as a testbed for studying single-molecule thermoelectricity. Reduced screening of the gate electric field compared to conventional metal electrodes allows control of the position of the dominant transport orbital by hundreds of meV. We find that the power factor of graphene-fullerene junctions can …
Not so long ago, thermoelectricity in superconductors was believed to be possible only by breaking explicitly the particle-hole symmetry. Recently, it has been theoretically predicted that a superconducting tunnel junction can develop bipolar thermoelectric phenomena in the presence of a large thermal gradient owing to non-equilibrium spontaneous PH symmetry breaking. The experimental realization of the first thermoelectric Josephson engine then followed. Here, we give a more extended discussion and focus on the impact of the Josephson contribution on thermoelectricity modulating the Cooper pa…
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…
We investigate the noise current in a thermally biased tunnel junction between two superconductors with different zero-temperature gaps. When the Josephson effect is suppressed, this structure can support a nonlinear thermoelectric effect due to the spontaneous breaking of electron-hole symmetry, as we recently theoretically predicted. We discuss the possibly relevant role played by the noise in the junction. While a moderate noise contribution assists the generation of the thermoelectric signal, further unveiling the spontaneous nature of the electron-hole symmetry breaking, a large noise con…
Thermoelectrics are promising by directly generating electricity from waste heat. However, (sub-)room-temperature thermoelectrics have been a long-standing challenge due to vanishing electronic entropy at low temperatures. Topological materials offer a new avenue for energy harvesting applications. Recent theories predicted that topological semimetals at the quantum limit can lead to a large, non-saturating thermopower and a quantized thermoelectric Hall conductivity approaching a universal value. Here, we experimentally demonstrate the non-saturating thermopower and quantized thermoelectric H…
Grain boundaries are commonly observed in carbon nanostructures, but their influence on thermal and electric properties are still not completely understood. Using a combined approach of density functional tight-binding theory and non-equilibrium Green functions we investigate electron and phonon transport in carbon based systems. In this work, quantum transport and thermoelectric properties are summarized for graphene sheets, graphene nanoribbons and carbon nanotubes with a variety of grain boundary types in a wide temperature range. Motivated by previous findings that disorder scatters phonon…
The energy efficiency and power of a three-terminal thermoelectric nanodevice are studied by considering elastic tunneling through a single quantum dot. Facilitated by the three-terminal geometry, the nanodevice is able to generate simultaneously two electrical powers by utilizing only one temperature bias. These two electrical powers can add up constructively or destructively, depending on their signs. It is demonstrated that the constructive addition leads to the enhancement of both energy efficiency and output power for various system parameters. In fact, such enhancement, dubbed as thermoe…
The thermoelectric figures of merit of pristine two-dimensional materials are predicted to be significantly less than unity, making them uncompetitive as thermoelectric materials. Here we elucidate a new strategy that overcomes this limitation by creating multi-layer nanoribbons of two different materials and allowing thermal and electrical currents to flow perpendicular to their planes. To demonstrate this enhancement of thermoelectric efficiency ZT, we analyse the thermoelectric performance of monolayer molybdenum disulphide (MoS2) sandwiched between two graphene monolayers and demonstrate t…
We apply the generalized Boltzmann theory to describe thermoelectric transport properties of monolayer phosphorene in the presence of short- and long-range charged impurity interactions. First, we propose a low-energy Hamiltonian to explore the accurate electronic band structure of phosphorene in comparison with those results obtained by density-functional simulations. We explain the effect of the coupling between the conduction and valence bands on the thermoelectric properties. We show that the electric conductivity of phosphorene is highly anisotropic, while the Seebeck coefficient and figu…
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…
Thermoelectric phenomena resulting from an interplay between particle flows induced by electric fields and temperature inhomogeneities are extremely insightful as a tool providing substantial knowledge about the microscopic structure of a given system. Tuning, e.g., parameters of a nanoscopic system coupled via tunneling mechanisms to two contacts one may achieve various situations where the electric current induced by an external bias voltage competes with the electric current excited by the temperature difference of the two contacts. Even more exciting physics emerges when the system's elect…
A theoretical study of the thermoelectric current and energy harvesting in an interacting double quantum dot system, connected to reservoirs held at different chemical potentials and temperatures is presented. Using a rate-equation approach, the current is evaluated for different energetic configurations of the double quantum dot. We discuss in detail the current-temperature gradient relations (the thermoelectric analog to current-voltage relations), and demonstrate that, due to interactions, the current is non-monotonically dependent on thermal bias. This interaction-induced non-monotonicity …
Thermoelectric effects, such as the generation of a particle current by a temperature gradient, have their origin in a reversible coupling between heat and particle flows. These effects are fundamental probes for materials and have applications to cooling and power generation. Here we demonstrate thermoelectricity in a fermionic cold atoms channel, ballistic or diffusive, connected to two reservoirs. We show that the magnitude of the effect and the efficiency of energy conversion can be optimized by controlling the geometry or disorder strength. Our observations are in quantitative agreement w…
In a previous work, we predicted that a thermally biased tunnel junction between two different superconductors can display a thermoelectric effect of nonlinear nature in the temperature gradient, under proper conditions. In this work we give a more extended discussion, and we focus on the two main features of the nonlinear contributions: i) the $linear-in-bias$ thermoelectricity, that can be associated to a spontaneous breaking of electron-hole symmetry, ii) the strong contribution at the matching peak singularity, which is typically associated to the maximum output power and efficiency. We di…
