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 discuss the nonlinear origin of the thermoelectricity and its relationship with the non-linear cooling mechanism in superconducting junctions previously discussed in the literature. Finally, we design and characterize the performance of the system as a heat engine, for a realistic design and experimental parameter values. We discuss possible non-idealities demonstrating that the system is amenable to current experimental realization.
We investigate transport and thermoelectric properties of hybrid systems based on a single-level quantum dot and one superconducting lead. The other lead is generally normal-metallic ferromagnet. In the latter case single-particle transport is spin-polarized. Our main interest is in the interplay of Andreev tunneling of Cooper pairs and single-particle tunneling. The latter is responsible for relatively large thermopower and figure of merit due to a diverging density of single-particle states at the superconducting gap edges. System with ferromagnetic and superconducting leads can also reveal …
Giant thermoelectric effects are known to arise at the interface between superconductors and strongly polarized ferromagnets, enabling the construction of efficient thermoelectric generators. We predict that the thermopower of such a generator can be completely controlled by a magnetic input signal: Not only can the thermopower be toggled on and off by rotating a magnet, but it can even be entirely reversed. This in situ control diverges from conventional thermoelectrics, where the thermopower is usually fixed by the device design.
We argue that spin-sensitive quasiparticle scattering may generate electron-hole imbalance in superconducting structures, such as, e.g., superconducting-normal hybrids with spin-active interfaces. We elucidate a transparent physical mechanism for this effect demonstrating that scattering rates for electrons and holes at such interfaces differ from each other. Explicitly evaluating the wave functions of electron-like and hole-like excitations in superconducting-normal bilayers we derive a general expression for the thermoelectric current and show that -- in the presence of electron-hole imbalan…
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…
Superconducting tunnel junctions constitute the units of superconducting quantum circuits and are massively used both for quantum sensing and quantum computation. In previous works, we predicted the existence of a nonlinear thermoelectric effect in a electron-hole symmetric system, namely, a thermally biased tunnel junction between two different superconductors, where the Josephson effect is suppressed. In this paper we investigate the impact of the phase-coherent contributions on the thermoelectric effect, by tuning the size of the Josephson coupling changing the flux of a direct-current Supe…
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 …
The thermoelectric performance of a topological Josephson nonlocal heat engine is thoroughly investigated. The nonlocal response is obtained by using a normal metal probe coupled with only one of the proximized helical edges in the middle of the junction. In this configuration, we investigate how the flux bias and the phase bias trigger the nonlocal thermoelectric effects under the application of a thermal difference between the superconducting terminals. Possible experimental nonidealities such as asymmetric proximized superconducting gaps are considered showing how the nonlocal response can …
We discuss the nonlinear current of an interacting quantum dot coupled to normal and superconducting reservoirs with applied voltage and temperature differences. Due to the particle-hole symmetry introduced by the superconducting lead, the pure (subgap) thermoelectric response vanishes. However, we show that the Andreev bound states shift as the thermal gradient increases. As a consequence, the $I$--$V$ characteristic can be tuned with a temperature bias if the system is simultaneously voltage biased. This is a cross effect that occurs beyond linear response only. Furthermore, we emphasize the…
It is well known that the transport properties of single-electron transistors with a superconducting island and normal-conducting leads (NSN SET) may depend on whether or not there is a single quasiparticle on the island. This parity effect has pronounced consequences for the linear transport properties. Here we analyze the thermopower of NSN SET with and without parity effect, for entirely realistic values of device parameters. Besides a marked dependence of the thermopower on the superconducting gap $Δ$ we observe an enhancement in the parity regime which is accompanied by a dramatic increas…
We investigate thermoelectric transport through Andreev interferometers. We show that the ratio of the thermal and the charge conductance exhibits large oscillations with the phase difference $ϕ$ between the two superconducting contacts, and that the Wiedemann-Franz law holds only when $ϕ=π$. A large average thermopower furthermore emerges whenever there is an asymmetry in the dwell times to reach the superconducting contacts. When this is the case, the thermopower is odd in $ϕ$. In contrast, when the average times to reach either superconducting contact are the same, the average thermopower i…
We discuss the nonlinear Andreev current of an interacting quantum dot coupled to spin-polarized and superconducting reservoirs when voltage and temperature biases are applied across the nanostructure. Due to the particle-hole symmetry introduced by the superconducting (S) lead, the subgap spin current vanishes identically. Nevertheless, the Andreev charge current depends on the degree of polarization in the ferromagnetic (F) contact since the shift of electrostatic internal potential of the conductor depends on spin orientation of the charge carrier. This spin-dependent potential shift charac…
I discuss thermoelectric properties of a quantum dot coupled to one normal and one superconducting lead in the presence of Kondo effect and Andreev scattering. I will focus on conductance, thermal conductance, thermopower and related quantities like thermoelectric figure of merit which is a direct measure of the usefulness of the system for applications and Wiedemann-Franz ratio which indicates if the system is in the Fermi liquid state. I will show that the superconductivity strongly modifies the thermal properties of the system. In particular, the thermopower is strongly enhanced near the su…
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 propose a simple classical dynamical model of a thermoelectric (or thermochemical) heat engine based on a pair of ideal gas containers connected by two unequal scattering channels. The model is solved analytically and it is shown that a suitable combination of parameters can be chosen such that the engine operates at Carnot's efficiency.
We establish a theory of optimal efficiency and power for three-terminal thermoelectric engines which have two independent output electric currents and one input heat current. This set-up goes beyond the conventional heat engines with only one output electric current. For such a set-up, we derive the optimal efficiency and power and their trade-off for three-terminal heat engines with and without time-reversal symmetry. The formalism goes beyond the known optimal efficiency and power for systems with or without time-reversal symmetry, showing interesting features that have not been revealed be…
Thermodynamic uncertainty relation, quantifying a trade-off among average current, the associated fluctuation (precision), and entropy production (cost), has been formulated in nonequilibrium steady state and various stochastic systems. Herein, we study the thermodynamic uncertainty relation in generic thermoelectric heat engines under a periodic control protocol, by uncovering the underlying Berry-phase-like contribution. We show that our thermodynamic uncertainty relation breaks the seminal steady-state results, originating from the non-vanishing geometric effect. Furthermore, by deriving th…
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…
We report on the experimental observation of nonlocal spin-dependent thermoelectric effects in superconductor-ferromagnet multiterminal structures. Our samples consist of a thin superconducting aluminum wire with several ferromagnetic tunnel junctions attached to it. When a thermal excitation is applied to one of the junctions in the presence of a Zeeman splitting of the density of states of the superconductor, a thermoelectric current is observed in remote junctions at distances exceeding $10~\mathrm{μm}$. The results can be explained by recent theories of coupled spin and heat transport in h…
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…
Superconducting spintronics is based on the creation of spin-triplet Cooper pairs in ferromagnet-superconductor (F-S) hybrid junctions. Previous proposals to manipulate spin-polarized supercurrents on-demand typically require the ability to carefully control magnetic materials. We, instead, propose a quantum heat engine that generates equal-spin Cooper pairs and drives supercurrents on-demand without manipulating magnetic components. We consider a S-F-S junction, connecting two leads at different temperatures, on top of the helical edge of a two-dimensional topological insulator. Heat and char…
We propose a near-field inelastic thermoelectric heat engine where quantum-dots are used to effectively rectify the charge flow of photo-carriers. The device converts near-field heat radiation into useful electrical power. Heat absorption and inelastic transport can be enhanced by introducing two continuous spectra separated by an energy gap. The thermoelectric transport properties of the heat engine are studied in the linear-response regime. Using a small band-gap semiconductor as the absorption material, we show that the device achieves very large thermopower and thermoelectric figure-of-mer…
This paper examines the thermoelectric response of a dissipative quantum dot heat engine based on the Anderson-Holstein model in two relevant operating limits: (i) when the dot phonon modes are out of equilibrium, and (ii) when the dot phonon modes are strongly coupled to a heat bath. In the first case, a detailed analysis of the physics related to the interplay between the quantum dot level quantization, the on-site Coulomb interaction and the electron-phonon coupling on the thermoelectric performance reveals that an n-type heat engine performs better than a p-type heat engine. In the second …
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…
We investigate a thermoelectric nano-engine whose properties are steered by Coulomb interaction. The device whose design decouples charge and energy currents is made up of two interacting quantum dots connected to three different reservoirs. We show that, by tailoring the tunnel couplings, this setup can be made very attractive for energy-harvesting prospects, due to a delivered power that can be of the order of the quantum bound [R. S. Whitney, Phys. Rev. Lett. 112, 130601 (2014); Entropy 18, 208 (2016)], with a concomitant fair efficiency. To unveil its properties beyond the sequential quant…
We analyze the noise properties of both electric charge and heat currents as well as their correlations in a quantum-dot based thermoelectric engine. The engine is a three-terminal conductor with crossed heat and charge flows where heat fluctuations can be monitored by a charge detector. We investigate the mutual influence of charge and heat dynamics and how it is manifested in the current and noise properties. In the presence of energy-dependent tunneling, operating conditions are discussed where a charge current can be generated by heat conversion. In addition, heat can be pumped into the ho…
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…
Thermodynamic bound on the Fano factor of a coherent thermoelectric heat engine
The Abdus Salam International Centre for Theoretical Physics（阿卜杜斯·萨拉姆国际理论物理中心）；Dipartimento di Fisica, Università di Napoli “Federico II”（那不勒斯费德里科二世大学物理系）
The thermoelectric properties of a three terminal quantum spin Hall (QSH) sample are examined. Inherent helicity of the QSH sample helps to generate a large charge power efficiently. Along with charge the system can be designed to work as a highly efficient spin heat engine too. The advantage of a helical over a chiral sample is that, while a multiterminal quantum Hall sample can only work as a quantum heat engine due to broken time reversal(TR) symmetry, a multiterminal QSH system can work effectively both as a charge/spin heat engine as well as a charge/spin refrigerator as TR symmetry is pr…
We study thermal and charge transport in a three-terminal setup consisting of one superconducting and two ferromagnetic contacts. We predict that the simultaneous presence of spin filtering and of spin- dependent scattering phase shifts at each of the two interfaces will lead to very large nonlocal thermo- electric effects both in clean and in disordered systems. The symmetries of thermal and electric transport coefficients are related to fundamental thermodynamic principles by the Onsager reciprocity. Our results show that a nonlocal version of the Onsager relations for thermoelectric current…
Efficiency at maximum power (EMP) is a very important specification for a heat engine to evaluate the capacity of outputting adequate power with high efficiency. It has been proved theoretically that the limit EMP of thermoelectric heat engine can be achieved with the hypothetical boxcar-shaped electron transmission, which is realized here by the resonant tunneling in the one-dimensional symmetric InP/InSe superlattice. It is found with the transfer matrix method that a symmetric mode is robust that regardless of the periodicity, and the obtained boxcar-like electron transmission stems from th…
We propose a possible route to achieve high thermoelectric efficiency in molecular junctions by combining a local chemical tuning of the molecular electronic states with the use of semiconducting electrodes. The former allows to control the position of the HOMO transmission resonance with respect to the Fermi energy while the latter fulfills a twofold purpose: the suppression of electron-like contributions to the thermopower and the cut-off of the HOMO transmission tails into the semiconductor band gap. As a result a large thermopower can be obtained. Our results strongly suggest that large fi…
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 quest to identify the best heat engine has been at the center of science and technology. Thermoelectric nanoscale heat engines convert heat flows into useful work in the form of electrical power and promise the realization of on-chip power production. Considerable studies have so far revealed the potentials to yield an enhanced efficiency originating from quantum confinement effects and energy-dependent transport properties. However, the full benefit of many-body interactions in thermoelectric is yet to be investigated; identifying the optimal interaction is a hard problem due to combinato…
Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriate in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the …
We review recent theoretical work on thermoelectric energy harvesting in multi-terminal quantum-dot setups. We first discuss several examples of nanoscale heat engines based on Coulomb-coupled conductors. In particular, we focus on quantum dots in the Coulomb-blockade regime, chaotic cavities and resonant tunneling through quantum dots and wells. We then turn towards quantum-dot heat engines that are driven by bosonic degrees of freedom such as phonons, magnons and microwave photons. These systems provide interesting connections to spin caloritronics and circuit quantum electrodynamics.
We consider a Josephson junction hosting a Kramers pair of helical edge states of a quantum spin Hall bar in contact with a normal-metal probe. In this hybrid system, the orbital phase induced by a small magnetic field threading the junction known as Doppler shift (DS), combines with the conventional Josephson phase difference and originates an effect akin to a Zeeman field in the spectrum. As a consequence, when a temperature bias is applied to the superconducting terminals, a thermoelectric current is established in the normal probe. We argue that this purely non-local thermoelectric effect …
The trade-off between large power output, high efficiency and small fluctuations in the operation of heat engines has recently received interest in the context of thermodynamic uncertainty relations (TURs). Here we provide a concrete illustration of this trade-off by theoretically investigating the operation of a quantum point contact (QPC) with an energy-dependent transmission function as a steady-state thermoelectric heat engine. As a starting point, we review and extend previous analysis of the power production and efficiency. Thereafter the power fluctuations and the bound jointly imposed …
