We suggest a new type of an ultrasensitive detector of electromagnetic fields exploiting the giant thermoelectric effect recently found in superconductor/ferromagnet hybrid structures. Compared to other types of superconducting detectors where the detected signal is based on variations of the detector impedance, the thermoelectric detector has the advantage of requiring no external driving fields. This becomes especially relevant in multi-pixel detectors where the number of bias lines and the heating induced by them becomes an issue. We propose different material combinations to implement the detector and provide a detailed analysis of its sensitivity and speed. In particular, we perform to our knowledge the first proper noise analysis that includes the cross correlation between heat and charge current noise and thereby describes also thermoelectric detectors with a large thermoelectric figure of merit.
For almost a century thermoelectricity in superconductors has been one of the most intriguing topics of physics. At the early stages in the 1920s, the mere existence of thermoelectric effects in superconductors was questioned. Theoretical breakthrough came in the 1970s, when the generation of a measurable thermoelectric magnetic flux in superconducting loops was predicted; however a major crisis developed when experiments showed a gross discrepancy with the theory. Moreover, different experiments disagreed with each other by orders of magnitude. This led to a stalemate in bringing theory and e…
We report thermal transport measurement of KxFe2-ySe2 superconducting single crystal. Significant peak anomaly in thermal conductivity is observed at nearly TC/2 indicating a large phonon mean-free-path in the superconducting state. The zero-temperature extrapolated thermoelectric power is smaller than the value in typical strongly correlated superconductors, implying large normalized Fermi temperature. In contrast to other iron superconductors, thermoelectric power in our sample does not exhibit significant anomalies. These findings indicate that KxFe2-ySe2 is a weakly or intermediately corre…
We show that a huge thermoelectric effect can be observed by contacting a superconductor whose density of states is spin-split by a Zeeman field with a ferromagnet with a non-zero polarization. The resulting thermopower exceeds $k_B/e$ by a large factor, and the thermoelectric figure of merit $ZT$ can far exceed unity, leading to heat engine efficiencies close to the Carnot limit. We also show that spin-polarized currents can be generated in the superconductor by applying a temperature bias.
We consider a mesoscopic four-terminal superconductor/normal metal (S/N) structure in the presence of a temperature gradient along the N wire. A thermoemf arises in this system even in the absence of the thermoelectric quasiparticle current if the phase difference between the superconductors is not zero. We show that the thermoemf is not small in the case of a negligible Josephson coupling between two superconductors. It is also shown that the thermoelectric voltage has two maxima: one at a low temperature and another at a temperature close to the critical temperature. The obtained temperature…
It is widely believed that temperature gradient does not induce electric field in the superconductor and consequently that thermoelectric effects do not exist, or are negligible in these materials. This statement is correct only as far as effective electric field or gradient of the electrochemical potential is concerned. In normal metals temperature gradient generates effective electric field, which nulls out thermally induced diffusion current. In superconductor the diffusion current of quasiparticles is canceled a counterflow of supercurrent. Superconducting current induces the true electric…
We present analytic and numerical results for the thermoelectric effect in unconventional superconductors with a dilute random distribution of impurities, each scattering isotropically but with a phase shift intermediate between the Born and unitary limits. The thermoelectric response function has a linear temperature dependence at low temperatures, with a slope that depends on the impurity concentration and phase shift. Although the thermoelectric effect vanishes identically in the strict Born and unitary limits, even a small deviation of the phase shift from these limits leads to a large res…
We have calculated the thermopower of the Bi2Sr2CuO6 and Bi2Sr2CaCu2O8 superconductors using an ARPES-derived dispersion, with a model pseudogap, and a marginal-Fermi liquid scattering rate that has a minimum with respect to energy at the van Hove singularity (vHs). Good fits with data are achieved across the entire phase diagram, thus confirming the dispersions, the locations of the vHs and the dominance of the diffusion thermopower over the phonon drag contribution.
We demonstrate that superconductors which break time-reversal symmetry can exhibit thermoelectric properties, which are entirely different from the Ginzburg mechanism. As an example, we show that in the $s+is$ superconducting state there is a reversible contribution to thermally induced supercurrent, whose direction is not invariant under time-reversal operation. Moreover in contrast to Ginzburg's mechanism it has a singular behavior near the time-reversal symmetry breaking phase transition. The effect can be used to confirm or rule out the $s+is$ state, which is widely expected to be realized…
We show that superconductors with broken time-reversal symmetry have very specific magnetic and electric responses to inhomogeneous heating. A local heating of such superconductors induces a magnetic field with a profile that is sensitive to the presence of domain walls and crystalline anisotropy of superconducting states. A nonstationary heating process produces an electric field and a charge imbalance in different bands. These effects can be measured and used to distinguish $s+is$ and $s+id$ superconducting states in the candidate materials such as Ba$_{1-x}$K$_x$Fe$_2$As$_2$.
We report on large thermoelectric effects in superconductor-ferromagnet tunnel junctions in proximity contact with the ferromagnetic insulator europium sulfide. The combination of a spin-splitting field and spin-polarized tunnel conductance in these systems breaks the electron-hole symmetry and leads to spin-dependent thermoelectric currents. We show that the exchange splitting induced by the europium sulfide boosts the thermoelectric effect in small applied fields and can therefore eliminate the need to apply large magnetic fields, which might otherwise impede applications in thermometry or c…
We studied the effects of multiband electronic structure on the thermoelectric and electrical transport properties in the normal state of kagome superconductors $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs). In all three members, the multiband nature is manifested by sign changes in the temperature dependence of the Seebeck and Hall resistivity, together with sublinear response of the isothermal Nernst and Hall effects to external magnetic fields in the charge ordered state. Moreover, ambipolar transport effects appear ubiquitously in all three systems, giving rise to sizable Nernst signal. Finally, possib…
The superconductor-ferromagnet thermoelectric detector (SFTED) is a novel ultrasensitive radiation detector based on the giant thermoelectric effect in superconductorferromagnet tunnel junctions. We demonstrate analytical models and solutions in the time domain for a SFTED operated as a microcalorimeter (pulse excitation), in the linear smallsignal limit. Based on these solutions, the signal current and temperature pulse response were studied for two different electrical circuit models, providing design conditions for stable and non-oscillatory response.
Thermoelectric effects result from the coupling of charge and heat transport, and can be used for thermometry, cooling and harvesting of thermal energy. The microscopic origin of thermoelectric effects is a broken electron-hole symmetry, which is usually quite small in metal structures, and vanishes at low temperatures. We report on a combined experimental and theoretical investigation of thermoelectric effects in superconductor/ferromagnet hybrid structures. We investigate the depencence of thermoelectric currents on the thermal excitation, as well as on the presence of a dc bias voltage acro…
We study the effects of spin-splitting and spin-flip scattering in a superconductor (S) on the thermoelectric properties of a tunneling contact to a metallic ferromagnet (F) using the Green's function method. A giant thermopower has been theoretically predicted and experimentally observed in such structures. This is attributed to the spin-dependent particle-hole asymmetry in the tunneling density of states in the S/F heterostructure. Here, we evaluate the S density of states and thermopower for a range of temperatures, Zeeman-splitting, and spin-flip scattering. In contrast to the naive expect…
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…
We report on the experimental observation of thermoelectric currents in superconductor-ferromagnet tunnel junctions in high magnetic fields. The thermoelectric signals are due to a spin-dependent lifting of particle-hole symmetry, and are found to be in excellent agreement with recent theoretical predictions. The maximum Seebeck coefficient inferred from the data is about $-100~\mathrm{μV/K}$, much larger than commonly found in metallic structures. Our results directly prove the coupling of spin and heat transport in high-field superconductors.
Studies of the copper-based superconductors demonstrate how their phase diagram becomes more complex as experimental probes improve, able to distinguish among subtly different electronic phases. One of those phases, nematicity, has become the matter of great interest also in the iron-based superconductors, where it is detected deep in the tetragonal state. Here we present the evolution of the in-plane Nernst effect anisotropy in the strain detwinned Ca(Fe1-xCox)2As2 single crystals, whose behaviour can be explained within the approach developed to describe the nematic order parameter in liquid…
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…
We explore the role of proximity-induced odd-frequency pairing in the thermoelectricity of a ferromagnet when coupled to a conventional $s$-wave spin-singlet superconductor through a spin-active interface. By varying both the polarization and its direction in the ferromagnet and the interfacial spin-orbit interaction strength, we analyze the behavior of all proximity-induced pair amplitudes in the ferromagnet and their contributions to the thermoelectric coefficients. Based on our results for the Seebeck coefficient, we predict that odd-frequency spin-triplet Cooper pairs are much efficient th…
Polycrystalline sample of the new layered superconductor Bi4O4S3 is successfully synthesized by solid-state reaction method by using Bi, S and Bi2O3 powders with one step reaction. The superconducting transition temperature (Tconset=4.5 K), the zero resistance transition temperature (Tc0=4.07 K) and the diamagnetic transition temperature (4.02 K at H=10 Oe) were confirmed by electrical transport and magnetic measurements. Also, our results indicate a typical type II-superconductor behavior. In addition, a large thermoelectric effect was observed with a dimensionless thermoelectric figure of me…
We have measured temperature dependence of thermoelectric power (TEP) on MgB$_2$ superconductor under hydrostatic pressure. The sign and temperature dependence of TEP shows metallic hole carriers are dominant with activation type contribution at higher temperature. TEP increases with pressure while $T_c$ decrease with ratio -0.136 K/kbar. The data are discussed in consideration of carriers from different bands and anisotropy of compressibility.
The theory of thermoelectric effects in superconductors is discussed in connection to the recent publication by Marinescu and Overhauser, Phys. Rev. B 55, 11637 (1997). We argue that the charge on-conservation arguments by Marinescu and Overhauser do not require any revision of the Boltzmann transport equation in superconductors, and show that their ``electron-conserving transport theory'' contradicts thermodynamics. Possible mechanisms responsible for the discrepancy between some experimental data and the theory by Galperin, Gurevich, and Kozub, JETP Lett. 17, 476 (1973) are discussed.
Using the Bogoliubov de-Gennes formalism, we investigate the charge and spin-dependent thermoelectric effects in superconductor graphene junctions. Results demonstrate that despite normal-superconductor junctions, there is a temperature-dependent spin thermopower both in the graphene-based ferromagnetic-superconductor (F-S) and ferromagnetic-Rashba spin-orbit region-superconductor (F-RSO-S) junctions. It is also shown that in the presence of Rashba spin-orbit interaction, the charge and spin-dependent Seebeck coefficients can reach to their maximum up to 3.5$k_B/e$ and 2.5$k_B/e$, respectively…
The usually negligibly small thermoelectric effects in superconducting heterostructures can be boosted dramatically due to the simultaneous effect of spin splitting and spin filtering. Building on an idea of our earlier work [Phys. Rev. Lett. $\textbf{110}$, 047002 (2013)], we propose realistic mesoscopic setups to observe thermoelectric effects in superconductor heterostructures with ferromagnetic interfaces or terminals. We focus on the Seebeck effect being a direct measure of the local thermoelectric response and find that a thermopower of the order of $\sim200$ $μV/K$ can be achieved in a …
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…
Magnetic susceptibility, M-H plot, magnetoresistance and thermoelectric power of the RuSr2Eu1.5Ce0.5Cu2O10 superconductor are measured. Values of the magnetic transition temperature Tmag, superconductivity transition temperature Tc, upper critical field Hc2, chemical potential mu, and energy width for electric conduction W(sigma) are obtained from these measurements. It has been found that Tmag = 140 K, Tc = 25 K (33 K) from susceptibility (magnetoresistance) measurements, Hc2 (0) > 32 T, mu = 8 meV, and W(sigma) = 58.5 meV. These values are compared with other ruthenate superconductors, and r…
We study heat transport and thermoelectric effects in two-dimensional superconductors in a magnetic field. These are modeled as granular Josephson-junction arrays, forming either regular or random lattices. We employ two different models for the dynamics, relaxational model-A dynamics or resistively and capacitively shunted Josephson junction (RCSJ) dynamics. We derive expressions for the heat current in these models, which are then used in numerical simulations to calculate the heat conductivity and the Nernst coefficient for different temperatures and magnetic fields. At low temperatures and…
The thermoelectric response of SND configuration is considered within the generalized Ginzburg-Landau theory for a homogeneous admixture of s-wave and d-wave superconductors. The resulting thermopower (TP) is found to strongly depend on the relative phase θ=ϕ_s-ϕ_d between the two superconductors. Two independent mechanisms are shown to contribute to the TP. One, based on the charge imbalance between the quasiparticles and Cooper pairs (described by the corresponding chemical potentials) due to the normal metal insert, results in a pronounced maximum of the peak near θ=π/2 (the so-called s+id …
Temperature dependence of thermoelectric power S(T) of three differently processed Bi2Sr2CaCu2O8 (Bi2212) samples, viz. as-processed melt quenched (Bi2212-MQ), 6000C N2-annealed (Bi2212-N2) and 6000C O2-annealed (Bi2212-O2) is reported here. All the samples possess single-phase character and their superconducting transition temperatures (TcR=0) are 85 K, 90 K and 72 K respectively for Bi2212-MQ, Bi2212-N2 and Bi2212-O2. While Bi2212-MQ and Bi2212-N2 samples are in near optimum doping regime, Bi2212-O2 is an over-doped sample. TcS=0 values obtained through S(T) data are also in line with those …
It has recently been proposed and experimentally demonstrated that it is possible to generate large thermoelectric effects in ferromagnet/superconductor structures due to a spin-dependent particle-hole asymmetry. Here, we theoretically show that quasiparticle tunneling between two spin-split superconductors enhances the thermoelectric response manyfold compared to when only one such superconductor is used, generating Seebeck coefficients ($\mathcal{S} > 1$ mV/K) and figures of merit ($ZT \simeq 40$) far exceeding the best bulk thermoelectric materials, and also becomes more resilient toward in…
Identifying materials and devices which offer efficient thermoelectric effects at low temperature is a major obstacle for the development of thermal management strategies for low-temperature electronic systems. Superconductors cannot offer a solution since their near perfect electron-hole symmetry leads to a negligible thermoelectric response; however, here we demonstrate theoretically a superconducting thermoelectric transistor which offers unparalleled figures of merit of up to $\sim 45$ and Seebeck coefficients as large as a few mV/K at sub-Kelvin temperatures. The device is also phase-tuna…
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…
UCoGe exhibits superconductivity in the presence of ferromagnetism. When a field is applied along the b axis (perpendicular to the easy axis), ferromagnetism is weakened and superconductivity is enhanced. This enhancement has been attributed to an increase in coupling as observed in the enhanced effective mass produced by the critical fluctuations as the ferromagnetic transition is strongly suppressed. However it is also important to know if and how the Fermi surface changes near the critical point. Here we report measurements of the thermoelectricity of UCoGe which reveal a low carrier densit…
Herewith, we review the available experimental data of thermoelectric transport properties of iron-based superconductors and parent compounds. We discuss possible physical mechanisms into play in determining the Seebeck effect, from whence one can extract information about Fermi surface reconstruction and Lifshitz transitions, multiband character, coupling of charge carriers with spin excitations and its relevance in the unconventional superconducting pairing mechanism, nematicity, quantum critical fluctuations close to the optimal doping for superconductivity, correlation. Additional informat…
We investigate thermoelectric properties of a ferromagnet-superconductor hybrid structure with Rashba spin-orbit interaction and delta function potential barrier at the interfacial layer. The exponential rise of thermal conductance with temperature manifests a cross-over temperature scale separating two opposite behaviors of it with the change of polarization in the ferromagnet whereas the inclusion of interfacial Rashba spin-orbit field results in a non-monotonic behavior of it with the strength of Rashba field. We employ scattering matrix approach to determine the amplitudes of all the scatt…
The nematic instability of iron-based superconductors is an undebatable ingredient of the physics of iron-based superconductors. Yet, its origin remains enigmatic as it involves a fermiology with an intricate interplay of lattice-, orbital- and spin- degrees of freedom. It is well known that thermoelectric transport is an excellent probe for revealing even subtle signatures of instabilities and pertinent fluctuations. In this paper, we report a strong response of the thermoelectric transport properties of two underdoped 1111 iron-based superconductors to a vanishingly small strain. By introduc…
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…
The thermoelectric coefficient $η(T)$ in unconventional superconductors is enhanced below $T_c$ by intermediate strength impurity scattering that is intrinsically particle-hole asymmetric. We compute $η(T)$ for a strong-coupling d-wave superconductor and investigate the effects of inelastic scattering originating from electron-boson interactions. We show that $η(T)$ is severely suppressed at temperatures just below $T_c$ by a particle-hole symmetric inelastic scattering rate. At lower temperatures inelastic scattering is frozen out and $η(T)$ recovers and regains its large amplitude. In the li…
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 investigate transport properties of a trilayer made of a d-wave superconductor connected to two ferromagnetic electrodes. Using Keldysh formalism we show that crossed Andreev reflection and elastic cotunneling exist also with d-wave superconductors. Their properties are controlled by the existence of zero energy states due to the anisotropy of the d-wave pair potential.
Superconductor-ferromagnet-superconductor Josephson junctions are known to exist in the $0$ and $π$ states with the transitions between them controlled by the temperature and ferromagnetic interlayer thickness. We demonstrate that these transitions can be controlled also by the external magnetic field directed perpendicular to the layers. By varying the ratio of diffusion coefficients in superconducting and ferromagnetic layers, these field-controlled transitions can be made detectable for arbitrary large value of the exchange energy in the ferromagnet. We also show that the $0$-$π$ transition…
We report the in-plane anisotropy of the Seebeck and Nernst coefficients as well as of the electrical resistivity determined for the series of the strain-detwinned single crystals of Ba(Fe1-xCox)2As2. Two underdoped samples (x = 0.024, 0.045) exhibiting the transition from the tetragonal paramagnetic phase to the orthorhombic spin density wave (SDW) phase (at Ttr = 100 and 60 K, respectively) show an onset of the Nernst anisotropy at temperatures above 200 K, which is significantly higher than Ttr. In the optimally doped sample (x = 0.06) the transport properties also appear to be in-plane ani…
We present a microscopic theory for the thermoelectric power (TEP) in high-Tc cuprates. Based on the general expression for the TEP, we perform the calculation of the TEP for a square lattice Hubbard model including all the vertex corrections necessary to satisfy the conservation laws. In the present study, characteristic anomalous temperature and doping dependences of the TEP in high-Tc cuprates, which have been a long-standing problem of high-Tc cuprates, are well reproduced for both hole- and electron-doped systems, except for the heavily under-doped case. According to the present analysis,…
The physics of superconductor-ferromagnet hybrid structures
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；HSE University（高等经济学院）；Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University（莫斯科国立大学索别利钦核物理研究所）；Technical University of Moldova（摩尔多瓦技术大学）
We predict a novel type of Josephson effect to occur in triplet superconductor - ferromagnet - triplet superconductor Josephson junctions. We show that the Josephson current, I_J, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d-vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional temperature dependence of I_J in which I_J changes sign with increasing temperature
We demonstrate that in multilayered superconductor-ferromagnet structures a non-collinear alignment of the magnetizations of different ferromagnetic layers generates a triplet superconducting condensate which is odd in frequency. This triplet condensate coexists in the superconductors with the conventional singlet one but decays very slowly in the ferromagnet, which should lead to a large Josephson effect between the superconductors separated by the ferromagnet. Depending on the mutual direction of the ferromagnetic moments the Josephson coupling can be both of 0 and $π$ type.
We study a magnetic proximity effect at superconductor (S) - ferromagnet (F) interface. It is shown that due to an exchange of electrons between the F and S metals ferromagnetic correlations extend into the superconductor, being dependent on interface parameters. We show that ferromagnetic exchange field pair breaking effect leads to a formation of subgap bands in the S layer local density of states, that accommodate only one spin-polarized quasiparticles. Equilibrium magnetization leakage into the S layer as function of SF interface quality and a value of ferromagnetic interaction have also b…
We consider some properties of odd frequency triplet superconducting condensates. In order to describe fluctuations we construct a supermatrix sigma-model for the superconductor/ferromagnet or superconductor/normal-metal structures. We show that an odd frequency triplet superconductor, when in isolation or coupled to a normal metal, generally displays behaviour comparable to a superconductor with the usual singlet pairings. However, for spin dependent systems such as the superconductor/ferromagnet the two types of superconductor have quite different behaviour. We discuss this difference by con…
We report on the synthesis and extensive characterization of layered Bi4O4S3 superconductor. This is the optimally doped sample with Tc ~5.3 K out of a series of Bi6O4S4(SO4)_1-x samples synthesized by solid state reaction. The series was synthesized towards establishing a phase diagram of transition temperature as a function of carrier concentration. Crystal structure for Bi4O4S3 shows larger bending of Bi2-S2-Bi2 bond in the BiS2 layer compared to that for the parent phase. Scanning electron microscopy images show platelets like morphology for Bi4O4S3 signifying the layered structure. While …
