Proposal for a phase-coherent thermoelectric transistor

Abstract

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 ∼ 45 and Seebeck coefficients as large as a few mV/K at sub-Kelvin temperatures. The device is also phasetunable meaning its thermoelectric response for power generation can be precisely controlled with a small magnetic field. Our concept is based on a superconductor-normal metal-superconductor interferometer in which the normal metal weak-link is tunnel coupled to a ferromagnetic insulator and a Zeeman split superconductor . Upon application of an external magnetic flux, the interferometer enables phase-coherent manipulation of thermoelectric properties whilst offering efficiencies which approach the Carnot limit.It is known that electron-hole symmetry breaking is essential for a material to posses a finite thermoelectric figure of merit 1,2 . In principle, conventional superconductors have a near perfect symmetric spectrum and therefore are not suitable for thermoelectric devices. However, if the density of states is spin-split by a Zeeman field a superconductor-ferromagnet hybrid device can provide a thermoelectric effect 3-5 with a figure of merit close to 1. Here we propose a multifunctional phase-coherent superconducting transistor in which the thermoelectric efficiency is tunable through an externally applied magnetic flux. A giant Seebeck coefficient of several mV/K and a figure of merit close to ∼ 45 is predicted for realistic materials parameters and materials combinations.The phase-coherent thermoelectric transistor is based on two building blocks. The first one is sketched in Fig. 1(a) and consists of a superconducting film (S R ) tunnel-coupled to a normal metal (N) by a ferromagnetic insulator (FI). The latter induces an exchange field (h) in S R which leads to a Zeeman spin-split superconducting DoS. The spectrum for spin-up (↑) and spin-down (↓) electrons is given bywhere| is the conventional Bardeen-Cooper-Schrieffer DoS in a superconductor, E is the energy, ∆ R is the order parameter, and Γ accounts for broadening. Due to the presence of the spin-splitting field, ∆ R depends on temperature (T ) and h. While the total DoS of S R , ν S R (E) = ν S R↑ (E) + ν S R↓ (E), is electron-hole symmetric [ Fig. 1(b)], the spin-dependent a) Electronic mail: giazotto@sns.it b) Electronic mail: jjr33@cam.ac.uk c) Electronic mail: sebastian bergeret@ehu.es ν S R↑(↓) (E) components are no longer even functions of the energy. This means that electron-hole imbalance can, in principle, be achieved using a spin-filter contact with a normal metal. This would yield a finite thermoelectric effect 3,4 in the N/FI/S R heterostructure shown in F...

Spin manipulation with magnetic semiconductor barriers

“…The dual functionalities of the magnetic semiconductors are cleverly explored in a superconductor-magnetic semiconductor-normal metal system: 91 interfacial exchange fields to remove the electron-hole symmetry on individual spin channels, while spin filter tunneling to select the desired spin channel only. This configuration offers thermoelectric efficiency much larger than conventional materials and approaching the Carnot limit.…”

Cross thermoelectric coupling in normal-superconductor quantum dots

“…Superconductivity can significantly alter these thermoelectric properties [14] and provide additional information, as demonstrated with Andreev interferometers [15,16]. Importantly, in hybrid nanostructures large values of S have been envisaged by breaking the particle-hole symmetry [17][18][19]. Here, we focus on N-QD-S setups that indeed preserve such symmetry and thereby avoid the generation of electrical currents by thermal gradients alone.…”

Andreev spectrum of a Josephson junction with spin-split superconductors

“…There has been a resurgence of interest in SS because of several theoretical studies proposing them as absolute spin-valves [6], heat-valves [7] and thermoelectric elements [8][9][10]. Moreover, superconducting heterostructures with spin-splitting fields have attracted the interest from theorists and experimentalists in the last years, mainly motivated by the possible detection of Majorana fermions [11][12][13][14] and elaboration of complex S-FI heterostructures [15][16][17], where S denotes a BCS superconducting lead.…”