Unconventional superconductivity in double quantum dots

Abstract

The formation of electron pairs is a prerequisite of superconductivity. The fermionic nature of electrons yields four classes of superconducting correlations with definite symmetry in spin, space and time. Here, we suggest double quantum dots coupled to conventional s-wave superconductors in the presence of inhomogeneous magnetic fields as a model system exhibiting unconventional pairing. Due to their small number of degrees of freedom, tunable by gate voltages, quantum-dot systems are ideal to gain fundamental insight in unconventional pairing. We propose two detection schemes for unconventional superconductivity, based on either Josephson or Andreev spectroscopy.PACS numbers: 73.23. Hk,74.45.+c,74.20.Rp,72.25.Mk Introduction.-Conventional superconductivity is well understood in terms of Bardeen-Cooper-Schrieffer (BCS) theory by the formation of spin-singlet Cooper pairs of electrons [1]. In certain unconventional superconductors, spin-triplet pairs are involved [2]. A further generalization is the notion of pairing of electrons at different times. There are four different classes of superconducting correlations with definite symmetries in spin, space (momentum), and time (frequency) under exchange of two electrons forming a Cooper pair. Even-frequency spin-singlet (odd in spin) Cooper pairs appear in conventional s-wave but also in high-T c d−wave [3] superconductors (even in space) while p-and f -wave pairing (odd in space) supports even-frequency spin triplets (even in spin). There is experimental evidence for triplet p-wave pairing (similar to superfluid 3 He [4]) in Sr 2 RuO 4 [2]. Recent proposals to induce triplet correlations in nanowires with strong spin-orbit interaction in proximity to s-wave superconductors were motivated by the prospect of creating Majorana fermions at the ends of the wire [5,6]. By a similar mechanism, Majorana fermions can also be generated in double quantum dots [7,8]. The idea of odd-frequency pairing has first been brought up by Berezinskii [9] as a possible explanation of superfluid 3 He but has experienced a revival in the context of superconductor-ferromagnet heterostructures [10].For noncollinear magnetizations, e.g., due to domain walls [11][12][13][14][15][16][17], spin-active interfaces [18,19], multiple noncollinear magnetized ferromagnetic layers [17,20,21], helical magnets [22][23][24], or spin-orbit coupling [25], odd-frequency correlations with finite spin polarization can penetrate deeply into ferromagnets, as confirmed in several experiments [26][27][28][29][30][31][32].Odd-frequency triplet pairing also appears in diffusive normal metals contacted by an even-frequency triplet superconductor [33].Finally, odd-frequency singlet superconductivity has only been theoretically predicted [34] without experimental confirmation so far. Quantum dots coupled to conventional superconductors show an interesting interplay of proximity effect and Coulomb interaction [35,36]. They have also been suggested as a tool to detect unconventional pairing [37]. In this Letter, we pr...

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