Resonant charge and spin transport in a T -stub coupled to a superconductor

We study transport through a single channel T -stub geometry strongly coupled to a superconducting reservoir. In contrast to the standard stub geometry which has both transmission resonances and anti-resonances in the coherent limit, we find that due to the proximity effect, this geometry shows neither a T = 1 resonance (T is the transmission probability for electrons incident on the T -stub) nor a T = 0 anti-resonance as we vary the energy of the incident electron. Instead, we find that there is only one resonant value at T = 1/4, where charge transport vanishes while the spin transport is perfect. Introduction. – One of the many intriguing issues in the subject of spintronics [1] concerns production and detection of pure spin current. A simple minded but popular proposal for production of pure spin current (SC) involves electrons flowing with equal flux in opposite directions with opposite spin polarizations. This situation results in the exact cancellation of the charge current while the spin current adds up. Alternatively one can also produce pure SC by having a unidirectional flow of electrons and holes together with equal flux and spin polarization. In this case also, the charge current cancels out leaving behind a pure spin current. In this paper we will work along the lines of the second proposal for production of pure SC . Situations involving current carried by an admixture of electrons and holes are naturally realized in systems involving superconductor-normal junctions [2–9] due to the interplay of Andreev reflection and normal reflection at the interface between the superconductor and the normal metal. A recent proposal by the present authors which exploited this fact for production of pure SC involved transport of electrons and holes across a normalsuperconducting-normal (NSN) junction [10]. The normal metals in the NSN junction were considered to be onedimensional interacting electron gases which were modelled as Luttinger liquid wires, and a situation corresponding to pure spin current was shown to be an unstable fixed point of the theory. In contrast to our previous study, here we work with free electrons and pure spin current is produced due to resonant conversion of incident electrons into transmitted electrons or holes with equal amplitude across a T -stub geometry which is strongly coupled to a superconducting reservoir. Inclusion of electron-electron interaction can lead to very interesting physics [11] in the presence of resonances but this is beyond the scope of the present work. Theoretically, although our model appears simple, it is one of the first models to realize resonant transmission of electrons through a complex barrier (in this case a stub, which hosts both electron and hole waves due to its coupling to superconductor at one end) with an amplitude which is not unimodular. To develop an understanding of the new resonance, we explore the analytic structure of the electron transmission amplitude in the complex energy plane. We show that the analytic structure of the transmission function is quite different from the cases of standard double barrier resonances or the resonance-anti resonance pairs of the normal stub geometry [12, 13]. In this article, we consider a single mode T -stub which is coupled to a superconducting reservoir at one end, and to a single mode wire at the other end, which is then connected to the left and right reservoirs (see Fig.1). We assume that the current injected from the left reservoir into the wire is completely spin polarized. Additionally we assume that the bias which drives current between the