Spintronics with NSN Junction of one-dimensional quantum wires : A study of Pure Spin Current and Magnetoresistance

We demonstrate possible scenarios for production of pure spin current and large tunnelling magnetoresistance ratios from elastic co-tunnelling and crossed Andreev reflection across a superconducting junction comprising of normal metal-superconductor-normal metal, where, the normal metal is a one-dimensional interacting quantum wire. We show that there are fixed points in the theory which correspond to the case of pure spin current. We analyze the influence of electron-electron interaction and see how it stabilizes or de-stabilizes the production of pure spin current. These fixed points can be of direct experimental relevance for spintronics application of normal metal-superconductor-normal metal junctions of one-dimensional quantum wires. We also calculate the power law temperature dependence of the crossed Andreev reflection enhanced tunnelling magnetoresistance ratio for the normal metal-superconductor-normal metal junction. Introduction. – Two fundamental degrees of freedom associated with an electron that are of direct interest to condensed matter physics are its charge and spin. Until very recently, all conventional electron-based devices have been solely based upon the utilization and manipulation of the charge degree of freedom of an electron. However, the realization of the fact that devices based on the spin degree of freedom can be almost dissipation-less and with very fast switching times, has led to an upsurge in research activity in this direction in recent years [1–3]. The first step towards realization of spin-based electronics (spintronics) would be to produce pure spin current (SC). From a purely theoretical point of view, it is straight forward to define a charge current as a product of local charge density with the charge velocity, but such a definition cannot be straight forwardly extended to the case of SC. This is because both spin ~ S and velocity ~v are vector quantities and hence the product of two such vectors will be a tensor. In this letter, we adopt the simple minded definition of SC, which is commonly used [4]. It is just the product of the local spin polarization density associated with the electron or hole, (a scalar s which is either positive for up-spin or negative for down-spin) and its velocity [4]. The most obvious scenario in which one can generate a pure SC in the sense defined above would be to have (a) an equal and opposite flow of identically spin-polarized electrons through a channel, such that the net charge current through the channel is nullified leaving behind a pure SC, or (b) alternatively, an equal flow of identically spin polarized electrons and holes in the same direction through a channel giving rise to pure SC with perfect cancellation of charge current. In this letter, we explore the second possibility for generating pure SC using a normal metal−superconductor−normal metal (NSN) junction. Proposed device and its theoretical modelling. – The configuration we have in mind for the production of pure SC is shown in Fig. 1. The idea is to induce a pair potential in a small region of a quantum wire (QW) by depositing a superconducting strip on top of the wire (which may be, for instance, a carbon nanotube) due to proximity effects. If the strip width on the wire is of the order of the phase coherence length of the superconductor, then both direct electron to electron co-tunnelling as well as crossed Andreev electron to hole tunnelling can occur across the superconducting region [5]. It is worth pointing out that in the case of a singlet superconductor, which is the case we consider, both the tunnelling processes will conserve spin. In order to describe the mode of operation of the device (see Fig. 1), we first assume that the S-matrix rep-