Resonant tunneling-based spin ratchets

We outline a generic ratchet mechanism for creating directed spin-polarized currents in ac-driven double well or double dot structures by employing resonant spin transfer through the system engineered by local external magnetic fields. We show its applicability to semiconductor nanostructures by considering coherent transport through two coupled lateral quantum dots, where the energy levels of the two dots exhibit opposite Zeeman spin splitting. We perform numerical quantum mechanical calculations for the I-V characteristics of this system in the nonlinear regime, which requires a self-consistent treatment of the charge redistribution due to the applied finite bias. We show that this setting enables nonzero averaged net spin currents in the absence of net charge transport. Introduction. – The field of semiconductor spintronics has seen rapid progress lately, yet there are still many obstacles on the way from fundamental research to operating spin-based devices [1]. The creation of spin polarized currents is one basic requirement for the realization of semiconductor spintronics systems that share the prospect of being able to outperform conventional electronics. Due to a better controlability and faster processing times it is favorable to generate those currents by electrical means, e.g. by the variation of (contact) voltages. Promising classes of devices include spin pumps [2–5], spin rectification [6] and spin ratchets [7–12]. These proposals share the common idea to generate directed spin currents, e.g. mediated by spin-orbit interaction, upon time variation of external potentials. Here we focus on spin ratchets, a generalization of the particle quantum ratchet mechanism [13–15]. In such systems with broken spatial symmetry, pure spin currents are generated by means of an ac-driving with no net average bias. This idea has been put forward for both, nonlinearly driven coherent conductors [7–9], as well as conductors in the dissipative regime, where Brownian particle motion is converted into directed spin currents [10–12]. While a net spin current could be shown to exist for the different settings, its magnitude is difficult to predict and an optimization towards larger spin currents is often not evident. Here we propose another, generic, spin ratchet mecha(a)[email protected] nism that is based on coherent resonant charge and spin transfer. It thereby leads to larger and controllable output and can be implemented in a variety of systems. Moreover, since the ratchet spin currents require operation under nonequilibrium conditions and since the spin currents can usually be enhanced for strong ac-bias, we employ a fully self-consistent treatment of the electrostatics for our quantum transport calculations in the nonequilibrium regime. This involves a self-consistent determination of the voltage drop across the ratchet, which has been approximated so far only by simple heuristic models [7–9]. After outlining the general working principle we focus on a setup invoking resonant tunneling through two quantum dots (QD) in a two-dimensional electron gas (2DEG). In the literature double QD systems have already been proposed as spin filters [16, 17] or sources for pure spin currents [18]. However, these proposals are based on QDs in the Coulomb blockade regime, whereas the double QDs considered here are strong coupled to the leads, i.e. transport is fully coherent and the conductance is larger. Mechanism. – To illustrate the envisioned spin ratchet mechanism, let us first consider the simplified onedimensional potential model shown in Fig. 1a). Three electrostatic barriers divide the system into four regions (R1-R4). While the regions R1 and R4 support states with a continuous energy spectrum, the regions R2 and R3, representing the double QD structure, accommodate discrete resonant states due to the confinement imposed