Dynamic nuclear polarisation in biased quantum wires with spin- orbit interaction

We propose a new method for dynamic nuclear polarisation in a quasi one-dimensional quantum wire utilising the spin-orbit interaction, the hyperfine interaction, and a finite sourcedrain potential difference. In contrast with current methods, our scheme does not rely on external magnetic or optical sources which makes independent control of closely placed devices much more feasible. Using this method, a significant polarisation of a few per cent is possible in currently available InAs wires which may be detected by conductance measurements. This may prove useful for nuclear magnetic resonance studies in nanoscale systems as well as in spin-based devices where external magnetic and optical sources will not be suitable. The ability to locally manipulate spin has been the subject of intense research recently. In particular, local control of nuclear polarisation in the vicinity of quantum dots and in wires has diverse uses such as in nuclear magnetic resonance (NMR) studies [1] or for control of nuclear spins in devices where external magnetic fields and/or optical sources will not be suitable or convenient as for instance in non-magnetic spin-filtering [2] and qubits [3]. In some very beautiful recent experiments related to spin-based qubits, dynamically-generated nuclear polarisation has been used to control the decoherence of electron spins in quantum dots [4, 5]. Nuclear polarisation can also be used to manipulate the electron spin-splitting in quantum wires [6] without using a magnetic field. Local control of nuclear polarisation in quantum wells using a gate contact has now been demonstrated [7]; however, the polarisation itself involved the use of an optical source. In this Letter, we propose a new method for dynamically generating and controlling nuclear polarisation, locally and without using magnetic and optical sources, in a nonequilibrium quasi one-dimensional quantum wire with spin-orbit interaction. By local we mean the nuclear polarisation is within the wire and not in the bulk surroundings. We argue that the role of spin-orbit interaction in creating a spin-polarised electron distribution cannot in this scheme be replaced with an external magnetic field. We estimate the magnitude and build-up time for the polarisation as around 2.5% and 200s respectively in typical InAs quantum wires which compares favourably with other methods. We discuss possible ways in which the nuclear polarisation may be detected and measured, as for instance through a measurement of the two-terminal conductance [6, 8]. The Overhauser effect [9] is used for dynamically polarising nuclei through their hyperfine coupling with electrons using a magnetic field and an external radio source tuned to the electron Zeeman splitting. The electron spin resonance (ESR) inducing radio source tends to equalise (saturate) the numbers of spin up and down electrons even though they have different Zeeman energies — this implies that the chemical potentials of the two spin species must be different and the spin distribution is not in equilibrium. The electron spins at the higher chemical potential ultimately relax with a spin flip to equalise the chemical potentials; and some of these spins can be exchanged with the nuclei. In this manner, a nonzero nuclear polarisation is built up. The key requirement for the Overhauser scheme is the creation of a nonequilibrium electron spin distribution. This usually involves pumping and satura-