All-optical injection and control of spin and electrical currents in quantum wells Ali Najmaie, R. D. R. Bhat, and J. E. Sipe Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7 Received 16 April 2003; published 30 October 2003 We show that quantum interference between one- and two-photon absorption can be used to inject spin currents, with or without an accompanying electrical current, in unbiased semiconductor quantum well struc- tures. The directions in which the electrical and spin currents are injected can be coherently controlled, with a relative phase parameter of the optical fields as the control parameter. We characterize the currents for an unstrained quantum well and a quantum well under biaxial compressive strain using the Luttinger-Kohn model; we work out particular examples. If compressive strain is used to appropriately rearrange the subbands, then a degree of spin polarization of the spin currents higher than possible in bulk GaAs can be achieved and maintained even for photon energies well above the band gap. DOI: 10.1103/PhysRevB.68.165348 PACS numbers: 78.20.Ls, 42.65.-k, 72.25.Fe, 73.63.Hs I. INTRODUCTION The control and manipulation of the spin degree of free- dom of electrons in semiconductor structures has received much attention in recent years and may be an important com- ponent of the future data storage and processing protocols. Since the 1970s it has been known that, due to spin-orbit interactions, spin-polarized carriers can be generated in semi- conductors through optical excitation with circularly polar- ized optical fields. 1 Using a bias voltage, this spin population can be dragged to produce a spin-polarized current; 2,3 such spin currents always have a net electrical current accompa- nying them. The degeneracy of the heavy- and light-hole bands at the  point in bulk semiconductors, such as GaAs, implies that any excitation across the band gap occurs from both the heavy- and light-hole bands; this leads to a reduc- tion in the degree of spin polarization of the injected carriers. This degeneracy is lifted in a quantum well semiconductor structure due to confinement and, further, via strain, thus leading to a higher degree of spin polarization of the injected carriers. 4 Recently it has been shown 5–7 that quantum mechanical interference between one- and two-photon excitation in bulk semiconductors can be used to induce spin currents in semi- conductors without the need of a bias voltage or magnetic field. In some configurations pure spin currents can be gen- erated, where no net electrical current is involved. Further- more, the direction of injection of the electrical and spin currents can be controlled using a relative phase parameter of the optical fields. The experimental verification of injection and control of the pure spin current has been performed by injecting carriers in the plane of a quantum well structure. 6 In this paper we present a detailed account of coherent injection of electrical and spin currents in the plane of a GaAs quantum well and its control through quantum me- chanical interference using a relative phase parameter of the beams responsible for one- and two-photon excitations. We further study the effects of biaxial compressive strain on the injected currents. Our goal here is to study the effects of these physical parameters on the injected currents in a gen- eral way. In a future publication we will apply this frame- work to address particular experimental results 6 in detail. We begin in Sec. II with the model used to describe the electronic states of a strained quantum well. In Sec. III, we use Fermi’s golden rule to describe and formulate suscepti- bilities describing the one, two, and interference components of the optical excitations; we also introduce quantities that are used to represent the degree of spin polarization of the spin currents and the velocity of the injected carriers. In Sec. IV we present the results for different polarization configu- rations, with the optical fields propagating along the growth axis. In Sec. V we summarize our results and conclude. II. QUANTUM WELL STATES We consider an isolated GaAs quantum well grown in the  001 direction, which we take as the quantization axis z, and set the boundaries of the quantum well at L /2. We use two Hamiltonians for the energy dispersion and eigenstates of the subbands, one for the valence subbands and another for the conduction subbands; these we now describe. All the calcu- lations neglect interactions between carriers, except to the extent they are described in the effective single-electron model of the bands. In the present work, we consider a quan- tum well subjected to photons with energies below that needed to couple the bound states to the continuum states associated with electrons or holes moving out of the well; the coherent control of spin currents due to this coupling is sub- ject of a future report. Indeed, we consider here excitation energies up to only about 100 meV above the band gap of the quantum well; for these energies there are no contributions from the barrier material and we approximate the barriers as infinite. A. Valence subbands We begin with the 4 4 Luttinger-Kohn Hamiltonian 8,9,11 to describe the valence subbands. The split-off subbands, ly- ing about 350 meV below the top of the valence subband, are neglected since we consider photons with 2   350 meV. 12 In the presence of (001) biaxial strain, 10 the Luttinger-Kohn Hamiltonian is modified by the appearance of Bir-Pikus strain terms 9 and takes the form PHYSICAL REVIEW B 68, 165348 2003 0163-1829/2003/6816/16534815/$20.00 ©2003 The American Physical Society 68 165348-1