Coherence control of electron spin currents in semiconductors

Transcription

1 phys. stat. sol. (b) 243, No. 10, (2006) / DOI /pssb Coherence control of electron spin currents in semiconductors Henry M. van Driel *, 1, John E. Sipe 1, and Arthur L. Smirl 2 1 Department of Physics and Institute for Optical Sciences, University of Toronto, Toronto M5S-1A7, Canada 2 Laboratory for Quantum Electronics, University of Iowa, Iowa City, USA Received 11 March 2006, revised 27 March 2006, accepted 27 March 2006 Published online 12 July 2006 PACS k, Ht, Dc, p, d We provide an overview of some of our recent work on the use of one color and two color optical techniques to generate and control electronic spin currents in semiconductors for which a spin orbit interaction exists. The generation process relies on the quantum interference between different absorption pathways, such as that between single and two photon absorption or those involving different polarization states of a monochromatic beam. For different crystal orientations and/or beam polarizations it is possible to generate a spin current with or without an electric current, and an electrical current with or without a spin current. In our experiments, which are conducted either at 80 K or 295 K, we typically employ nominally 100 fs pulses centered near 1500 and 750 nm. The currents generated are quasi-ballistic and the carriers typically move distances of ~1 10 nm, determined by the momentum relaxation time, which is of the order of 100 fs. The transient characteristics of spin-polarized electrical currents generated in strained GaAs at room temperature by ~100 fs pulses is detected by the emitted THz radiation. Pure spin currents can be detected by taking advantage of the accumulation of up and down spins on opposite sides of tightly focused pump beams. The spin states are detected through differential transmission measurements of tightly focused right and left circularly polarized, near-band-edge probe pulses, delayed by several picoseconds from the pump pulses to allow carrier thermalization to occur. By spatial scanning across the differential spin profiles and determining the amplitude of the response we are able to translate this into nm spatial resolution of spin displacement. Finally, the ability to generate ballistic currents using purely optical techniques allows us to generate transverse Hall-like currents, with transverse charge currents generated from pure spin currents and transverse spin currents generated from pure charge currents. 1 Introduction The absorption of light in a direct gap semiconductors via valence conduction band transitions leads to the formation of electron hole plasmas, the study of which, especially on an ultra short time scale, has led to much of the insight we have into the properties of non-equilibrium carriers in semiconductors [1]. However, the absorption of linearly polarized light leads to equal populations of spin up and spin down electrons and holes, but no net spin or electrical currents in the semiconductors. For many semiconductors, the existence of a spin orbit interaction leads to a splitting of the top six valence band states in a semiconductor into heavy, light and spin orbit split off valence bands. For absorption of circularly polarized light with the photon energy less than that separating the conduction and spin orbit split off bands, it is possible to generate a spin-polarized electron plasma [2]; the holes relax their spin in a time scale in <100 fs and will be ignored in this and subsequent discussions [3]. In zinc-blende semiconduc- * Corresponding author: vandriel@physics.utoronto.ca, Phone: , Fax:

2 Original Paper phys. stat. sol. (b) 243, No. 10 (2006) 2279 tors such as GaAs, a 50% net electron spin population is possible. The spin population can only be controlled by the optical intensity, but it is generally thought not possible to generate a spin current. However, because of the importance of spin in future applications, a technology which has come to be called spintronics [4], it is desirable to investigate ways in which one can generate spin currents and detect them in simple, non-magnetic semiconductors such as GaAs or Si. Beginning about 13 years ago [5, 6] using two-color techniques, together with other colleagues we showed how it is possible to use quantum interference between single and two photon absorption pathways to generate electrical current in a semiconductor. This was stimulated by earlier suggestions of Manykin and Afanas ev [7] and by Brumer and Shapiro [8] who theoretically discussed how one could use the coherence properties of optical beams to control atomic and molecular processes. Indeed, Dan Elliott s group demonstrated directional ionization of an atom, [9] and Paul Corkum and co-workers [10] later demonstrated directional ionization from a GaAs/AlGaAs quantum well at 80 K using 10.6 and 5.3 µm light. Later, we also showed how it is possible to coherently control carrier populations [11] and spin populations [12]. Various optical based schemes to generate electrical currents have also been discussed in the context of various photovoltaic or photogalvanic effects [13, 14] and their symmetry properties analyzed but their relationship to coherence control or quantum interference has often not been understood or emphasized. In this conference report we review the salient features of our recent work on the use of coherence control techniques to generate and control spin currents in GaAs and we describe one and two color schemes we have used to do so. Due to limited space no attempt will be made to be complete in reference to our own work, or indeed, to the many fine contributions of others. We first describe (for historical reasons) the two-color scheme. This is followed by a discussion of our more recent work on single beam schemes to generate spin-polarized electrical currents or pure spin currents. The role of beam polarization and sample geometry is emphasized. Finally we discuss the possibility of generating pure spin currents using Raman techniques as well as the use of pure ballistic spin currents to generate Hall-like transverse electrical currents, and, vice-versa, the use of ballistic spin-currents to generate purely transverse electrical currents. 2 Two-color schemes The basic idea behind two-color quantum interference control (QUIC) for an electrical or spin current in a semiconductor [15] is shown in Fig. 1 where we have schematically illustrated conduction band and valence band states in k-space. Consider that we have two phase related beams with photon energy ħ ω Conduction Band 2ω ω Valence Band Fig. 1 (online colour at: Illustration of the two-color absorption pathways leading to coherent electrical current control.

3 2280 H. M. van Driel et al.: Coherence control of electron spin currents and 2ħ ω and phase φ ω and φ 2ω with ħω < Eg < 2ħω. Quantum mechanics tells us that to calculate the current density produced by the simultaneous presence of both beams, we must add the transition amplitudes, a ω ( k ) and a 2 ω ( k ), take the modulus squared, multiply by the group velocity and sum over all the coupled states, i.e. dj 2ω ω 2 = Â evk a ( k) + a ( k ). (1) dt k For the two-photon transition amplitude, which is governed by 2 nd order perturbation theory and in principle involves an infinite number of intermediate states, it turns out that the dominant intermediate state,2,2 is the same as the final state. If we take the perturbation Hamiltonian to be of the form H ω ω µ E ω ω p, where E and p are the electric field and momentum operator, the matrix element associated with the second stage of the transition is a ω µ c p còµ k. Because the two-photon transition amplitude depends not only on the magnitude but also on the sign of k, interference between the single and two photon transition amplitudes will be destructive for one sign of k if it is positive for the other sign. The other point to make is that the group velocity v k has the same parity properties. Hence the only terms that survive in the summation over k-space are the interference terms. Because of the manner by which constructive and destructive interference occurs one finds that there is a preferential population of carriers at k vs. k and an electrical current occurs. One finds that the current generation rate then takes the form i ijkl j k l J I = iηi E * 2ωEωEω + c.c. µ sin ( φ), (2) where φ = φ2ω - 2φω and η ijkl is a fourth rank tensor which, because of its rank, allows the effect to occur in centro-symmetric and non-centrosymmetric materials. The nature of the current generation process reflects the symmetry properties of the crystal and the polarization states of the optical beams and the crystal orientation that is employed. One can similarly develop an expression for the spin current generation rate, which will reflect particular polarization properties of the beam and the crystal orientation [15]. The governing tensor is a fifth rank tensor, with the additional rank related to the specification of a spin orientation. With orthogonal, linearly polarized beams it is possible to generate a pure spin current (along the direction of the polarization of the fundamental field, or into the sample) without generating a spin polarization; the magnitude and direction is controlled by the phase parameter φ. For co-circularly polarized pump beams it is possible to generate a spin population but it is also possible to generate a spin-polarized electrical current in the polarization plane with vector direction controlled by the phase parameter φ. As with the spin generation process by a single beam the spin current generation process is based on the spin orbit interaction, which determines the particular spin properties of the heavy and light hole bands. We have observed purely electrical currents in GaAs and GaAs/AlGaAs quantum wells using parallel, co-polarized, 1550 and 775 nm, 150 fs beams. The currents were detected by charging electrodes on the surface [6] or through observation of the THz generation [16] from the time dependent, transient currents. Pure spin currents have also been generated by using tightly focused two color pump beams and observed using spatially resolved transmission [17] or luminescence [18] of circularly polarized light in GaAs multi-quantum wells or ZnSe respectively. As shown in Figs. 2 and 3 in both cases, the spatial profiles of spin-up and spin-down electrons are separated by an amount d, after momentum relaxation stops the current flow. Since the spin relaxation time is typically much longer (>10 ps) than the momentum or current relaxation time (<100 fs) one can simply probe the displaced spin distributions using transmission or luminescence properties of circularly polarized light. Because the displacements are small (~10 nm) for carriers typically injected with speeds of 250 kms 1, the difference in the two Gaussian profiles is directly related to the derivative of one of the spin spatial profiles. From measurements of the differential transmission of the spatial profiles using circularly polarized pump beams in the case of the GaAs experiments, and using ~1 µm thin samples, one can determine the spin separation of the spins to within nm using optical beams! In the case of the GaAs experiments the pump beams were 1420 nm and 710 nm. The carrier densities generated by both beams are of the order of cm 3. Because we

4 Original Paper phys. stat. sol. (b) 243, No. 10 (2006) 2281 d [010] x z [100]- [001] n n y y n n Fig. 2 (online colour at: Displacement of Gaussian distributions of up and down spins and the spin difference profile. Fig. 3 (online colour at: Spin displacements following spin current generation by two-color pump beams in GaAs. have no direct way of monitoring spin currents, as we do for the charge currents through the THz radiation they emit, in order to observe them we have generated spin current gratings and observed their evolution [19]. The spin current gratings can be formed by allowing the two orthogonally polarized pump beams at 1550 nm and 775 nm to interact non-collinearly in a 1 µm thick GaAs sample. The phase parameter φ is automatically varied in the line determined by the plane of incidence and the plane of the sample. The current grating establishes a population grating whose amplitude can be monitored using appropriately polarized probe beams. From such measurements we have determined that the spin population is restored to spatial equilibrium on a time scale determined by the electron diffusion time. 3 One-color schemes While the generation of pure spin currents using two color pump beams is interesting, because of the need to use two different beams if not the need to have a high intensity for one of them, we have sought ways to utilize only one beam. Indeed, this can be done if one lowers the symmetry from T d, the symmetry for GaAs. In certain classes of materials it is possible to inject a spin-polarized electrical current via interference in absorption pathways for orthogonal components of elliptically polarized light. The injection current takes the form i ijk j k J = γ E E sin ( φ - φ ), (3) ω ω j k where φ j(k) are the phases associated with the orthogonal polarized components. From nature of the interaction process it is necessary that the tensor be antisymmetric with respect to exchange of the last two indices. This property only occurs for certain crystal classes and unfortunately, normal crystalline GaAs is not one of them. However, Wurtzite structure CdSe is, and we initially demonstrated the current generation properties of this material [20]. Because the total current generation (integrated over the illumination area) is directly proportional to the beam power one can use a low power, continuous beam to generate this effect and indeed we did so using a simple He Ne laser operating at 632 nm and by charging electrodes on the material. Because of the phase dependence one obtains the largest signals for right and left circularly polarized light. While we did not directly verify the spin characteristics of the electrical current, it must indeed be spin polarized because circularly polarized light is used to generate the electron hole pairs.

5 2282 H. M. van Driel et al.: Coherence control of electron spin currents Fig. 4 THz signature of spin polarized electrical current in InGaAs/GaAs strained material. Fig. 5 Differential transmission measurements (+, right circularly polarized;, left circularly polarized) of pure spin currents for [001]-polarized (solid circles) and [ 110] -polarized light (solid triangles) incident on a (110) GaAs QW. The empty squares denote the profile of either up or down spin species. In order to generate a similar spin-polarized current in GaAs it is necessary to lower its symmetry. This we have done by straining GaAs using GaAs/InGaAs quantum wells with the InGaAs quantum wells only serving to strain the GaAs through lattice mismatch. We have observed [21] transient currents in the strained GaAs by monitoring the emitted THz radiation following illumination by 60 fs, 810 nm optical pulses. The basic features are shown in Fig. 4 where it is clearly observed that the THz signal changes sign when the incident light polarization changes from right to left circularly polarized. We find that the peak current generated is ~10 ka cm 2 for a peak light intensity of 250 MW cm 2. Recently we have discovered that one can generate a pure spin current using a single beam if one takes unstrained GaAs and illuminates certain crystal orientations [22]. The pure spin current occurs for linearly polarized light incident on certain crystal faces of GaAs (such as (110)) and it reflects the nature of the influence of the spin orbit interaction on the band structure. Indeed such a spin current has likely been generated by many researchers in the past without their knowledge. The pure spin current generation can be understood as the result of quantum interference between absorption pathways for right and left circularly polarized components of the linearly polarized light. When the polarization of the linearly + - polarized light is rotated by 90, the light polarization can be thought of as changing from σ + σ to + - σ - σ and the spin current direction changes sign. This is illustrated in Fig. 5 which indicates the results of experiments [23] undertaken with tightly focused 70 fs, 750 nm pulses with the spin accumulation determined using differential transmission techniques similar to that discussed above. 4 Spin Hall currents The Hall effect has been one of the cornerstones of condensed matter physics since it was first discovered over 120 years ago. Recently, within the family of various types of Hall effects it has been suggested that spin polarized electrical currents will experience a skew type of deflection leading to a transverse pure spin current and spin current of opposite types on either side of the electrical current in the absence of any applied magnetic field [26]. This has been demonstrated by Awschalom and co-workers [27], and Wunderlich et al. [28]. However our sources of ballistic pure electrical and spin currents give us the opportunity to generate and control ballistic, as opposed to thermalized, Hall type currents without the need to apply electrical or magnetic fields. By measuring spin and charge accumulation on sides of a tightly focused beam profile we have recently demonstrated [29] the observation of such effects.

6 Original Paper phys. stat. sol. (b) 243, No. 10 (2006) Conclusions and outlook We have illustrated here some of the wide variety of processes that might be used to generate pure electrical currents, pure spin currents and spin-polarized electrical currents. The currents have been typically generated at room temperature but they would be, and in some cases have been, enhanced at low temperatures. There are many aspects of these current generation processes which we could not cover here, but the reader is referred to the set of references at the end of this article. There are also other schemes which we have not discussed here such as the use of inter-subband infrared absorption in quantum wells [30] and the use of stimulated Raman processes [30] involving inter-conduction band processes employing spin split conduction band states in a doped semiconductor or. Typically the splitting is measured in mev. This process would have the advantage of allowing spin current to be generated throughout a bulk material (if the incident beams are both below the semiconductor band-gap) and would not consume large amounts of energy from the optical beams. Acknowledgements The research overviewed here is based on the hard work and insight provided by many of our graduate students and postdoctoral fellows, including Ravi Bhat, Norman Laman, Petr Nemec, Mark Bieler, Hui Zhao, Marty Stevens, Eric Loren, Ali Najmaie, and Yaser Kerachian. Research support from the Natural Sciences and Engineering Research Council of Canada, Photonics Research Ontario, the Office of Naval Research and DARPA are gratefully acknowledged. References [1] J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, 2 nd ed. (Springer Verlag, New York, 1999). [2] R. R. Parsons, Phys. Rev. Lett. 23, 1152 (1969). M. I. D yakonov and V. I. Perel, JETP Lett. 13, 467 (1971); Phys. Lett. A 35, 459 (1971). [3] D. J. Hilton and C. L. Tang, Phys. Rev. Lett. 89, (2002). [4] D. D. Awschalom, D. Loss, and N. Samarath, Semiconductor Spintronics and Quantum Computation (Springer Verlag, New York, 2002). [5] A. Khan, H. M. van Driel, and X.-Q. Zhou, 1993 Canadian Association of Physics Congress, Phys. in Can., paper HB6 (1993). [6] R. Atanasov, A. Haché, J. L. P. Hughes, H. M. van Driel, and J. E. Sipe, Phys. Rev. Lett. 76, 1703 (1996). A. Haché, Y. Kostoulas, R. Atanasov, J. L. Hughes, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 78, 306 (1997). [7] E. A. Manykin and A. M. Afanas ev, Sov. Phys. JETP 25, (1967); Zh. Eksp. Teor. Fiz. 52, (1967). [8] P. Brumer and M. Shapiro, Accts. Chem. Res. 22, 407 (1989). P. Brumer and M. Shapiro, Sci. Amer. 272(3), 34 (1995). [9] Y.-Y. Yin, C. Chen, D. S. Elliott, and A. V. Smith, Phys. Rev. Lett. 69, 2353 (1992). [10] E. Dupont, P. B. Corkum, H. C. Liu, M. Buchanan, and Z. R. Wasilewski, Phys. Rev. Lett. 74, 3596 (1995). [11] J. M. Fraser, A. I. Shkrebtii, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 83, 4192 (1999). [12] X. Y. Pan, M. J. Stevens, R. D. R. Bhat, H. M. van Driel, J. E. Sipe, and A. L. Smirl, J. Appl. Phys. 97, (2005). [13] B. I. Sturman and V. M. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials (Gordon and Breach, Philadelphia, 1992). [14] S. D. Ganichev, E. L. Ivchenko, V. V. Bel kov, S. A. Tarasenko, M. Sollinger, D. Weiss, W. Wegscheider, and W. Prettl, Nature 417, 153 (2002). [15] R. D. R. Bhat and J. E. Sipe, Phys. Rev. Lett. 85, 5432 (2000). [16] D. Côté, J. M. Fraser, M. DeCamp, P. H. Bucksbaum, and H. M. van Driel, Appl. Phys. Lett. 75, 3959 (1999). [17] M. J. Stevens, A. L. Smirl, R. Bhat, A. Nahmaie, J. Sipe, and H. M. van Driel, Phys. Rev. Lett. 90, (2003). [18] J. Hübner, W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, Phys. Rev. Lett. 90, (2003). [19] Y. Kerachian, P. Nemec, H. M. van Driel, and A. L. Smirl, J. Appl. Phys. 96, 430 (2004).

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