Abstract

The two-color optical coherence absorption spectrum (QUIC-AB) of semiconductors in the presence of a charge current is investigated. We find that the QUIC-AB depends strongly not only on the amplitude of the electron current but also on the direction of the electron current. Thus, the amplitude and the angular distribution of current in semiconductors can be detected directly in real time with the QUIC-AB.

© 2012 OSA

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  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [CrossRef] [PubMed]
  2. Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
    [CrossRef] [PubMed]
  3. T. Hyart, N. V. Alexeeva, J. Mattas, and K. N. Alekseev, “Terahertz bloch oscillator with a modulated bias,” Phys. Rev. Lett. 102, 140405 (2009).
    [CrossRef] [PubMed]
  4. J. Rammer, “Quantum transport theory of electrons in solids: a single-particle approach,” Rev. Mod. Phys. 63, 781–817 (1991), and references therein.
    [CrossRef]
  5. M. I. Dyakonov and V. I. Perel, “Current-induced spin orientation of electrons in semiconductors,” Phys. Lett. A 35, 459–460 (1971).
    [CrossRef]
  6. J. E. Hirsch, “Spin Hall effect,” Phys. Rev. Lett. 83, 1834–1837 (1999).
    [CrossRef]
  7. S. Zhang, “Spin Hall effect in the presence of spin diffusion,” Phys. Rev. Lett. 85, 393–396 (2000).
    [CrossRef] [PubMed]
  8. W. Yang, K. Chang, and S. C. Zhang, “Intrinsic spin Hall effect induced by quantum phase transition in HgCdTe quantumwells,” Phys. Rev. Lett. 100, 056602 (2008).
    [CrossRef] [PubMed]
  9. J. Yan and M. S. Fuhrer, “Correlated charged impurity scattering in graphene,” Phys. Rev. Lett. 107, 206601 (2011).
    [CrossRef] [PubMed]
  10. J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nature Phys. 4, 377–381 (2008).
    [CrossRef]
  11. J. Smit, “The spontaneous Hall effect in ferromagnetics II,” Physica 24, 39–51 (1958).
    [CrossRef]
  12. S. Hüfner, Photoelectron Spectroscopy, (Springer-Verlag, 1995).
  13. A. Damascelli, Z. Hussain, and Z. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75, 473–541 (2003).
    [CrossRef]
  14. J. Güde, M. Rohleder, T. Meier, S. W. Koch, and U. Höer, “Time-resolved investigation of coherently controlled electric currents at a metal surface,” Science 318, 1287–1291 (2007).
    [CrossRef]
  15. J. B. Khurgin, “Current induced second harmonic generation in semiconductors,” Appl. Phys. Lett. 67, 1113–1115 (1995).
    [CrossRef]
  16. B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
    [CrossRef] [PubMed]
  17. J. B. Khurgin, “Generation of the theraherz radiation using χ(3) in semiconductor,” J. Nonlinear Opt. Phys. Mater. 4, 163–189 (1995).
    [CrossRef]
  18. R. D. R. Bhat and J. E. Sipe, “Optically injected spin currents in semiconductors,” Phys. Rev. Lett. 85, 5432–5435 (2000).
    [CrossRef]
  19. M. J. Stevens, A. L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
    [CrossRef] [PubMed]
  20. J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
    [CrossRef] [PubMed]
  21. L. K. Werake, B. A. Ruzicka, and H. Zhao, “Observation of intrinsic inverse spin Hall effect,” Phys. Rev. Lett. 106, 107205 (2011).
    [CrossRef] [PubMed]
  22. J. T. Liu, F. H. Su, and H. Wang, “Model of the optical Stark effect in semiconductor quantum wells: evidence for asymmetric dressed exciton bands,” Phys. Rev. B 80, 113302 (2009).
    [CrossRef]
  23. M. Sheik-Bahae, “Quantum interference control of current in semiconductors: universal scaling and polarization effects,” Phys. Rev. B 60, R11257–R11260 (1999).
    [CrossRef]
  24. J. T. Liu and K. Chang, “Proposal for the direct optical detection of pure spin currents in semiconductors,” Phys. Rev. B 78, 113304 (2008).
    [CrossRef]
  25. J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
    [CrossRef] [PubMed]
  26. J. M. Luttinger and W. Kohn, “Motion of electrons and holes in perturbed periodic fields,” Phys. Rev. 97, 869–883 (1955).
    [CrossRef]
  27. J. M. Luttinger, “Quantum theory of cyclotron resonance in semiconductors: general theory,” Phys. Rev. 102, 1030–1041 (1956).
    [CrossRef]
  28. J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, 1979), 216–219.

2012 (1)

B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
[CrossRef] [PubMed]

2011 (3)

J. Yan and M. S. Fuhrer, “Correlated charged impurity scattering in graphene,” Phys. Rev. Lett. 107, 206601 (2011).
[CrossRef] [PubMed]

L. K. Werake, B. A. Ruzicka, and H. Zhao, “Observation of intrinsic inverse spin Hall effect,” Phys. Rev. Lett. 106, 107205 (2011).
[CrossRef] [PubMed]

J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
[CrossRef] [PubMed]

2010 (1)

Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
[CrossRef] [PubMed]

2009 (2)

T. Hyart, N. V. Alexeeva, J. Mattas, and K. N. Alekseev, “Terahertz bloch oscillator with a modulated bias,” Phys. Rev. Lett. 102, 140405 (2009).
[CrossRef] [PubMed]

J. T. Liu, F. H. Su, and H. Wang, “Model of the optical Stark effect in semiconductor quantum wells: evidence for asymmetric dressed exciton bands,” Phys. Rev. B 80, 113302 (2009).
[CrossRef]

2008 (3)

J. T. Liu and K. Chang, “Proposal for the direct optical detection of pure spin currents in semiconductors,” Phys. Rev. B 78, 113304 (2008).
[CrossRef]

W. Yang, K. Chang, and S. C. Zhang, “Intrinsic spin Hall effect induced by quantum phase transition in HgCdTe quantumwells,” Phys. Rev. Lett. 100, 056602 (2008).
[CrossRef] [PubMed]

J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nature Phys. 4, 377–381 (2008).
[CrossRef]

2007 (1)

J. Güde, M. Rohleder, T. Meier, S. W. Koch, and U. Höer, “Time-resolved investigation of coherently controlled electric currents at a metal surface,” Science 318, 1287–1291 (2007).
[CrossRef]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

2003 (3)

A. Damascelli, Z. Hussain, and Z. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75, 473–541 (2003).
[CrossRef]

M. J. Stevens, A. L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
[CrossRef] [PubMed]

J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
[CrossRef] [PubMed]

2000 (2)

R. D. R. Bhat and J. E. Sipe, “Optically injected spin currents in semiconductors,” Phys. Rev. Lett. 85, 5432–5435 (2000).
[CrossRef]

S. Zhang, “Spin Hall effect in the presence of spin diffusion,” Phys. Rev. Lett. 85, 393–396 (2000).
[CrossRef] [PubMed]

1999 (2)

J. E. Hirsch, “Spin Hall effect,” Phys. Rev. Lett. 83, 1834–1837 (1999).
[CrossRef]

M. Sheik-Bahae, “Quantum interference control of current in semiconductors: universal scaling and polarization effects,” Phys. Rev. B 60, R11257–R11260 (1999).
[CrossRef]

1995 (2)

J. B. Khurgin, “Generation of the theraherz radiation using χ(3) in semiconductor,” J. Nonlinear Opt. Phys. Mater. 4, 163–189 (1995).
[CrossRef]

J. B. Khurgin, “Current induced second harmonic generation in semiconductors,” Appl. Phys. Lett. 67, 1113–1115 (1995).
[CrossRef]

1991 (1)

J. Rammer, “Quantum transport theory of electrons in solids: a single-particle approach,” Rev. Mod. Phys. 63, 781–817 (1991), and references therein.
[CrossRef]

1971 (1)

M. I. Dyakonov and V. I. Perel, “Current-induced spin orientation of electrons in semiconductors,” Phys. Lett. A 35, 459–460 (1971).
[CrossRef]

1958 (1)

J. Smit, “The spontaneous Hall effect in ferromagnetics II,” Physica 24, 39–51 (1958).
[CrossRef]

1956 (1)

J. M. Luttinger, “Quantum theory of cyclotron resonance in semiconductors: general theory,” Phys. Rev. 102, 1030–1041 (1956).
[CrossRef]

1955 (1)

J. M. Luttinger and W. Kohn, “Motion of electrons and holes in perturbed periodic fields,” Phys. Rev. 97, 869–883 (1955).
[CrossRef]

Adam, S.

J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nature Phys. 4, 377–381 (2008).
[CrossRef]

Alekseev, K. N.

T. Hyart, N. V. Alexeeva, J. Mattas, and K. N. Alekseev, “Terahertz bloch oscillator with a modulated bias,” Phys. Rev. Lett. 102, 140405 (2009).
[CrossRef] [PubMed]

Alexeeva, N. V.

T. Hyart, N. V. Alexeeva, J. Mattas, and K. N. Alekseev, “Terahertz bloch oscillator with a modulated bias,” Phys. Rev. Lett. 102, 140405 (2009).
[CrossRef] [PubMed]

Avouris, P.

Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
[CrossRef] [PubMed]

Bhat, R. D. R.

M. J. Stevens, A. L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
[CrossRef] [PubMed]

J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
[CrossRef] [PubMed]

R. D. R. Bhat and J. E. Sipe, “Optically injected spin currents in semiconductors,” Phys. Rev. Lett. 85, 5432–5435 (2000).
[CrossRef]

Chang, K.

J. T. Liu and K. Chang, “Proposal for the direct optical detection of pure spin currents in semiconductors,” Phys. Rev. B 78, 113304 (2008).
[CrossRef]

W. Yang, K. Chang, and S. C. Zhang, “Intrinsic spin Hall effect induced by quantum phase transition in HgCdTe quantumwells,” Phys. Rev. Lett. 100, 056602 (2008).
[CrossRef] [PubMed]

Chen, J. H.

J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nature Phys. 4, 377–381 (2008).
[CrossRef]

Chiu, H.Y.

Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
[CrossRef] [PubMed]

Choi, S. B.

J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
[CrossRef] [PubMed]

Cundiff, S. T.

J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
[CrossRef] [PubMed]

Damascelli, A.

A. Damascelli, Z. Hussain, and Z. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75, 473–541 (2003).
[CrossRef]

Dessau, D. S.

J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
[CrossRef] [PubMed]

Dimitrakopoulos, C.

Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
[CrossRef] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Dyakonov, M. I.

M. I. Dyakonov and V. I. Perel, “Current-induced spin orientation of electrons in semiconductors,” Phys. Lett. A 35, 459–460 (1971).
[CrossRef]

Farmer, D. B.

Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
[CrossRef] [PubMed]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Fuhrer, M. S.

J. Yan and M. S. Fuhrer, “Correlated charged impurity scattering in graphene,” Phys. Rev. Lett. 107, 206601 (2011).
[CrossRef] [PubMed]

J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nature Phys. 4, 377–381 (2008).
[CrossRef]

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Grill, A.

Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
[CrossRef] [PubMed]

Güde, J.

J. Güde, M. Rohleder, T. Meier, S. W. Koch, and U. Höer, “Time-resolved investigation of coherently controlled electric currents at a metal surface,” Science 318, 1287–1291 (2007).
[CrossRef]

Hirsch, J. E.

J. E. Hirsch, “Spin Hall effect,” Phys. Rev. Lett. 83, 1834–1837 (1999).
[CrossRef]

Höer, U.

J. Güde, M. Rohleder, T. Meier, S. W. Koch, and U. Höer, “Time-resolved investigation of coherently controlled electric currents at a metal surface,” Science 318, 1287–1291 (2007).
[CrossRef]

Hommel, D.

J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
[CrossRef] [PubMed]

Hübner, J.

J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
[CrossRef] [PubMed]

Hüfner, S.

S. Hüfner, Photoelectron Spectroscopy, (Springer-Verlag, 1995).

Hussain, Z.

A. Damascelli, Z. Hussain, and Z. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75, 473–541 (2003).
[CrossRef]

Hyart, T.

T. Hyart, N. V. Alexeeva, J. Mattas, and K. N. Alekseev, “Terahertz bloch oscillator with a modulated bias,” Phys. Rev. Lett. 102, 140405 (2009).
[CrossRef] [PubMed]

Ishigami, M.

J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nature Phys. 4, 377–381 (2008).
[CrossRef]

Jang, C.

J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nature Phys. 4, 377–381 (2008).
[CrossRef]

Jenkins, K. A.

Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
[CrossRef] [PubMed]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Kannan, S.

J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
[CrossRef] [PubMed]

Khurgin, J. B.

B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
[CrossRef] [PubMed]

J. B. Khurgin, “Current induced second harmonic generation in semiconductors,” Appl. Phys. Lett. 67, 1113–1115 (1995).
[CrossRef]

J. B. Khurgin, “Generation of the theraherz radiation using χ(3) in semiconductor,” J. Nonlinear Opt. Phys. Mater. 4, 163–189 (1995).
[CrossRef]

Klude, M.

J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
[CrossRef] [PubMed]

Koch, S. W.

J. Güde, M. Rohleder, T. Meier, S. W. Koch, and U. Höer, “Time-resolved investigation of coherently controlled electric currents at a metal surface,” Science 318, 1287–1291 (2007).
[CrossRef]

Kohn, W.

J. M. Luttinger and W. Kohn, “Motion of electrons and holes in perturbed periodic fields,” Phys. Rev. 97, 869–883 (1955).
[CrossRef]

Lin, Y. M.

Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
[CrossRef] [PubMed]

Liu, J. T.

J. T. Liu, F. H. Su, and H. Wang, “Model of the optical Stark effect in semiconductor quantum wells: evidence for asymmetric dressed exciton bands,” Phys. Rev. B 80, 113302 (2009).
[CrossRef]

J. T. Liu and K. Chang, “Proposal for the direct optical detection of pure spin currents in semiconductors,” Phys. Rev. B 78, 113304 (2008).
[CrossRef]

Luttinger, J. M.

J. M. Luttinger, “Quantum theory of cyclotron resonance in semiconductors: general theory,” Phys. Rev. 102, 1030–1041 (1956).
[CrossRef]

J. M. Luttinger and W. Kohn, “Motion of electrons and holes in perturbed periodic fields,” Phys. Rev. 97, 869–883 (1955).
[CrossRef]

Mattas, J.

T. Hyart, N. V. Alexeeva, J. Mattas, and K. N. Alekseev, “Terahertz bloch oscillator with a modulated bias,” Phys. Rev. Lett. 102, 140405 (2009).
[CrossRef] [PubMed]

Meier, T.

J. Güde, M. Rohleder, T. Meier, S. W. Koch, and U. Höer, “Time-resolved investigation of coherently controlled electric currents at a metal surface,” Science 318, 1287–1291 (2007).
[CrossRef]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Najmaie, Ali

M. J. Stevens, A. L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
[CrossRef] [PubMed]

Novoselov, K. S.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Perel, V. I.

M. I. Dyakonov and V. I. Perel, “Current-induced spin orientation of electrons in semiconductors,” Phys. Lett. A 35, 459–460 (1971).
[CrossRef]

Rammer, J.

J. Rammer, “Quantum transport theory of electrons in solids: a single-particle approach,” Rev. Mod. Phys. 63, 781–817 (1991), and references therein.
[CrossRef]

Rohleder, M.

J. Güde, M. Rohleder, T. Meier, S. W. Koch, and U. Höer, “Time-resolved investigation of coherently controlled electric currents at a metal surface,” Science 318, 1287–1291 (2007).
[CrossRef]

Rühle, W. W.

J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
[CrossRef] [PubMed]

Ruzicka, B. A.

B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
[CrossRef] [PubMed]

L. K. Werake, B. A. Ruzicka, and H. Zhao, “Observation of intrinsic inverse spin Hall effect,” Phys. Rev. Lett. 106, 107205 (2011).
[CrossRef] [PubMed]

Sheik-Bahae, M.

M. Sheik-Bahae, “Quantum interference control of current in semiconductors: universal scaling and polarization effects,” Phys. Rev. B 60, R11257–R11260 (1999).
[CrossRef]

Shen, Z.

A. Damascelli, Z. Hussain, and Z. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75, 473–541 (2003).
[CrossRef]

Sherman, E. Ya.

B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
[CrossRef] [PubMed]

Sipe, J. E.

J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
[CrossRef] [PubMed]

M. J. Stevens, A. L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
[CrossRef] [PubMed]

J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
[CrossRef] [PubMed]

R. D. R. Bhat and J. E. Sipe, “Optically injected spin currents in semiconductors,” Phys. Rev. Lett. 85, 5432–5435 (2000).
[CrossRef]

Smirl, A. L.

M. J. Stevens, A. L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
[CrossRef] [PubMed]

Smit, J.

J. Smit, “The spontaneous Hall effect in ferromagnetics II,” Physica 24, 39–51 (1958).
[CrossRef]

Stevens, M. J.

M. J. Stevens, A. L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
[CrossRef] [PubMed]

Su, F. H.

J. T. Liu, F. H. Su, and H. Wang, “Model of the optical Stark effect in semiconductor quantum wells: evidence for asymmetric dressed exciton bands,” Phys. Rev. B 80, 113302 (2009).
[CrossRef]

van Driel, H. M.

J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
[CrossRef] [PubMed]

M. J. Stevens, A. L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
[CrossRef] [PubMed]

Wahlstrand, J. K.

J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
[CrossRef] [PubMed]

Wang, H.

J. T. Liu, F. H. Su, and H. Wang, “Model of the optical Stark effect in semiconductor quantum wells: evidence for asymmetric dressed exciton bands,” Phys. Rev. B 80, 113302 (2009).
[CrossRef]

Werake, L. K.

B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
[CrossRef] [PubMed]

L. K. Werake, B. A. Ruzicka, and H. Zhao, “Observation of intrinsic inverse spin Hall effect,” Phys. Rev. Lett. 106, 107205 (2011).
[CrossRef] [PubMed]

Williams, E. D.

J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nature Phys. 4, 377–381 (2008).
[CrossRef]

Wu, J. Z.

B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
[CrossRef] [PubMed]

Xu, G. W

B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
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J. Yan and M. S. Fuhrer, “Correlated charged impurity scattering in graphene,” Phys. Rev. Lett. 107, 206601 (2011).
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W. Yang, K. Chang, and S. C. Zhang, “Intrinsic spin Hall effect induced by quantum phase transition in HgCdTe quantumwells,” Phys. Rev. Lett. 100, 056602 (2008).
[CrossRef] [PubMed]

Zhang, H.

J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
[CrossRef] [PubMed]

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S. Zhang, “Spin Hall effect in the presence of spin diffusion,” Phys. Rev. Lett. 85, 393–396 (2000).
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W. Yang, K. Chang, and S. C. Zhang, “Intrinsic spin Hall effect induced by quantum phase transition in HgCdTe quantumwells,” Phys. Rev. Lett. 100, 056602 (2008).
[CrossRef] [PubMed]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Zhao, H.

B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
[CrossRef] [PubMed]

L. K. Werake, B. A. Ruzicka, and H. Zhao, “Observation of intrinsic inverse spin Hall effect,” Phys. Rev. Lett. 106, 107205 (2011).
[CrossRef] [PubMed]

Ziman, J. M.

J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, 1979), 216–219.

Appl. Phys. Lett. (1)

J. B. Khurgin, “Current induced second harmonic generation in semiconductors,” Appl. Phys. Lett. 67, 1113–1115 (1995).
[CrossRef]

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[CrossRef]

Nature Phys. (1)

J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nature Phys. 4, 377–381 (2008).
[CrossRef]

Phys. Lett. A (1)

M. I. Dyakonov and V. I. Perel, “Current-induced spin orientation of electrons in semiconductors,” Phys. Lett. A 35, 459–460 (1971).
[CrossRef]

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[CrossRef]

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J. T. Liu, F. H. Su, and H. Wang, “Model of the optical Stark effect in semiconductor quantum wells: evidence for asymmetric dressed exciton bands,” Phys. Rev. B 80, 113302 (2009).
[CrossRef]

M. Sheik-Bahae, “Quantum interference control of current in semiconductors: universal scaling and polarization effects,” Phys. Rev. B 60, R11257–R11260 (1999).
[CrossRef]

J. T. Liu and K. Chang, “Proposal for the direct optical detection of pure spin currents in semiconductors,” Phys. Rev. B 78, 113304 (2008).
[CrossRef]

Phys. Rev. Lett. (11)

J. K. Wahlstrand, H. Zhang, S. B. Choi, S. Kannan, D. S. Dessau, J. E. Sipe, and S. T. Cundiff, “Optical coherent control induced by an electric field in a semiconductor: a new manifestation of the Franz–Keldysh effect,” Phys. Rev. Lett. 106, 247404 (2011).
[CrossRef] [PubMed]

B. A. Ruzicka, L. K. Werake, G. W Xu, J. B. Khurgin, E. Ya. Sherman, J. Z. Wu, and H. Zhao, “Second-harmonic generation induced by electric currents in GaAs,” Phys. Rev. Lett. 108, 077403 (2012).
[CrossRef] [PubMed]

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[CrossRef]

S. Zhang, “Spin Hall effect in the presence of spin diffusion,” Phys. Rev. Lett. 85, 393–396 (2000).
[CrossRef] [PubMed]

W. Yang, K. Chang, and S. C. Zhang, “Intrinsic spin Hall effect induced by quantum phase transition in HgCdTe quantumwells,” Phys. Rev. Lett. 100, 056602 (2008).
[CrossRef] [PubMed]

J. Yan and M. S. Fuhrer, “Correlated charged impurity scattering in graphene,” Phys. Rev. Lett. 107, 206601 (2011).
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R. D. R. Bhat and J. E. Sipe, “Optically injected spin currents in semiconductors,” Phys. Rev. Lett. 85, 5432–5435 (2000).
[CrossRef]

M. J. Stevens, A. L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
[CrossRef] [PubMed]

J. Hübner, W. W. Rühle, M. Klude, D. Hommel, R. D. R. Bhat, J. E. Sipe, and H. M. van Driel, “Direct observation of optically injected spin-polarized currents in semiconductors,” Phys. Rev. Lett. 90, 216601 (2003).
[CrossRef] [PubMed]

L. K. Werake, B. A. Ruzicka, and H. Zhao, “Observation of intrinsic inverse spin Hall effect,” Phys. Rev. Lett. 106, 107205 (2011).
[CrossRef] [PubMed]

Physica (1)

J. Smit, “The spontaneous Hall effect in ferromagnetics II,” Physica 24, 39–51 (1958).
[CrossRef]

Rev. Mod. Phys. (2)

A. Damascelli, Z. Hussain, and Z. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys. 75, 473–541 (2003).
[CrossRef]

J. Rammer, “Quantum transport theory of electrons in solids: a single-particle approach,” Rev. Mod. Phys. 63, 781–817 (1991), and references therein.
[CrossRef]

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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Y. M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.Y. Chiu, A. Grill, and P. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662–662 (2010).
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J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, 1979), 216–219.

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic illustration of the transition of two parallel-linearly polarized beams in semiconductor materials. (b) Illustration of the detection of the angular distribution of pure charge current by using two-color optical coherence absorption spectrum.

Fig. 2
Fig. 2

(a) Polar contour plot of the electron distribution function fe(k,θ) − fe(k,θ + π) under an electric field. (b) Polar contour plot of QUIC-AB Δ �� QUIC / J e x × 10 6 as a function of the energy E2ω and the angle θal between the electron wave vector and the polarization direction of laser beam.

Fig. 3
Fig. 3

(a) The maximum QUIC-AB Δ �� QUIC / J e x × 10 6 as a function of temperature. (b) The maximum QUIC-AB Δ �� QUIC / J e x × 10 6 as a function of electron relaxation time τe with different applied electric field, E = 5 V/cm (black solid line), E = 10 V/cm (red dashed line), E = 30 V/cm, (blue dotted line).

Equations (5)

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W ( k ) = 2 π ( e 2 h ¯ m c ) 2 δ [ ω c v ( k ) 2 ω ] × ( W k n + W k i ) [ f v ( k ) f c ( k ) ] ,
W k n = ( k a 1 ) 2 | p v c a 1 | 2 η 1 2 A 1 2 + | p v c a 2 | 2 A 2 2 , W k i = k a 1 η 1 A 1 A 2 [ ( p v c a 1 ) * ( p v c a 2 ) e i Δ φ + c . c . ] ,
α QUIC ( ω ) = α Δ φ = 0 ( ω ) α Δ φ = 90 ° ( ω ) .
α QUIC ( ω ) = π 2 e 2 h ¯ c n 0 m 2 ω A 2 η 1 A 1 2 ζ h , l P 2 × k [ f v ( k ) f c ( k ) ] δ [ ω c v ( k ) 2 ω ] k cos θ ,
Δ 𝒜 QUIC ( ω ) = Δ φ = 0 ( ω ) Δ φ = 90 ° ( ω ) [ α QUIC 0 ( ω ) α QUIC ( ω ) ] L ,

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