Proposal for the momentum-resolved and time-resolved optical measurement of the current distribution in semiconductors

doi:10.1364/OE.20.011694

Proposal for the momentum-resolved and time-resolved optical measurement of the current distribution in semiconductors

Jiang-Tao Liu, Fu-Hai Su, Xin-Hua Deng, and Hai Wang »View Author Affiliations

Optics Express, Vol. 20, Issue 11, pp. 11694-11699 (2012)
http://dx.doi.org/10.1364/OE.20.011694

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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.

OCIS Codes
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter
(300.6470) Spectroscopy : Spectroscopy, semiconductors
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 11, 2012
Revised Manuscript: May 3, 2012
Manuscript Accepted: May 3, 2012
Published: May 8, 2012

Citation
Jiang-Tao Liu, Fu-Hai Su, Xin-Hua Deng, and Hai Wang, "Proposal for the momentum-resolved and time-resolved optical measurement of the current distribution in semiconductors," Opt. Express 20, 11694-11699 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-11694

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References

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,” Science306, 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,” Science327, 662–662 (2010). [CrossRef] [PubMed]
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. Rammer, “Quantum transport theory of electrons in solids: a single-particle approach,” Rev. Mod. Phys.63, 781–817 (1991), and references therein. [CrossRef]
M. I. Dyakonov and V. I. Perel, “Current-induced spin orientation of electrons in semiconductors,” Phys. Lett. A35, 459–460 (1971). [CrossRef]
J. E. Hirsch, “Spin Hall effect,” Phys. Rev. Lett.83, 1834–1837 (1999). [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). [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]
J. Smit, “The spontaneous Hall effect in ferromagnetics II,” Physica24, 39–51 (1958). [CrossRef]
S. Hüfner, Photoelectron Spectroscopy, (Springer-Verlag, 1995).
A. Damascelli, Z. Hussain, and Z. Shen, “Angle-resolved photoemission studies of the cuprate superconductors,” Rev. Mod. Phys.75, 473–541 (2003). [CrossRef]
J. Güde, M. Rohleder, T. Meier, S. W. Koch, and U. Höer, “Time-resolved investigation of coherently controlled electric currents at a metal surface,” Science318, 1287–1291 (2007). [CrossRef]
J. B. Khurgin, “Current induced second harmonic generation in semiconductors,” Appl. Phys. Lett.67, 1113–1115 (1995). [CrossRef]
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, “Generation of the theraherz radiation using χ(3) in semiconductor,” J. Nonlinear Opt. Phys. Mater.4, 163–189 (1995). [CrossRef]
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]
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. B80, 113302 (2009). [CrossRef]
M. Sheik-Bahae, “Quantum interference control of current in semiconductors: universal scaling and polarization effects,” Phys. Rev. B60, R11257–R11260 (1999). [CrossRef]
J. T. Liu and K. Chang, “Proposal for the direct optical detection of pure spin currents in semiconductors,” Phys. Rev. B78, 113304 (2008). [CrossRef]
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]
J. M. Luttinger and W. Kohn, “Motion of electrons and holes in perturbed periodic fields,” Phys. Rev.97, 869–883 (1955). [CrossRef]
J. M. Luttinger, “Quantum theory of cyclotron resonance in semiconductors: general theory,” Phys. Rev.102, 1030–1041 (1956). [CrossRef]
J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, 1979), 216–219.

Adam, S.
Alekseev, K. N.
Alexeeva, N. V.
Avouris, P.
Bhat, R. D. R.
Chang, K.
Chen, J. H.
Chiu, H.Y.
Choi, S. B.
Cundiff, S. T.
Damascelli, A.
Dessau, D. S.
Dimitrakopoulos, C.
Dubonos, S. V.
Dyakonov, M. I.
Farmer, D. B.
Firsov, A. A.
Fuhrer, M. S.
Geim, A. K.
Grigorieva, I. V.
Grill, A.
Güde, J.
Hirsch, J. E.
Höer, U.
Hommel, D.
Hübner, J.
Hüfner, S.
Hussain, Z.
Hyart, T.
Ishigami, M.
Jang, C.
Jenkins, K. A.
Jiang, D.
Kannan, S.
Khurgin, J. B.
Klude, M.
Koch, S. W.
Kohn, W.
Lin, Y. M.
Liu, J. T.
Luttinger, J. M.
Mattas, J.
Meier, T.
Morozov, S. V.
Najmaie, Ali
Novoselov, K. S.
Perel, V. I.
Rammer, J.
Rohleder, M.
Rühle, W. W.
Ruzicka, B. A.
Sheik-Bahae, M.
Shen, Z.
Sherman, E. Ya.
Sipe, J. E.
Smirl, A. L.
Smit, J.
Stevens, M. J.
Su, F. H.
van Driel, H. M.
Wahlstrand, J. K.
Wang, H.
Werake, L. K.
Williams, E. D.
Wu, J. Z.
Xu, G. W
Yan, J.
Yang, W.
Zhang, H.
Zhang, S.
Zhang, S. C.
Zhang, Y.
Zhao, H.
Ziman, J. M.

Appl. Phys. Lett.

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

J. Nonlinear Opt. Phys. Mater.

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

Nature Phys.

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

M. I. Dyakonov and V. I. Perel, “Current-induced spin orientation of electrons in semiconductors,” Phys. Lett. A35, 459–460 (1971). [CrossRef]

Phys. Rev.

J. M. Luttinger and W. Kohn, “Motion of electrons and holes in perturbed periodic fields,” Phys. Rev.97, 869–883 (1955). [CrossRef]
J. M. Luttinger, “Quantum theory of cyclotron resonance in semiconductors: general theory,” Phys. Rev.102, 1030–1041 (1956). [CrossRef]

Phys. Rev. B

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. B80, 113302 (2009). [CrossRef]
M. Sheik-Bahae, “Quantum interference control of current in semiconductors: universal scaling and polarization effects,” Phys. Rev. B60, R11257–R11260 (1999). [CrossRef]
J. T. Liu and K. Chang, “Proposal for the direct optical detection of pure spin currents in semiconductors,” Phys. Rev. B78, 113304 (2008). [CrossRef]

Phys. Rev. Lett.

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

J. Smit, “The spontaneous Hall effect in ferromagnetics II,” Physica24, 39–51 (1958). [CrossRef]

Rev. Mod. Phys.

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]

Science

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,” Science306, 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,” Science327, 662–662 (2010). [CrossRef] [PubMed]
J. Güde, M. Rohleder, T. Meier, S. W. Koch, and U. Höer, “Time-resolved investigation of coherently controlled electric currents at a metal surface,” Science318, 1287–1291 (2007). [CrossRef]

Other

S. Hüfner, Photoelectron Spectroscopy, (Springer-Verlag, 1995).
J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, 1979), 216–219.

2012, Ruzicka, Phys. Rev. Lett.
2011, Yan, Phys. Rev. Lett.
2011, Werake, Phys. Rev. Lett.
2011, Wahlstrand, Phys. Rev. Lett.
2010, Lin, Science
2009, Hyart, Phys. Rev. Lett.
2009, Liu, Phys. Rev. B
2008, Liu, Phys. Rev. B
2008, Yang, Phys. Rev. Lett.
2008, Chen, Nature Phys.
2007, Güde, Science
2004, Novoselov, Science
2003, Damascelli, Rev. Mod. Phys.
2003, Stevens, Phys. Rev. Lett.
2003, Hübner, Phys. Rev. Lett.
2000, Bhat, Phys. Rev. Lett.
2000, Zhang, Phys. Rev. Lett.
1999, Hirsch, Phys. Rev. Lett.
1999, Sheik-Bahae, Phys. Rev. B
1995, Khurgin, J. Nonlinear Opt. Phys. Mater.
1995, Khurgin, Appl. Phys. Lett.
1991, Rammer, Rev. Mod. Phys.
1971, Dyakonov, Phys. Lett. A
1958, Smit, Physica
1956, Luttinger, Phys. Rev.
1955, Luttinger, Phys. Rev.

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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,” Science306, 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,” Science327, 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. A35, 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,” Physica24, 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,” Science318, 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. B80, 113302 (2009). [CrossRef]

[23] M. Sheik-Bahae, “Quantum interference control of current in semiconductors: universal scaling and polarization effects,” Phys. Rev. B60, 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. B78, 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.

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Proposal for the momentum-resolved and time-resolved optical measurement of the current distribution in semiconductors

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Abstract

References

Appl. Phys. Lett.

J. Nonlinear Opt. Phys. Mater.

Nature Phys.

Phys. Lett. A

Phys. Rev.

Phys. Rev. B

Phys. Rev. Lett.

Physica

Rev. Mod. Phys.

Science

Other

Cited By

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