Abstract

We develop a new characteristic matrix-based method to analyze cyclotron resonance experiments in high mobility two-dimensional electron gas samples where direct interference between primary and satellite reflections has previously limited the frequency resolution. This model is used to simulate experimental data taken using terahertz time-domain spectroscopy that show multiple pulses from the substrate with a separation of 15 ps that directly interfere in the time-domain. We determine a cyclotron dephasing lifetime of 15.1±0.5 ps at 1.5 K and 5.0±0.5 ps at 75 K.

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  1. C. K. Sarkar and R. J. Nicholas, “Cyclotron resonance linewidth in a two-dimensional electron gas,” Surf. Sci.113, 326–332 (1982).
    [CrossRef]
  2. M. Chou, D. Tsui, and G. Weimann, “Cyclotron resonance of high-mobility two-dimensional electrons at extremely low densities,” Phys. Rev. B37, 848–854 (1988).
    [CrossRef]
  3. D. J. Hilton, T. Arikawa, and J. Kono, “Cyclotron resonance,” in Characterization of Materials, E. N. Kaufmann, ed. (John Wiley and Sons, Inc, New York, 2012), p. 2438.
  4. D. C. Tsui, H. Stormer, and A. C. Gossard, “Two-dimensional magnetotransport in the extreme quantum limit,” Phys. Rev. Lett.48, 1559–1562 (1982).
    [CrossRef]
  5. X. Wang, D. J. Hilton, J. L. Reno, D. M. Mittleman, and J. Kono, “Direct measurement of cyclotron coherence times of high-mobility two-dimensional electron gases,” Opt. Express18, 12354–12361 (2010).
    [CrossRef] [PubMed]
  6. X. Wang, D. J. Hilton, L. Ren, D. M. Mittleman, J. Kono, and J. L. Reno, “Terahertz time-domain magnetospectroscopy of a high-mobility two-dimensional electron gas,” Opt. Lett.32, 1845–1847 (2007).
    [CrossRef] [PubMed]
  7. L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Quantum Electron.2, 739–746 (1996).
    [CrossRef]
  8. Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B18, 823–831 (2001).
    [CrossRef]
  9. D. Mittleman, ed., Sensing with Terahertz Radiation (Springer, Berlin, 2002).
  10. M. C. Nuss and J. Orenstein, Terahertz Time-Domain Spectroscopy, vol. 74 (Springer, Berlin, 1998).
  11. G. Landwehr, Landau Level Spectroscopy (North-Holland, New York, 1990).
  12. T. Arikawa, X. Wang, D. J. Hilton, J. L. Reno, W. Pan, and J. Kono, “Quantum control of a Landau-quantized two-dimensional electron gas in a GaAs quantum well using coherent terahertz pulses,” Phys. Rev. B84, 241307 (2011).
    [CrossRef]
  13. S. E. Ralph, S. Perkowitz, N. Katzenellenbogen, and D. Grischkowsky, “Terahertz spectroscopy of optically thick multilayered semiconductor structures,” J. Opt. Soc. Am. B11, 2528–2532 (1994).
    [CrossRef]
  14. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).
  15. J. W. Goodman, Introduction To Fourier Optics (McGraw-Hill, New York, 1996).
  16. S. Teitler and B. W. Henvis, “Refraction in stratified, anisotropic media,” J. Opt. Soc. Am.60, 830–834 (1970).
    [CrossRef]
  17. D. W. Berreman, “Optics in stratified and anisotropic media: 4 × 4-matrix formulation,” J. Opt. Soc. Am.62, 502–510 (1972).
    [CrossRef]
  18. H. Wöhler, M. Fritsch, G. Haas, and D. A. Mlynski, “Characteristic matrix method for stratified anisotropic media: optical properties of special configurations,” J. Opt. Soc. Am. A8, 536–540 (1991).
    [CrossRef]
  19. J. S. Blakemore, “Intrinsic density ni(T) in GaAs: Deduced from band gap and effective mass parameters and derived independently from Cr acceptor capture and emission coefficients,” J. Appl. Phys.53, 520–531 (1981).
    [CrossRef]
  20. R. W. Boyd, Nonlinear Optics (Academic Press, 1991).
  21. A. Kawabata, “Theory of cyclotron resonance line width,” J. Phys. Soc. Jpn.23, 999–1006 (1967).
    [CrossRef]
  22. P. Argyres and J. Sigel, “Theory of cyclotron-resonance absorption,” Phys. Rev. B10, 1139–1148 (1974).
    [CrossRef]
  23. V. K. Arora and H. N. Spector, “Quantum-limit cyclotron resonance linewidth in semiconductors,” phys. stat. sol. (b)94, 701–709 (1979).
    [CrossRef]

2011 (1)

T. Arikawa, X. Wang, D. J. Hilton, J. L. Reno, W. Pan, and J. Kono, “Quantum control of a Landau-quantized two-dimensional electron gas in a GaAs quantum well using coherent terahertz pulses,” Phys. Rev. B84, 241307 (2011).
[CrossRef]

2010 (1)

2007 (1)

2001 (1)

1996 (1)

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Quantum Electron.2, 739–746 (1996).
[CrossRef]

1994 (1)

1991 (1)

1988 (1)

M. Chou, D. Tsui, and G. Weimann, “Cyclotron resonance of high-mobility two-dimensional electrons at extremely low densities,” Phys. Rev. B37, 848–854 (1988).
[CrossRef]

1982 (2)

D. C. Tsui, H. Stormer, and A. C. Gossard, “Two-dimensional magnetotransport in the extreme quantum limit,” Phys. Rev. Lett.48, 1559–1562 (1982).
[CrossRef]

C. K. Sarkar and R. J. Nicholas, “Cyclotron resonance linewidth in a two-dimensional electron gas,” Surf. Sci.113, 326–332 (1982).
[CrossRef]

1981 (1)

J. S. Blakemore, “Intrinsic density ni(T) in GaAs: Deduced from band gap and effective mass parameters and derived independently from Cr acceptor capture and emission coefficients,” J. Appl. Phys.53, 520–531 (1981).
[CrossRef]

1979 (1)

V. K. Arora and H. N. Spector, “Quantum-limit cyclotron resonance linewidth in semiconductors,” phys. stat. sol. (b)94, 701–709 (1979).
[CrossRef]

1974 (1)

P. Argyres and J. Sigel, “Theory of cyclotron-resonance absorption,” Phys. Rev. B10, 1139–1148 (1974).
[CrossRef]

1972 (1)

1970 (1)

1967 (1)

A. Kawabata, “Theory of cyclotron resonance line width,” J. Phys. Soc. Jpn.23, 999–1006 (1967).
[CrossRef]

Argyres, P.

P. Argyres and J. Sigel, “Theory of cyclotron-resonance absorption,” Phys. Rev. B10, 1139–1148 (1974).
[CrossRef]

Arikawa, T.

T. Arikawa, X. Wang, D. J. Hilton, J. L. Reno, W. Pan, and J. Kono, “Quantum control of a Landau-quantized two-dimensional electron gas in a GaAs quantum well using coherent terahertz pulses,” Phys. Rev. B84, 241307 (2011).
[CrossRef]

D. J. Hilton, T. Arikawa, and J. Kono, “Cyclotron resonance,” in Characterization of Materials, E. N. Kaufmann, ed. (John Wiley and Sons, Inc, New York, 2012), p. 2438.

Arora, V. K.

V. K. Arora and H. N. Spector, “Quantum-limit cyclotron resonance linewidth in semiconductors,” phys. stat. sol. (b)94, 701–709 (1979).
[CrossRef]

Berreman, D. W.

Blakemore, J. S.

J. S. Blakemore, “Intrinsic density ni(T) in GaAs: Deduced from band gap and effective mass parameters and derived independently from Cr acceptor capture and emission coefficients,” J. Appl. Phys.53, 520–531 (1981).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 1991).

Chen, Q.

Chou, M.

M. Chou, D. Tsui, and G. Weimann, “Cyclotron resonance of high-mobility two-dimensional electrons at extremely low densities,” Phys. Rev. B37, 848–854 (1988).
[CrossRef]

Coutaz, J.-L.

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Quantum Electron.2, 739–746 (1996).
[CrossRef]

Duvillaret, L.

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Quantum Electron.2, 739–746 (1996).
[CrossRef]

Fritsch, M.

Garet, F.

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Quantum Electron.2, 739–746 (1996).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction To Fourier Optics (McGraw-Hill, New York, 1996).

Gossard, A. C.

D. C. Tsui, H. Stormer, and A. C. Gossard, “Two-dimensional magnetotransport in the extreme quantum limit,” Phys. Rev. Lett.48, 1559–1562 (1982).
[CrossRef]

Grischkowsky, D.

Haas, G.

Henvis, B. W.

Hilton, D. J.

T. Arikawa, X. Wang, D. J. Hilton, J. L. Reno, W. Pan, and J. Kono, “Quantum control of a Landau-quantized two-dimensional electron gas in a GaAs quantum well using coherent terahertz pulses,” Phys. Rev. B84, 241307 (2011).
[CrossRef]

X. Wang, D. J. Hilton, J. L. Reno, D. M. Mittleman, and J. Kono, “Direct measurement of cyclotron coherence times of high-mobility two-dimensional electron gases,” Opt. Express18, 12354–12361 (2010).
[CrossRef] [PubMed]

X. Wang, D. J. Hilton, L. Ren, D. M. Mittleman, J. Kono, and J. L. Reno, “Terahertz time-domain magnetospectroscopy of a high-mobility two-dimensional electron gas,” Opt. Lett.32, 1845–1847 (2007).
[CrossRef] [PubMed]

D. J. Hilton, T. Arikawa, and J. Kono, “Cyclotron resonance,” in Characterization of Materials, E. N. Kaufmann, ed. (John Wiley and Sons, Inc, New York, 2012), p. 2438.

Jiang, Z.

Katzenellenbogen, N.

Kawabata, A.

A. Kawabata, “Theory of cyclotron resonance line width,” J. Phys. Soc. Jpn.23, 999–1006 (1967).
[CrossRef]

Kono, J.

T. Arikawa, X. Wang, D. J. Hilton, J. L. Reno, W. Pan, and J. Kono, “Quantum control of a Landau-quantized two-dimensional electron gas in a GaAs quantum well using coherent terahertz pulses,” Phys. Rev. B84, 241307 (2011).
[CrossRef]

X. Wang, D. J. Hilton, J. L. Reno, D. M. Mittleman, and J. Kono, “Direct measurement of cyclotron coherence times of high-mobility two-dimensional electron gases,” Opt. Express18, 12354–12361 (2010).
[CrossRef] [PubMed]

X. Wang, D. J. Hilton, L. Ren, D. M. Mittleman, J. Kono, and J. L. Reno, “Terahertz time-domain magnetospectroscopy of a high-mobility two-dimensional electron gas,” Opt. Lett.32, 1845–1847 (2007).
[CrossRef] [PubMed]

D. J. Hilton, T. Arikawa, and J. Kono, “Cyclotron resonance,” in Characterization of Materials, E. N. Kaufmann, ed. (John Wiley and Sons, Inc, New York, 2012), p. 2438.

Landwehr, G.

G. Landwehr, Landau Level Spectroscopy (North-Holland, New York, 1990).

Mittleman, D. M.

Mlynski, D. A.

Nicholas, R. J.

C. K. Sarkar and R. J. Nicholas, “Cyclotron resonance linewidth in a two-dimensional electron gas,” Surf. Sci.113, 326–332 (1982).
[CrossRef]

Nuss, M. C.

M. C. Nuss and J. Orenstein, Terahertz Time-Domain Spectroscopy, vol. 74 (Springer, Berlin, 1998).

Orenstein, J.

M. C. Nuss and J. Orenstein, Terahertz Time-Domain Spectroscopy, vol. 74 (Springer, Berlin, 1998).

Pan, W.

T. Arikawa, X. Wang, D. J. Hilton, J. L. Reno, W. Pan, and J. Kono, “Quantum control of a Landau-quantized two-dimensional electron gas in a GaAs quantum well using coherent terahertz pulses,” Phys. Rev. B84, 241307 (2011).
[CrossRef]

Perkowitz, S.

Ralph, S. E.

Ren, L.

Reno, J. L.

Sarkar, C. K.

C. K. Sarkar and R. J. Nicholas, “Cyclotron resonance linewidth in a two-dimensional electron gas,” Surf. Sci.113, 326–332 (1982).
[CrossRef]

Sigel, J.

P. Argyres and J. Sigel, “Theory of cyclotron-resonance absorption,” Phys. Rev. B10, 1139–1148 (1974).
[CrossRef]

Spector, H. N.

V. K. Arora and H. N. Spector, “Quantum-limit cyclotron resonance linewidth in semiconductors,” phys. stat. sol. (b)94, 701–709 (1979).
[CrossRef]

Stormer, H.

D. C. Tsui, H. Stormer, and A. C. Gossard, “Two-dimensional magnetotransport in the extreme quantum limit,” Phys. Rev. Lett.48, 1559–1562 (1982).
[CrossRef]

Tani, M.

Teitler, S.

Tsui, D.

M. Chou, D. Tsui, and G. Weimann, “Cyclotron resonance of high-mobility two-dimensional electrons at extremely low densities,” Phys. Rev. B37, 848–854 (1988).
[CrossRef]

Tsui, D. C.

D. C. Tsui, H. Stormer, and A. C. Gossard, “Two-dimensional magnetotransport in the extreme quantum limit,” Phys. Rev. Lett.48, 1559–1562 (1982).
[CrossRef]

Wang, X.

Weimann, G.

M. Chou, D. Tsui, and G. Weimann, “Cyclotron resonance of high-mobility two-dimensional electrons at extremely low densities,” Phys. Rev. B37, 848–854 (1988).
[CrossRef]

Wöhler, H.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).

Zhang, X.-C.

IEEE J. Quantum Electron. (1)

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Quantum Electron.2, 739–746 (1996).
[CrossRef]

J. Appl. Phys. (1)

J. S. Blakemore, “Intrinsic density ni(T) in GaAs: Deduced from band gap and effective mass parameters and derived independently from Cr acceptor capture and emission coefficients,” J. Appl. Phys.53, 520–531 (1981).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

J. Phys. Soc. Jpn. (1)

A. Kawabata, “Theory of cyclotron resonance line width,” J. Phys. Soc. Jpn.23, 999–1006 (1967).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (3)

M. Chou, D. Tsui, and G. Weimann, “Cyclotron resonance of high-mobility two-dimensional electrons at extremely low densities,” Phys. Rev. B37, 848–854 (1988).
[CrossRef]

P. Argyres and J. Sigel, “Theory of cyclotron-resonance absorption,” Phys. Rev. B10, 1139–1148 (1974).
[CrossRef]

T. Arikawa, X. Wang, D. J. Hilton, J. L. Reno, W. Pan, and J. Kono, “Quantum control of a Landau-quantized two-dimensional electron gas in a GaAs quantum well using coherent terahertz pulses,” Phys. Rev. B84, 241307 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

D. C. Tsui, H. Stormer, and A. C. Gossard, “Two-dimensional magnetotransport in the extreme quantum limit,” Phys. Rev. Lett.48, 1559–1562 (1982).
[CrossRef]

phys. stat. sol. (b) (1)

V. K. Arora and H. N. Spector, “Quantum-limit cyclotron resonance linewidth in semiconductors,” phys. stat. sol. (b)94, 701–709 (1979).
[CrossRef]

Surf. Sci. (1)

C. K. Sarkar and R. J. Nicholas, “Cyclotron resonance linewidth in a two-dimensional electron gas,” Surf. Sci.113, 326–332 (1982).
[CrossRef]

Other (7)

D. J. Hilton, T. Arikawa, and J. Kono, “Cyclotron resonance,” in Characterization of Materials, E. N. Kaufmann, ed. (John Wiley and Sons, Inc, New York, 2012), p. 2438.

D. Mittleman, ed., Sensing with Terahertz Radiation (Springer, Berlin, 2002).

M. C. Nuss and J. Orenstein, Terahertz Time-Domain Spectroscopy, vol. 74 (Springer, Berlin, 1998).

G. Landwehr, Landau Level Spectroscopy (North-Holland, New York, 1990).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).

J. W. Goodman, Introduction To Fourier Optics (McGraw-Hill, New York, 1996).

R. W. Boyd, Nonlinear Optics (Academic Press, 1991).

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Figures (3)

Fig. 1
Fig. 1

A diagram of a typical terahertz time-domain spectrometer with an external magnetic field in the Faraday geometry (B perpendicular to the 2DEG). There exist four quartz windows on either the entrance or exit of the split coil magnet, which generate satellite pulses in addition to the gallium arsenide 2DEG/Substrate. The ŷẑ 2DEG sample coordinate system, as defined in the manuscript, is indicated in this diagram. The polarization of the input terahertz pulse is perpendicular to the page (x̂), while the transmitted pulse field is polarized in the x̂– ŷ plane. ZnTe = zinc telluride, OAP = off-axis parabolic mirror, PBS = pellicle beam splitter, QWP = quarter wave plate.

Fig. 2
Fig. 2

Terahertz time-domain waveforms taken in the high mobility 2DEG/substrate sample. The presence of multiple pulses in these data results from multiple passes for the single incident terahertz pulse in the substrate, as discussed in the text. Part (a) shows data taken at T = 75 K in an external magnetic field, Bext = 1.25 T, while part (b) shows data taken at T = 1.5 K under the same experimental conditions. (c) The simulated terahertz electric field shows the formation of a sequence of satellite pulses after transmission through the substrate at Bext. (d) The y-component of the transmitted terahertz electric field, assuming an external magnetic field of Bext = ±1.25 T and a dephasing time of T2 = 5.0 ps, which represents a best fit to the experimental data in Fig. 2(a). (e) The y-component of the transmitted terahertz electric field, under the same conditions with a dephasing time of T2 = 15.1 ps. This reproduces features of the experimental data shown in Fig. 2(b), where the deviations are likely due to the model for the complex susceptibility and are discussed in the manuscript text.

Fig. 3
Fig. 3

(a) Propagation of a normally incident electromagnetic wave through an arbitrary stratified medium with layers located at z ∈ [z0, z1 ... z−1, z], where the terahertz frequency admittance, Yj, describes the optical properties of the jth layer. In this geometry, the two polarizations (σ̂+ and σ̂) are independent and described by two total characteristic matrices, ��̄±,T, as defined in Eq. (9a) in the text. (b) The simplified two layer model of the 2DEG that consists of the conducting layer with a thickness, d, and admittance, Y±,1(ν). This 2DEG is on a substrate with a thickness, L, and admittance, Y2. The primary terahertz pulse results from the direct propagation through the sample (solid), while satellite pulses (dashed) occur a time delay due to multiple passes through the substrate.

Equations (30)

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D ( z , ν ) = ρ f ( z , ν )
B ( z , ν ) = 0
× E ( z , ν ) = + i 2 π ν μ ¯ ( z , ν ) H ( z , ν )
× H ( z , ν ) = i 2 π ν ε ¯ ( z , ν ) E ( z , ν )
ε ¯ ( ε x x + ε x y 0 ε x y ε x x 0 0 0 ε z z )
[ ε p p 0 0 0 ε m m 0 0 0 ε z z ]
E ( z , ν ) = U ( z , ν ) σ ^ + + P ( z , ν ) σ ^
H ( z , ν ) = V ( z , ν ) σ ^ + + Q ( z , ν ) σ ^
d U d z = 2 π ν μ V
d V d z = + 2 π ν ε p p U
d P d z = + 2 π ν μ Q
d Q d z = 2 π ν ε m m P
P ( z ) = P ( z j ) cos [ κ ( z z j ) ] + Q ( z j ) { + Y 1 sin [ κ ( z z j ) ] }
Q ( z ) = Q ( z j ) cos [ κ ( z z j ) ] + P ( z j ) { Y sin [ κ ( z z j ) ] }
U ( z ) = U ( z j ) cos [ κ + ( z z j ) ] + V ( z j ) { Y + 1 sin [ κ + ( z z j ) ] }
V ( z ) = V ( z j ) cos [ κ + ( z z j ) ] + U ( z j ) { + Y + sin [ κ + ( z z j ) ] }
+ ( z , ν ) [ U ( z , ν ) V ( z , ν ) ]
( z , ν ) [ P ( z , ν ) Q ( z , ν ) ]
± ( z j , ν ) = 𝕄 ¯ ± , j ± ( z j + 1 , ν )
𝕄 ¯ ± [ cos ( κ ± d ) ± Y ± 1 sin ( κ ± d ) Y ± sin ( κ ± d ) cos ( κ ± d ) ]
𝕄 ¯ ± , T = 𝕄 ¯ ± , 0 𝕄 ¯ ± , 1 𝕄 ¯ ± , 1
[ A ± B ± C ± D ± ]
t + U t ( z ) U i ( z 0 )
t P t ( z ) P i ( z 0 )
t ± ( ν ) = 2 ( A ± + Y t Y i 1 D ± ) ± i ( Y i 1 C ± Y t B ± )
χ ˜ ( ν ) = χ 0 [ i 2 π ( ν ν C R ) T 2 1 + 4 π 2 ( ν ν C R ) 2 T 2 2 ] χ r + i χ i
A ± = sin φ ± sin θ Y ± , 1 1 Y 2 cos φ ± cos θ
B ± = ± [ ( Y 2 1 cos θ sin φ ± + Y ± , 1 1 cos φ ± sin θ ) ]
C ± = [ Y 2 cos θ sin φ ± + Y ± , 1 cos φ ± sin θ ]
D ± = sin φ ± sin θ Y ± , 1 Y 2 1 cos φ ± cos θ

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