Abstract

We have observed long-lived (~30 ps) coherent oscillations of charge carriers due to cyclotron resonance (CR) in high-mobility two-dimensional electrons in GaAs in perpendicular magnetic fields using time-domain terahertz spectroscopy. The observed coherent oscillations were fitted well by sinusoids with exponentially-decaying amplitudes, through which we were able to provide direct and precise measures for the decay times and oscillation frequencies simultaneously. This method thus overcomes the CR saturation effect, which is known to prevent determination of true CR linewidths in high-mobility electron systems using Fourier-transform infrared spectroscopy.

© 2010 Optical Society of America

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References

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  1. A. Petrou, and B. D. McCombe, “Magnetospectroscopy of confined semiconductor systems,” in Landau Level Spectroscopy, Volume 27.2 of Modern Problems in Condensed Matter Sciences, G. Landwehr and E. I. Rashba, eds. (Elsevier Science, Amsterdam, 1991), pp. 679–775.
  2. R. J. Nicholas, “Intraband optical properties of low-dimensional semiconductor systems,” in Handbook on Semiconductors, Vol. 2 “Optical Properties”, M. Balkanski, ed. (Elsevier, Amsterdam, 1994), pp. 385–461.
  3. J. Kono, “Cyclotron resonance,” in Methods in Materials Research, E. N. Kaufmann, R. Abbaschian, A. Bocarsly, C.-L. Chien, D. Dollimore, B. Doyle, A. Goldman, R. Gronsky, S. Pearton, and J. Sanchez, eds. (John Wiley & Sons, New York, 2001), chap. 9b.2.
  4. J. Kono, and N. Miura, “Cyclotron resonance in high magnetic fields,” in High Magnetic Fields: Science and Technology, Volume III, N. Miura and F. Herlach, eds. (World Scientific, Singapore, 2006), pp. 61–90.
  5. M. J. Chou, and D. C. Tsui, “Cyclotron resonance of high-mobility electrons at extremely low densities,” Phys. Rev. B 37, 848–854 (1988).
    [CrossRef]
  6. S. A. Studenikin, M. Potemski, A. Sachrajda, M. Hillke, L. N. Pfeiffer, and K. W. West, “Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: exact waveform, absorption/reflection and temperature damping,” Phys. Rev. B 71, 245313–245322 (2005).
    [CrossRef]
  7. S. A. Mikhailov, “Microwave-induced magnetotransport phenomena in two-dimensional electron systems: important of electodynamic effects,” Phys. Rev. B 70, 165311–165315 (2004).
    [CrossRef]
  8. 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]
  9. X. Wang, A. A. Belyanin, S. A. Crooker, D. M. Mittleman, and J. Kono, “Interference-induced terahertz transparency in a semiconductor magneto-plasma,” Nat. Phys. 6, 126–130 (2010).
    [CrossRef]
  10. D. Grischkowsky, S. Keiding, M. V. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
    [CrossRef]
  11. M. C. Nuss, and J. Orenstein, “Terahertz time-domain spectroscopy,” in Millimeter and Submillimeter Wave Spectroscopy of Solids, G. Grüner, ed. (Springer-Verlag, Berlin, 1998), pp. 7–50.
  12. Z. Jiang, and X.-C. Zhang, “Free-space electro-optic techniques,” in Sensing with Terahertz Radiation, D. Mittleman, ed. (Springer-Verlag, Berlin, 2003), pp. 155–192.

2010 (1)

X. Wang, A. A. Belyanin, S. A. Crooker, D. M. Mittleman, and J. Kono, “Interference-induced terahertz transparency in a semiconductor magneto-plasma,” Nat. Phys. 6, 126–130 (2010).
[CrossRef]

2007 (1)

2005 (1)

S. A. Studenikin, M. Potemski, A. Sachrajda, M. Hillke, L. N. Pfeiffer, and K. W. West, “Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: exact waveform, absorption/reflection and temperature damping,” Phys. Rev. B 71, 245313–245322 (2005).
[CrossRef]

2004 (1)

S. A. Mikhailov, “Microwave-induced magnetotransport phenomena in two-dimensional electron systems: important of electodynamic effects,” Phys. Rev. B 70, 165311–165315 (2004).
[CrossRef]

1990 (1)

1988 (1)

M. J. Chou, and D. C. Tsui, “Cyclotron resonance of high-mobility electrons at extremely low densities,” Phys. Rev. B 37, 848–854 (1988).
[CrossRef]

Belyanin, A. A.

X. Wang, A. A. Belyanin, S. A. Crooker, D. M. Mittleman, and J. Kono, “Interference-induced terahertz transparency in a semiconductor magneto-plasma,” Nat. Phys. 6, 126–130 (2010).
[CrossRef]

Chou, M. J.

M. J. Chou, and D. C. Tsui, “Cyclotron resonance of high-mobility electrons at extremely low densities,” Phys. Rev. B 37, 848–854 (1988).
[CrossRef]

Crooker, S. A.

X. Wang, A. A. Belyanin, S. A. Crooker, D. M. Mittleman, and J. Kono, “Interference-induced terahertz transparency in a semiconductor magneto-plasma,” Nat. Phys. 6, 126–130 (2010).
[CrossRef]

Exter, M. V.

Fattinger, C.

Grischkowsky, D.

Hillke, M.

S. A. Studenikin, M. Potemski, A. Sachrajda, M. Hillke, L. N. Pfeiffer, and K. W. West, “Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: exact waveform, absorption/reflection and temperature damping,” Phys. Rev. B 71, 245313–245322 (2005).
[CrossRef]

Hilton, D. J.

Keiding, S.

Kono, J.

X. Wang, A. A. Belyanin, S. A. Crooker, D. M. Mittleman, and J. Kono, “Interference-induced terahertz transparency in a semiconductor magneto-plasma,” Nat. Phys. 6, 126–130 (2010).
[CrossRef]

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]

Mikhailov, S. A.

S. A. Mikhailov, “Microwave-induced magnetotransport phenomena in two-dimensional electron systems: important of electodynamic effects,” Phys. Rev. B 70, 165311–165315 (2004).
[CrossRef]

Mittleman, D. M.

X. Wang, A. A. Belyanin, S. A. Crooker, D. M. Mittleman, and J. Kono, “Interference-induced terahertz transparency in a semiconductor magneto-plasma,” Nat. Phys. 6, 126–130 (2010).
[CrossRef]

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]

Pfeiffer, L. N.

S. A. Studenikin, M. Potemski, A. Sachrajda, M. Hillke, L. N. Pfeiffer, and K. W. West, “Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: exact waveform, absorption/reflection and temperature damping,” Phys. Rev. B 71, 245313–245322 (2005).
[CrossRef]

Potemski, M.

S. A. Studenikin, M. Potemski, A. Sachrajda, M. Hillke, L. N. Pfeiffer, and K. W. West, “Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: exact waveform, absorption/reflection and temperature damping,” Phys. Rev. B 71, 245313–245322 (2005).
[CrossRef]

Ren, L.

Reno, J. L.

Sachrajda, A.

S. A. Studenikin, M. Potemski, A. Sachrajda, M. Hillke, L. N. Pfeiffer, and K. W. West, “Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: exact waveform, absorption/reflection and temperature damping,” Phys. Rev. B 71, 245313–245322 (2005).
[CrossRef]

Studenikin, S. A.

S. A. Studenikin, M. Potemski, A. Sachrajda, M. Hillke, L. N. Pfeiffer, and K. W. West, “Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: exact waveform, absorption/reflection and temperature damping,” Phys. Rev. B 71, 245313–245322 (2005).
[CrossRef]

Tsui, D. C.

M. J. Chou, and D. C. Tsui, “Cyclotron resonance of high-mobility electrons at extremely low densities,” Phys. Rev. B 37, 848–854 (1988).
[CrossRef]

Wang, X.

X. Wang, A. A. Belyanin, S. A. Crooker, D. M. Mittleman, and J. Kono, “Interference-induced terahertz transparency in a semiconductor magneto-plasma,” Nat. Phys. 6, 126–130 (2010).
[CrossRef]

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]

West, K. W.

S. A. Studenikin, M. Potemski, A. Sachrajda, M. Hillke, L. N. Pfeiffer, and K. W. West, “Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: exact waveform, absorption/reflection and temperature damping,” Phys. Rev. B 71, 245313–245322 (2005).
[CrossRef]

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

Nat. Phys. (1)

X. Wang, A. A. Belyanin, S. A. Crooker, D. M. Mittleman, and J. Kono, “Interference-induced terahertz transparency in a semiconductor magneto-plasma,” Nat. Phys. 6, 126–130 (2010).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (3)

M. J. Chou, and D. C. Tsui, “Cyclotron resonance of high-mobility electrons at extremely low densities,” Phys. Rev. B 37, 848–854 (1988).
[CrossRef]

S. A. Studenikin, M. Potemski, A. Sachrajda, M. Hillke, L. N. Pfeiffer, and K. W. West, “Microwave-induced resistance oscillations on a high-mobility two-dimensional electron gas: exact waveform, absorption/reflection and temperature damping,” Phys. Rev. B 71, 245313–245322 (2005).
[CrossRef]

S. A. Mikhailov, “Microwave-induced magnetotransport phenomena in two-dimensional electron systems: important of electodynamic effects,” Phys. Rev. B 70, 165311–165315 (2004).
[CrossRef]

Other (6)

A. Petrou, and B. D. McCombe, “Magnetospectroscopy of confined semiconductor systems,” in Landau Level Spectroscopy, Volume 27.2 of Modern Problems in Condensed Matter Sciences, G. Landwehr and E. I. Rashba, eds. (Elsevier Science, Amsterdam, 1991), pp. 679–775.

R. J. Nicholas, “Intraband optical properties of low-dimensional semiconductor systems,” in Handbook on Semiconductors, Vol. 2 “Optical Properties”, M. Balkanski, ed. (Elsevier, Amsterdam, 1994), pp. 385–461.

J. Kono, “Cyclotron resonance,” in Methods in Materials Research, E. N. Kaufmann, R. Abbaschian, A. Bocarsly, C.-L. Chien, D. Dollimore, B. Doyle, A. Goldman, R. Gronsky, S. Pearton, and J. Sanchez, eds. (John Wiley & Sons, New York, 2001), chap. 9b.2.

J. Kono, and N. Miura, “Cyclotron resonance in high magnetic fields,” in High Magnetic Fields: Science and Technology, Volume III, N. Miura and F. Herlach, eds. (World Scientific, Singapore, 2006), pp. 61–90.

M. C. Nuss, and J. Orenstein, “Terahertz time-domain spectroscopy,” in Millimeter and Submillimeter Wave Spectroscopy of Solids, G. Grüner, ed. (Springer-Verlag, Berlin, 1998), pp. 7–50.

Z. Jiang, and X.-C. Zhang, “Free-space electro-optic techniques,” in Sensing with Terahertz Radiation, D. Mittleman, ed. (Springer-Verlag, Berlin, 2003), pp. 155–192.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Calculated absorptance A, reflectance R, and transmittance T versus CR mobility at a fixed density n = 2 × 1011 cm−2. (b) Calculated linewidths of the real part of the conductivity and transmittance at n = 2 × 1010, 2 × 1011, and 2 × 1012 cm−2. The mobility was changed from 1 × 104 to 1 × 108 cm2/Vs in (a) and (b). (c, d, e, and f) Calculated real part of the conductivity σ′ (blue lines) and 1−T (red lines) for different mobilities: (c) 3 × 104, (d) 3 × 105, (e) 3 × 106, and (f) 3 × 107 cm2/Vs, respectively. The deviation of the transmittance peak linewidth from the real conductivity linewidth becomes more significant with increasing mobility.

Fig. 2.
Fig. 2.

THz waveforms transmitted through a high-mobility 2DEG at 0 T and at 1.42 T at 1.6 K. The coherent cyclotron resonance oscillations, present only in the 1.42 T waveform, are isolated by subtracting the 0 T waveform from the 1.42 T waveform.

Fig. 3.
Fig. 3.

Coherent cyclotron resonance oscillations of a GaAs 2DEG at magnetic fields from 0.6 to 2.2 T at 1.6 K, measured by time-domain THz magneto-spectroscopy. The traces are vertically offset for clarity. These CR oscillations are isolated by subtracting the transmitted THz waveform at 0 T from the transmitted THz waveforms at different magnetic fields.

Fig. 4.
Fig. 4.

Time-domain cyclotron resonance oscillations at 1.8, 1.1, and 0.9 T obtained by subtracting the transmitted THz waveform at 0 T from the transmitted THz waveforms at these three magnetic fields (red curves). We fit these oscillations using an exponentially-decaying sinusoid [see Eq. (4)]. Fitting curves are shown as blue curves.

Tables (1)

Tables Icon

Table 1. CR decay times (τ CR) and CR frequencies (fc ) obtained through fitting time-domain CR oscillations at 1.8, 1.1, and 0.9 T. Standard deviations of the fittings are also shown. For comparison, CR decay times that would be obtained from transmittance linewithds (τ Tr) are shown in the last column.

Equations (5)

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T = E ( B ) E ( 0 ) = 2 Y 2 Y + σ
R = σ 2 Y + σ
σ = σ + i σ = ne 2 m * 1 τ CR 1 τ CR 2 + 4 π 2 ( f f c ) 2 + i ne 2 m * 2 π ( f f c ) 1 τ CR 2 + 4 π 2 ( f f c ) 2
E ( t ) = E 0 + A exp ( t τ CR ) sin ( 2 π f c t + θ 0 )
E ( v ) = [ 1 + Σ j = 1 N A j exp ( i 2 π T j v ) ] × E 0 ( v )

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