1. Terahertz studies of collective excitations and microscopic physics in semiconductor magneto-plasmas
Alexey Belyanin
Texas A&M University
A. Wojcik TAMU
X. Wang, D.M. Mittleman, and J. Kono Rice
S.A. Crooker NHMFL, Los Alamos
NSF CAREER
NSF OISE 1

2. N-doped InSb: a classic narrow-gap semiconductor
~ 0.2 eV
~ 0.8 eV
Small band gap
Small electron mass ~ m0
Strong non-parabolicity;
Non-equidistant cyclotron transitions
Palik & Furdyna 1970
McCombe & Wagner 1975

3. Many frequency scales in doped semiconductors fall into
the THz spectral range
1 THz = 4.1 meV
Plasma frequency
Fermi energy
Electron scattering rates
Cyclotron frequency in the magnetic field of ~ 1 Tesla
Intra-donor transition frequencies
Phonon frequencies
Rich information can be extracted from THz spectroscopic studies
Exotic conditions for atoms and plasma in superstrong magnetic fields
Potential for optoelectronic devices utilizing THz coherence

4. THz time-domain spectroscopy
Delay stage
CPA laser
1 KHz, 800 nm
Receiver
Transmitter
ZnTe B
ZnTe WC
1/4
Current Amplifier
Lock_in amplifier
Sample: n-doped InSb crystal
Sample #1: density = 2.1E14 cm-3
Sample #2: density = 3.5E14 cm-3
Sample #3 density = 6.1E14 cm-3
T = K
f = THz
B = 0-10 T

5. Incident and transmitted THz pulses

6. The transmittance contour map of sample # 1
T = 1.6 K
T = 40 K
Frequency, THz
Magnetic field, Tesla
Plasma edge
Cyclotron resonance
Intra-donor transition lines at low T and high B
Interference features

7. Transmittance at 40 K: only free-carrier effects expected

8. Ei Free-carrier effects: interference of normal magnetoplasmon modes
“Cold” plasma approximation: n2
FMS
~ 16  
CRI
CRA
CRI
CRA Ei B

9. Transmittance at 40 K: only free-carrier effects expected
CRI
CRA

10. experiment
theory
Interference structure is very sensitive to the cyclotron transition energy and the density of free electrons
Yields information on the electron cyclotron mass, band non-parabolicity, compensation ratio, and binding energy on donors (Tellurium) as a function of magnetic field

11. Temperature map at B = 0.9 T experiment
Position of the peak is very sensitive to thermal band gap EgT :
EgT = eV
theory

12. Electron scattering rate
Temperature dependence at B = 0.9 T
Scattering mechanisms:
Ionized and neutral impurities
Acoustic deformation potential
Piezoelectric
Optical deformation potential
Polar optical phonons
intrinsic carriers
Impurity scattering
Polar optical phonons
Electron-hole scattering

13. Electron-”ion” scattering in a strong magnetic field
Debye radius
Gyroradius:
Similar to magnetic white dwarfs and neutron stars!

14. Low-temperature effects: donor absorption lines and field-induced localization
Nn = 2.1x1014 cm-3
40 K
1.6 K
measurements

15. Donor (tellurium) transition lines
Cyclotron resonance
CRA 1s-2p+ transition (000)-(110)
CRI 1s-2p- transition (000)-(0-10)
McCombe & Wagner 1975

16. Low-temperature effects: field-induced localization
T = 1.6 K, Nn = 2.1x1014 cm-3
Edwards & Sienko 1978
Quantum phase transition metal-insulator?
Gradual magnetic freeze-out of carriers?
B = 0: Nn ~ 6x1013 cm-3

17. Freeze-out picture: Gao et al., APL 2006 Shayegan et al. PRB 1988
Mani et al., PRB 1989,1991

18. Low-temperature effects: field-induced localization
T = 1.6 K, Nn = 2.1x1014 cm-3
Not compatible with a gradual magnetic freeze-out?
Trying scaling behavior of dielectric constant …
“Releasing” electrons at B ~ Bc
Efros & Shklovskii 1976 etc.

19. Conclusions
Coherent time-domain THz spectroscopy provides quantitative information on the band structure, electron scattering processes, and collective excitations
Intriguing low-temperature behavior of the dielectric response; nature of the magnetic field-induced localization is still unclear
Also for future studies: dispersion , deviation from ideal plasma, kinetic effects near the cyclotron resonance