A. Wojcik TAMUX. Wang, D.M. Mittleman, and J. Kono RiceS.A. Crooker NHMFL, Los Alamos

Alexey Belyanin

Texas A&M University

Terahertz studies of collective excitations and microscopic physics in semiconductor

magneto-plasmas

NSF CAREERNSF OISE

N-doped InSb: a classic narrow-gap semiconductor

~ 0.2 eV

~ 0.8 eV

McCombe & Wagner 1975

Strong non-parabolicity;Non-equidistant cyclotron transitions

Small band gapSmall electron mass ~ 0.014 m0

Palik & Furdyna 1970

Many frequency scales in doped semiconductors fall intothe 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

THz time-domain spectroscopy

B

TransmitterReceiver

CPA laser1 KHz, 800 nm

CPA laser1 KHz, 800 nm

Current Amplifier

Lock_in amplifier

ZnTe1/4

WC

Delay stage

ZnTe

Sample: n-doped InSb crystalSample #1: density = 2.1E14 cm-3 Sample #2: density = 3.5E14 cm-3Sample #3 density = 6.1E14 cm-3

T = 1.6-300 Kf = 0.1-2.5THzB = 0-10 T

Incident and transmitted THz pulses

15

10

5

0

-5

x10-3

-30 -20 -10 0 10 20 30

1.375 Tesla

main peak1st multiple refleciton (MR) peak (sample)

2nd MR peak (sample)

1st MR peak from inner window

1st MR from outer window

The transmittance contour map of sample # 1

Magnetic field, Tesla

Fre

qu

ency

, T

Hz

• Plasma edge• Cyclotron resonance• Intra-donor transition lines at low T and high B• Interference features

T = 1.6 K T = 40 K

0.4

0.2

0.0210

1.5 Te

0.4

0.2

0.0

1 Td

0.4

0.2

0.0

0.25 Tb

0.4

0.2

0.0

0 T

a

0.4

0.2

0.0

Tra

nsm

ittan

ce

0.5 Tc

Experiment Theory

210

1.5 Tj

1 Ti

0.5 Th

0.25 Tg

0 T

f

Frequency (THz)

Transmittance at 40 K: only free-carrier effects expected

Free-carrier effects: interference of normal magnetoplasmon modes

“Cold” plasma approximation: ,,|| FTVk

FMS

n2

impuritiesphononsii

nhBh

ph

eBe

pee

)()(

222

...)()(

222

hBh

ph

eBe

peo iin

CRI CRA

BEi

~ 16

CRACRI

he

hehpe m

Ne

,

,2

2,

4 cm

Be

hehBe

,,

||

BepeBeoe 22,0 4

2

1

0.4

0.2

0.0210

1.5 Te

0.4

0.2

0.0

1 Td

0.4

0.2

0.0

0.25 Tb

0.4

0.2

0.0

0 T

a

0.4

0.2

0.0

Tra

nsm

ittan

ce

0.5 Tc

Experiment Theory

210

1.5 Tj

1 Ti

0.5 Th

0.25 Tg

0 T

f

Frequency (THz)

Transmittance at 40 K: only free-carrier effects expected

0.5 1 1.5 2 2.5

0.1

0.2

0.3

0.4

0.5 1 1.5 2 2.5

0.1

0.2

0.3

0.4

0.5 1 1.5 2 2.5

0.1

0.2

0.3

0.4

0.5 1 1.5 2 2.5

0.05

0.1

0.15

0.2

CRI

CRA

a

dc

b

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

2/1

*2||

22

||2

1

22

1

4

Bg

m

knE

EE B

eBeg

gn

]2/exp[~ TkENN Bbindne

3/13/12*

2

~)(

~ Bra

eE

BBohrstbind

eB

crB

2 A

ema

e

stBohr 600~~

2

2*

a

dc

bexperiment

theory

Temperature map at B = 0.9 T

0.20

0.15

0.10

0.05

0.00

Tra

nsm

ittan

ce

250200150100500

Temperature (K)

e

experiment

-0.2

-0.1

0.0

0.1

0.2

Tra

nsm

itted

Fie

ld

250200150100500

Temperature (K)

b

ordinary extraordinary interference

100

80

60

40

20

0

Imag

inar

y n e

, o

250200150100500

Temperature (K)

d

ne

no

400

300

200

100

0

Rea

l ne,

o

250200150100500

Temperature (K)

c

ne

no

0.20

0.15

0.10

0.05

0.00

Tra

nsm

ittan

ce

250200150100500

Temperature (K)

f

theory

5x1014

4

3

2

1

0

n i (

cm-3

)

20016012080

Temperature (K)

a

doping density

Position of the peak is very sensitive to thermal band gap EgT :

]2/exp[~ 2/3 TkETn BgTi

EgT = 0.215 eV

Electron scattering rate

0.4

0.3

0.2

0.1

0.0

(T

Hz)

3002001000Temperature (K)

(a)

8x105

6

4

2

0

(c

m-2

/Vs)

3002001000

Temperature (K)

(b)

Temperature dependence at B = 0.9 T

Impurity scattering

Polar optical phononsElectron-hole scattering

Scattering mechanisms:

• Ionized and neutral impurities• Acoustic deformation potential• Piezoelectric• Optical deformation potential• Polar optical phonons• intrinsic carriers

Electron-”ion” scattering in a strong magnetic field

http://hyperphysics.phy-astr.gsu.edu

TkEb

e

Tk

eb

b

LbrLbB

BkinsstBst

s

s

DsBDs

~~from~where

,ln~:or,0

22

2

Debye radius pe

FermiTD

VVL

],max[

~

s

BsDBs b

rbLrb ln~: 2Gyroradius:

classical~

quantum

pe

ThermalB

B

Vr

eB

cr

2

)(~from~where~:

223/1

2

23/42 effBe

effststeffeffDsB

bm

b

e

B

mcbBbLbr

Similar to magnetic white dwarfs and neutron stars!

Low-temperature effects: donor absorption lines and field-induced localization

measurements

1.6 K 40 KNn = 2.1x1014 cm-3

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Tra

nsm

ittan

ce (a.

u)

1.00.80.60.40.2

Frequency (THz)

2T

2.5T

3T

4T

5T

6T

7T

8T

8.5T

9T

9.5T

10T

Donor (tellurium) transition lines

McCombe & Wagner 1975

CRA 1s-2p+ transition (000)-(110)

CRI 1s-2p- transition (000)-(0-10)

Cyclotron resonance

Low-temperature effects: field-induced localization

T = 1.6 K, Nn = 2.1x1014 cm-3

Quantum phase transition metal-insulator?

Gradual magnetic freeze-out of carriers?

25.0~*3/1Bohrn aN

B = 0: Nn ~ 6x1013 cm-3

Edwards & Sienko 1978

T1~3/1*2*

cBohrBBohr Bara

Gao et al., APL 2006Shayegan et al. PRB 1988

]2/exp[~ TkENN Bbindne

3/13/12*

2

~)(

~ Bra

eE

BBohrbind

Mani et al., PRB 1989,1991

Freeze-out picture:

3/1]/1ln[~ln BNexx

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 … scBB

Efros & Shklovskii 1976 etc.

“Releasing” electrons at B ~ Bc

• 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

Conclusions

)(k