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Magnetothermopower
in high-mobility 2D electron gas:
effect of microwave irradiation
Oleg Raichev
Department of Theoretical Physics
Institute of Semiconductor Physics, Kiev, Ukraine
[email protected]
MIRO in high-mobility 2D electron gas in magnetic field. Photonassisted electron scattering in the regime of Landau quantization.
displacement
inelastic
MIRO in high-mobility 2D electron gas in magnetic field. Photonassisted electron scattering in the regime of Landau quantization.
displacement
inelastic
What about transport coefficients other than resistance?
The same mechanisms are involved.
Motivation: 1. Search for new effects
2. Verification of theoretical concepts
Let us study the magnetothermoelectric phenomena!
Outline

Brief review of thermoelectric physics and experimental
studies of thermopower in 2D systems.
 What is expected under microwave irradiation?
 Theoretical approach to the problem of thermoelectric
current and thermopower in the presence of microwaves.
 Presentation of results, discussion, conclusions.
V
Seebeck (1821)
Nernst, Ettingshausen
Longitudinal thermovoltage
Transverse thermovoltage
jT  ̂T
ˆ and ˆ have similar symmetry
 yy   xx ,  yx    xy ~ (c tr )  xx
j  ˆE  ˆT
j  0  E  ˆT , ˆ  ˆˆ , ˆ  ˆ 1
̂ is the thermopow er tensor (V/K)
Two mechanisms
Diffusive
Phonon drag
 f p 
e

 f p
T   eE  [ v p  B]  
v p  
 J pim  J pph
c

 p
 T 
2
ˆ
ˆ  
T
3 | e |  F
E ph
Mott relation
Degenerate electron gas
Quasi-equilibrium
ms  

T Effective “electric field”

 | e | T tr , ph
 yy   xx ,  yx    xy  (c tr )  xx
ˆ  ˆ 1ˆ ~ 1̂ (diagonal)
Quantum magnetotransport: Shubnikov-de Haas oscillations.
For 2D electrons phonon drag dominates at T> 0.5 K
(experiments in GaAs QWs)
J. Zhang, et al.
PRL 92, 156802 (2004)
GaAs, m2 x 106 cm2/Vs
Longitudinal thermopower
SdH oscillations at B>0.5 T
Magnetophonon oscillations (similar to PIRO in resistance).
Mechanism: resonant phonon-assisted backscattering of electrons.
 ph  qs  2 pF s  nc
MIRO are observed in samples of similar mobility
in the same region of magnetic fields
Under MW irradiation
1. 2DEG is far away from equilibrium: distribution function is strongly
modified near Fermi energy.
Violation of Mott relation for diffusive mechanism.
Additional terms in thermopower appear in the quantum transport regime.
Under MW irradiation
1. 2DEG is far away from equilibrium: distribution function is strongly
modified near Fermi energy.
Violation of Mott relation for diffusive mechanism.
Additional terms in thermopower appear in the quantum transport regime.
2. Influence of MWs on electron-phonon interaction: combined phononand photon-assisted scattering.
Contribution of phonon drag mechanism is modified.
Picture of quantum oscillations is changed (combined resonances).
Under MW irradiation
1. 2DEG is far away from equilibrium: distribution function is strongly
modified near Fermi energy.
Violation of Mott relation for diffusive mechanism.
Additional terms in thermopower appear in the quantum transport regime.
2. Influence of MWs on electron-phonon interaction: combined phononand photon-assisted scattering.
Contribution of phonon drag mechanism is modified.
Picture of quantum oscillations is changed (combined resonances).
3. Polarization of MW field is a source of transport anisotropy.
Symmetry of thermopower tensor is changed. Sensitivity to polarization.
Under MW irradiation
1. 2DEG is far away from equilibrium: distribution function is strongly
modified near Fermi energy.
Violation of Mott relation for diffusive mechanism.
Additional terms in thermopower appear in the quantum transport regime.
2. Influence of MWs on electron-phonon interaction: combined phononand photon-assisted scattering.
Contribution of phonon drag mechanism is modified.
Picture of quantum oscillations is changed (combined resonances).
3. Polarization of MW field is a source of transport anisotropy.
Symmetry of thermopower tensor is changed. Sensitivity to polarization.
4. Since the drift current compensates thermoelectric current, longitudinal
resistivity, which is strongly modified by MWs, enters the thermopower.
MIRO can be seen in transverse thermopower.
 xx   xy  yx   xx  xx   xy  yx [(c tr ) 2  1]
 xy   xy  xx   xx  xy   xy( 0)  (  xx   xx( 0) )  xy( 0)
Theoretical approach
Quantum Boltzmann equation
jT  ̂T
ˆ  ˆˆ
approximations: overlapping Landau levels, neglect of SdH oscillations
Dark thermopower results (phonon drag only):
G1 : B-independent (classical TP)
Gc1: oscillating with B (quantum TP)
q scattering angle
j polar angle of phonon wave vector (in 2D plane)
z inclination angle of phonon wave vector
Calculated dark thermopower (both mechanisms included)
Magnetophonon oscillations both in longitudinal and transverse TP
Amplitude increases until Bloch-Gruneisen temperature is reached
MW-induced longitudinal thermopower
inelastic and displacement mechanisms (the same as in resistance)
b describes MW polarization effect
  polarization angle
p – radiative decay rate
Calculated MW-induced longitudinal thermopower
inelastic mechanism
displacement mechanism
Calculated MW-induced longitudinal thermopower
inelastic mechanism
displacement mechanism
Effect of MW on TP is small
compared to effect on resistance
impurity-assisted (resistance)
fixed transition energy
phonon-assisted (TP)
average over phonon energies
MW-induced transverse thermopower
Polarization-dependent term in transverse TP is of dissipationless nature.
MW-induced anisotropy
Dissipationless thermoinduced current is not perpendicular toT
T
no MW
E
j
E
j
T
Vx
E
T
with MW
T
Vx
Vy
Calculated MW-induced transverse thermopower
dash: dark thermopower
Small T and B : mostly MIRO in transverse TP
Higher T and B: polarization dependent transverse TP
For higher mobility the polarization dependent part is more important
Amplitude of polarization dependent term in transverse thermopower
Conclusions
A theory is developed to describe effects of Landau quantization
in thermopower (TP) both without and with MW irradiation

Magnetophonon oscillations due to phonon drag are present
both in longitudinal and transverse TP.

Microwave irradiation adds quantum corrections to TP tensor.
Relative changes are small for longitudinal TP and large for
transverse TP.
MIRO can be observed in the transverse TP.
Transverse TP, unlike the resistance, is strongly sensitive to
linear polarization of microwaves.


Experimental studies are desirable
Thank you for the attention
Description of microwave field
MW
Et(i)
incident Et(i) : linear polarization
in plane Et : elliptical polarization
Et
2D plane
  polarization angle
p – radiative decay
rate
Expressions for collision integrals
3D phonon model
spatially anisotropic phonon distribution
Thermoelectric tensor (phonon-drag)
Thermoelectric tensor (diffusive)