Magnetothermopower in high-mobility 2D electron gas:
effect of microwave irradiation
Oleg Raichev
Department of Theoretical PhysicsInstitute of Semiconductor Physics, Kiev, Ukraine
displacement inelastic
MIRO in high-mobility 2D electron gas in magnetic field. Photon-assisted electron scattering in the regime of Landau quantization.
MIRO in high-mobility 2D electron gas in magnetic field. Photon-assisted electron scattering in the regime of Landau quantization.
What about transport coefficients other than resistance? The same mechanisms are involved.
Motivation: 1. Search for new effects 2. Verification of theoretical conceptsLet us study the magnetothermoelectric phenomena!
displacement inelastic
OutlineOutline
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.
Seebeck (1821)Longitudinal thermovoltage
Nernst, EttingshausenTransverse thermovoltage
TT j
T ˆˆEj
1ˆˆ,ˆˆˆ,ˆ0 TEj
(V/K) er tensor thermopow theis
xxtrcxyyxxxyy )(~, symmetrysimilar have ˆ andˆ
V
Two mechanisms
F
Te
ˆ
||3ˆ
2 Mott relation Degenerate electron gasQuasi-equilibrium
TTems
phtrph
,||E Effective “electric field”
Diffusive
Phonon drag
xxtrcxyyxxxyy )(, (diagonal) 1~ˆˆˆ 1
Quantum magnetotransport: Shubnikov-de Haas oscillations.
phim JJf
ce
eTT
fpp
pp
pp p
BvEv
][
For 2D electrons phonon drag dominates at T> 0.5 K (experiments in GaAs QWs)
J. Zhang, et al. PRL 92, 156802 (2004)GaAs,x 106 cm2/Vs
Longitudinal thermopower
SdH oscillations at B>0.5 T
cFph nspqs 2
Magnetophonon oscillations (similar to PIRO in resistance).Mechanism: resonant phonon-assisted backscattering of electrons.
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 phonon- and 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 phonon- and 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 phonon- and 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, longitudinalresistivity, which is strongly modified by MWs, enters the thermopower. MIRO can be seen in transverse thermopower.
)0()0()0(
2
)(
]1)[(
xyxxxxxyxyxxxxxyxy
trcyxxyxxxxyxxyxx
Theoretical approach
Quantum Boltzmann equation
approximations: overlapping Landau levels, neglect of SdH oscillations
ˆˆˆ TT j
Dark thermopower results (phonon drag only):
scattering anglepolar angle of phonon wave vector (in 2D plane)inclination angle of phonon wave vector
B-independent (classical TP)
c1: oscillating with B (quantum TP)
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 anglep – radiative decay rate
Calculated MW-induced longitudinal thermopowerinelastic mechanism displacement mechanism
Calculated MW-induced longitudinal thermopowerinelastic mechanism displacement mechanism
Effect of MW on TP is small compared to effect on resistance
impurity-assisted (resistance) phonon-assisted (TP)fixed transition energy average over phonon energies
MW-induced transverse thermopower
T
Ej
T
j
xV
E T T
E
xV
yV
Polarization-dependent term in transverse TP is of dissipationless nature. MW-induced anisotropy Dissipationless thermoinduced current is not perpendicular to
no MW with MW
T
Calculated MW-induced transverse thermopower
Small T and B : mostly MIRO in transverse TPHigher T and B: polarization dependent transverse TP
For higher mobility the polarization dependent part is more important
dash: dark thermopower
Amplitude of polarization dependent term in transverse thermopower
Conclusions Conclusions
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
A theory is developed to describe effects of Landau quantization in thermopower (TP) both without and with MW irradiation
Thank you for the attention Thank you for the attention
incident Et(i) : linear polarization in plane Et : elliptical polarization
MWEt(i)
Et
2D plane
Description of microwave field
polarization anglep – radiative decay rate
3D phonon model
spatially anisotropic phonon distribution
Expressions for collision integrals
Thermoelectric tensor (phonon-drag)
Thermoelectric tensor (diffusive)