Magnetothermopower in high-mobility 2D electron gas:

effect of microwave irradiation

Oleg Raichev

Department of Theoretical PhysicsInstitute of Semiconductor Physics, Kiev, Ukraine

raichev@isp.kiev.ua

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)