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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 ˆT j 0 E ˆT , ˆ ˆˆ , 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 1ˆ ~ 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, m2 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 nc 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 ˆˆ 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 toT 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)