1. Dynamics of Quantal Heating in Electron Systems with Discrete Spectra William Mayer 1,2, S. Dietrich 1,2, S. Vitkalov 1, A. A. Bykov 3,4 1. City College of City University of New York, New York 10031, USA 2. Graduate Center of City University of New York, New York 10016, USA 3. A. V. Rzhanov Institute of Semiconductor Physics, Novosibirsk 630090, Russia 4. Novosibirsk State University, Novosibirsk 630090, Russia Thursday, May 28, 2015 Quantum transport in 2D systems May 23 - 30, 2015, Luchon, France

2. Strong nonlinear responses in 2DEG Due to MW pumpingDue to DC bias J.Q. Zhang, S. Vitkalov, A.A. Bykov Phys. Rev. B 80, 045310 (2009) M. A. Zudov, R. R. Du, L. N. Pfeiffer and K. W. West, Phys. Rev.Lett. 90, 046807 (2003) I. A. Dmitriev, M. G. Vavilov, I. L.Aleiner, A. D. Mirlin, and D.G. Polyakov, Phys. Rev. B 71, 115316 (2005) S. I. Dorozhkin, JETP Lett, 77, 577 (2003)

3. Quantal Heating is effect of quantum mechanics on Joule Heating decreases conductivity occurs in electron systems with quantized spectrum does not exist in classical electron systems J.Q. Zhang, S. Vitkalov, A.A. Bykov, Phys. Rev. B 80, 045310 (2009)

4. Quantal Heating is… Lower longitudinal conductivity I. A. Dmitriev, M. G. Vavilov, I. L.Aleiner, A. D. Mirlin, and D.G. Polyakov, Phys. Rev. B 71, 115316 (2005)

5. Quantal Heating in the dc-domain

6. Why dynamics? There is a difficulty with the inelastic mechanism in MW domain: the polarization dependence seems does not agree with experiment. There is a nonlinearity related to spatial electron redistribution due to applied bias. The nonlinearity is comparable with quantal heating in SdH regime. SdH method indicates inelastic rate proportional to temperature T M.G. Blyumina, A. G. Denisov, T. A. Polyanskaya, I. G. Savel’ev, A. P. Senichkin, and Yu. V. Schmartsev, JETP Lett., 44,257 (1986) Scott Dietrich, S. A. Vitkalov, D. V. Dmitriev and A. A. Bykov, Phys. Rev. B 85, 115312 (2012). J. H. Smet, et al Phys. Rev. Lett. 95, 116804 (2005).

7. Samples r 2 =1mm r 1 =0.9mm MBE grown Selectively doped single GaAs quantum wells GaAs/AlAs superlattice barriers Corbino geometry provides well determined radial field distribution. Important for nonlinear measurements High electron density  decreases e-e scattering High mobility  strong variations in the density of states GaAs/AlAs GaAs QW 13nm Si

8. Dynamics of Quantal Heating: Difference Frequency Method LPF Bias-Tee Lockin Scott Dietrich, William Mayer, Sergey Vitkalov, A. A. Bykov, cond-mat > arXiv:1410.2618, Phys. Rev. B 91, 205439 (2015).

9. Dynamics of Quantal Heating Heating (excitation) Now time dependent & modulated by beating of two sources. Cooling (relaxation) &

10. Magnetic Field Dependence

11. Dc Bias Dependence

12. Power Dependence

13. Dynamics of Quantal Heating

14. electron-phonon interactions electron-electron interactions

15. e-e interaction dominates Dynamics of Quantal Heating CVCV e-phonon interaction dominates J.Q. Zhang, S. Vitkalov, A.A. Bykov, Phys. Rev. B 80, 045310 (2009)

16. Comparison of two methods Order of magnitude agreement ω-signal is direct measurement dc-domain may experience electron spatial redistribution

17. Conclusions Scott Dietrich, William Mayer, Sergey Vitkalov, A. A. Bykov, cond-mat > arXiv:1410.2618, Phys. Rev. B 91, 205439 (2015)

18. Acknowledgements https://sites.google.com/site/ccnymw NSF DMR 1104503 & RFBR #14-02-01158 Thank You