Dynamics of Quantal Heating in Electron Systems with

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 Quantum transport in 2 D systems May 23 - 30, 2015, Luchon, France Thursday, May 28, 2015

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

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)

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)

Quantal Heating in the dc-domain

Why dynamics? • There is a difficulty with the inelastic mechanism in MW domain: the polarization dependence seems does not agree with experiment. J. H. Smet, et al Phys. Rev. Lett. 95, 116804 (2005). • There is a nonlinearity related to spatial electron redistribution due to applied bias. The nonlinearity is comparable with quantal heating in Sd. H regime. Scott Dietrich, S. A. Vitkalov, D. V. Dmitriev and A. A. Bykov, Phys. Rev. B 85, 115312 (2012). • Sd. H 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)

Samples Si Ga. As/Al. As • MBE grown • Selectively doped single Ga. As quantum wells • Ga. As/Al. As superlattice barriers • High electron density decreases e-e scattering • High mobility strong variations in the density of states Ga. As QW r 1=0. 9 mm r 2=1 mm 13 nm Corbino geometry provides well determined radial field distribution. Important for nonlinear measurements

Dynamics of Quantal Heating: Difference Frequency Method LPF Bias-Tee Lockin Scott Dietrich, William Mayer, Sergey Vitkalov, A. A. Bykov, cond-mat > ar. Xiv: 1410. 2618, Phys. Rev. B 91, 205439 (2015)

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

Magnetic Field Dependence

Dc Bias Dependence •

Power Dependence

Dynamics of Quantal Heating

Dynamics of Quantal Heating electron-phonon interactions electron-electron interactions

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

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

Conclusions • Scott Dietrich, William Mayer, Sergey Vitkalov, A. A. Bykov, cond-mat > ar. Xiv: 1410. 2618, Phys. Rev. B 91, 205439 (2015)

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