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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
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Page 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.

Dynamics of Quantal Heating in Electron Systems with Discrete Spectra

William Mayer1,2, S. Dietrich1,2, S. Vitkalov1, A. A. Bykov3,4

1. City College of City University of New York, New York 10031, USA2. Graduate Center of City University of New York, New York 10016, USA3. A. V. Rzhanov Institute of Semiconductor Physics, Novosibirsk 630090, Russia4. Novosibirsk State University, Novosibirsk 630090, Russia

Thursday, May 28, 2015

Quantum transport in 2D systemsMay 23 - 30, 2015, Luchon, France

Page 2: 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.

Strong nonlinear responses in 2DEG

โ€ขDue to MW pumping

โ€ขDue 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)

Page 3: 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.

Quantal Heating is effect of quantum mechanics on Joule Heating

โ€ข decreases conductivity

โ€ข occurs in electron systems with quantized spectrum

โ€ข does not exist in classical electron systems

J.Q. Zhang, S. Vitkalov, A.A. Bykov , Phys. Rev. B 80, 045310 (2009)

Page 4: 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.

Quantal Heating isโ€ฆ Apply bias , E

Spatial Spectral Diffusion

๏ฟฝโƒ—๏ฟฝ

Selective Flattening of

โˆ’๐œ• ๐‘“๐œ•๐‘ก

+๐ธ2๐œŽ ๐ท

โ‘

๐œˆ (๐œ– )๐œ•๐œ– [ ๐œˆ (๐œ– )2

๐œˆ02 ๐œ•๐œ– ๐‘“ (๐œ– )]= ๐‘“ (๐œ– )โˆ’ ๐‘“ ๐‘‡ (๐œ–)

๐œ ๐‘–๐‘›

Lower longitudinal conductivity

๐œŽ ๐‘›๐‘™=โˆซ๐œŽ (๐œ– )(โˆ’ ๐œ• ๐‘“๐œ•๐œ– )๐‘‘๐œ–

๐œ–๐‘ก๐‘œ๐‘ก๐‘Ž๐‘™=๐œ– ๐พ (๐‘ก)+๐‘’๐ธ x (t)

๐‘ฅ

I. A. Dmitriev, M. G. Vavilov, I. L.Aleiner, A. D. Mirlin, and D.G. Polyakov, Phys. Rev. B 71, 115316 (2005)

Page 5: 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.

Quantal Heating in the dc-domain

โˆ’๐œ• ๐‘“๐œ•๐‘ก

+๐ธ2๐œŽ ๐ท๐ถ

โ‘

๐œˆ (๐œ– )๐œ•๐œ– [๐œˆ (๐œ– )2

๐œˆ02 ๐œ• ๐‘“ (๐œ– )]= ๐‘“ (๐œ– )โˆ’ ๐‘“ ๐‘‡ (๐œ– )

๐œ ๐‘–๐‘›

โ€ข Gaussian DOS for electronsโ€ข Conductivity:โ€ข No electron spatial

redistribution from dc bias

๐œŽ ๐‘›๐‘™=โˆซ๐œŽ (๐œ– )(โˆ’ ๐œ• ๐‘“๐œ•๐œ– )๐‘‘๐œ–

Inelastic rate

Page 6: 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.

Why dynamics?โ€ข There is a difficulty with the inelastic

mechanism in MW domain: the polarization dependence seems does not agree with experiment.

โ€ข There is a nonlinearity related to spatial electron redistribution due to applied bias. The nonlinearity is comparable with quantal heating in SdH regime.

โ€ข SdH method indicates inelastic rate proportional to temperature TM.G. Blyumina, A. G. Denisov, T. A.

Polyanskaya, I. G. Savelโ€™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).

Page 7: 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.

Samples

r2=1mm

r1=0.9mm

โ€ข MBE grownโ€ข Selectively doped single

GaAs quantum wellsโ€ข GaAs/AlAs superlattice

barriers

Corbino geometry provides well determined radial field distribution. Important for nonlinear measurements

โ€ข High electron density decreases e-e scattering

โ€ข High mobility strong variations in the density of states

GaAs/AlAs

GaAs QW 13nm

Si

Page 8: 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.

๐œ”1๐œ”2

๐œ”=๐œ”1โˆ’๐œ”2

Dynamics of Quantal Heating:Difference Frequency Method

Total field:

where

Analyzer measures signal

Analyzer:

SRC: SRC:

LPF Bias-Tee

Lockin

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

Page 9: 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.

Dynamics of Quantal Heating

๐‘— ๐œ”=๐ธ0โˆซ๐œŽ ๐œ– [โˆ’๐œ•๐œ– ( ๐›ฟ ๐‘“ ๐œ” ) ] ๐‘‘ ๐œ–=2๐ธ0๐ธ1๐ธ2exp (๐‘–๐œ”๐‘ก )

๐‘– ๐œ”+1/๐œ ๐‘–๐‘›ฮฃ(๐ต)

โˆ’๐œ• ๐‘“๐œ•๐‘ก

+๐ธ2๐œŽ ๐ท

โ‘

๐œˆ (๐œ– )๐œ•๐œ– [ ๐œˆ (๐œ– )2

๐œˆ02 ๐œ•๐œ– ๐‘“ (๐œ– )]= ๐‘“ (๐œ– )โˆ’ ๐‘“ ๐‘‡ (๐œ–)

๐œ ๐‘–๐‘›

Heating (excitation)

Now time dependent & modulated by beating of two sources.

Cooling (relaxation)

๐‘“ = ๐‘“ ๐‘‡+๐›ฟ ๐‘“ ๐œ”&

We measure -signalโˆ๐ธ0๐ธ1๐ธ2

โˆš๐œ” 2+1/๐œ ๐‘–๐‘›2

Page 10: 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.

Magnetic Field Dependence

0.0 0.1 0.2 0.3 0.4 0.5 0.60

1

2

3

4

5

0.0

0.2

0.4

0.6

R(k

)

-s

igna

l (V

)

B (T)

f=1.0 MHz

Page 11: 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.

Dc Bias Dependence-signal โˆ

๐‘ฌ ๐ŸŽ ๐ธ1๐ธ2โˆš๐œ” 2+1/๐œ ๐‘–๐‘›2

-30 -20 -10 0 10 20 300.0

0.1

0.2

0.3

0.4

0.2

0.3

0.4

0.5

-s

ign

al (m

V)

Vdc

(mV)

1 MHz

r(k

)

1 GHz

1.5 GHz

T=4.8 KB=0.333 T

Page 12: 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.

Power Dependence-signal โˆ๐ธ0๐‘ฌ ๐Ÿ ๐‘ฌ ๐Ÿ

โˆš๐œ” 2+1/๐œ ๐‘–๐‘›2

-25 -15 -5 50.01

0.1

1

10

0 2 4 6 8 10 12 14 16185

190

195

200

205

210

215

220

225

20log(E1E

2) (dBm)

-s

ignal (m

V)

1 MHz 1 GHz 1.5GHz

T=4.8KB=0.33T

1.5 GHz

1 MHz

R (

Oh

m)

P1+P

2 (mW)

1 GHz

Page 13: 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.

Dynamics of Quantal Heating

-signal โˆ๐ธ0๐ธ1๐ธ2

โˆš๐Ž 2+1/๐œ ๐‘–๐‘›2/

Page 14: 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.

Dynamics of Quantal Heating

electron-phonon interactions

โˆ๐‘‡ 3

electron-electron interactions

โˆ๐‘‡ 2

Page 15: 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.

โˆ๐‘‡ 2

e-e interaction dominates

Dynamics of Quantal Heating

CV

๐‘˜๐‘‡ โ‰ซั›๐œ” ๐‘

e-phonon interaction dominates

โˆ๐‘‡ 3

๐‘˜๐‘‡ โ‰ˆั›๐œ”๐‘

J.Q. Zhang, S. Vitkalov, A.A. Bykov , Phys. Rev. B 80, 045310 (2009)

Page 16: 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.

Comparison of two methods

โ€ขOrder of magnitude agreement

โ€ข ฯ‰-signal is direct measurement

โ€ขdc-domain may experience electron spatial redistribution

Page 17: 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.

Conclusionsโ€ข direct

measurements of inelastic relaxation

โ€ข Observe T2 dependence for

โ€ข Approaches T3 dependence for

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

Page 18: 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.

Acknowledgements

https://sites.google.com/site/ccnymw

NSF DMR 1104503 & RFBR #14-02-01158

Thank You


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