Date post: | 21-Dec-2015 |
Category: |
Documents |
Upload: | mervin-green |
View: | 215 times |
Download: | 0 times |
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
Strong nonlinear responses in 2DEG
โขDue to MW pumping
โขDue 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)
Quantal Heating is effect of quantum mechanics on Joule Heating
โข decreases conductivity
โข occurs in electron systems with quantized spectrum
โข does not exist in classical electron systems
J.Q. Zhang, S. Vitkalov, A.A. Bykov , Phys. Rev. B 80, 045310 (2009)
Quantal Heating isโฆ Apply bias , E
Spatial Spectral Diffusion
๏ฟฝโ๏ฟฝ
Selective Flattening of
โ๐ ๐๐๐ก
+๐ธ2๐ ๐ท
โ
๐ (๐ )๐๐ [ ๐ (๐ )2
๐02 ๐๐ ๐ (๐ )]= ๐ (๐ )โ ๐ ๐ (๐)
๐ ๐๐
Lower longitudinal conductivity
๐ ๐๐=โซ๐ (๐ )(โ ๐ ๐๐๐ )๐๐
๐๐ก๐๐ก๐๐=๐ ๐พ (๐ก)+๐๐ธ x (t)
๐ฅ
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
โ๐ ๐๐๐ก
+๐ธ2๐ ๐ท๐ถ
โ
๐ (๐ )๐๐ [๐ (๐ )2
๐02 ๐ ๐ (๐ )]= ๐ (๐ )โ ๐ ๐ (๐ )
๐ ๐๐
โข Gaussian DOS for electronsโข Conductivity:โข No electron spatial
redistribution from dc bias
๐ ๐๐=โซ๐ (๐ )(โ ๐ ๐๐๐ )๐๐
Inelastic rate
Why dynamics?โข There is a difficulty with the inelastic
mechanism in MW domain: the polarization dependence seems does not agree with experiment.
โข There is a nonlinearity related to spatial electron redistribution due to applied bias. The nonlinearity is comparable with quantal heating in SdH regime.
โข SdH method indicates inelastic rate proportional to temperature TM.G. Blyumina, A. G. Denisov, T. A.
Polyanskaya, I. G. Savelโev, 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).
Samples
r2=1mm
r1=0.9mm
โข MBE grownโข Selectively doped single
GaAs quantum wellsโข GaAs/AlAs superlattice
barriers
Corbino geometry provides well determined radial field distribution. Important for nonlinear measurements
โข High electron density decreases e-e scattering
โข High mobility strong variations in the density of states
GaAs/AlAs
GaAs QW 13nm
Si
๐1๐2
๐=๐1โ๐2
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).
Dynamics of Quantal Heating
๐ ๐=๐ธ0โซ๐ ๐ [โ๐๐ ( ๐ฟ ๐ ๐ ) ] ๐ ๐=2๐ธ0๐ธ1๐ธ2exp (๐๐๐ก )
๐ ๐+1/๐ ๐๐ฮฃ(๐ต)
โ๐ ๐๐๐ก
+๐ธ2๐ ๐ท
โ
๐ (๐ )๐๐ [ ๐ (๐ )2
๐02 ๐๐ ๐ (๐ )]= ๐ (๐ )โ ๐ ๐ (๐)
๐ ๐๐
Heating (excitation)
Now time dependent & modulated by beating of two sources.
Cooling (relaxation)
๐ = ๐ ๐+๐ฟ ๐ ๐&
We measure -signalโ๐ธ0๐ธ1๐ธ2
โ๐ 2+1/๐ ๐๐2
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
Dc Bias Dependence-signal โ
๐ฌ ๐ ๐ธ1๐ธ2โ๐ 2+1/๐ ๐๐2
-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
Power Dependence-signal โ๐ธ0๐ฌ ๐ ๐ฌ ๐
โ๐ 2+1/๐ ๐๐2
-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
Dynamics of Quantal Heating
-signal โ๐ธ0๐ธ1๐ธ2
โ๐ 2+1/๐ ๐๐2/
Dynamics of Quantal Heating
electron-phonon interactions
โ๐ 3
electron-electron interactions
โ๐ 2
โ๐ 2
e-e interaction dominates
Dynamics of Quantal Heating
CV
๐๐ โซั๐ ๐
e-phonon interaction dominates
โ๐ 3
๐๐ โั๐๐
J.Q. Zhang, S. Vitkalov, A.A. Bykov , Phys. Rev. B 80, 045310 (2009)
Comparison of two methods
โขOrder of magnitude agreement
โข ฯ-signal is direct measurement
โขdc-domain may experience electron spatial redistribution
Conclusionsโข direct
measurements of inelastic relaxation
โข Observe T2 dependence for
โข Approaches T3 dependence for
Scott Dietrich, William Mayer, Sergey Vitkalov, A. A. Bykov, cond-mat > arXiv:1410.2618, Phys. Rev. B 91, 205439 (2015)
Acknowledgements
https://sites.google.com/site/ccnymw
NSF DMR 1104503 & RFBR #14-02-01158
Thank You