Adiabatic quantum pumping in Adiabatic quantum pumping in nanoscale electronic devices nanoscale electronic devices Huan-Qiang Zhou, Sam Young Cho , Urban Lundin, and Ross H. McKenzie The University of Queensland [2] H. -Q. Zhou, U. Lundin, S. Y. Cho, and R. H. McKenzie, cond-mat/0309096 (2003) [1] H. -Q. Zhou, S. Y. Cho, and R. H. McKenzie, Phys. Rev. Lett. 91, 186803 (2003) Frontiers of Science & Technology Workshop on Condensed Matter & Nanoscale Physics and 13 th Gordon Godfrey Workshop on Recent Advances in Condensed Matter Physics
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Adiabatic quantum pumping in nanoscale electronic devices Adiabatic quantum pumping in nanoscale electronic devices Huan-Qiang Zhou, Sam Young Cho, Urban.
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outgoing scattering states = scattering matrix . incoming scattering states
At any given “frozen” time t
r
r
t
t=B
FAG
= AG
S
Scattering Geometric PhaseScattering Geometric PhaseScattering Geometric PhaseScattering Geometric Phase[H. -Q. Zhou, S. Y. Cho, and R. H. McKenzie, Phys. Rev. Lett. 91, 186803 (2003)]
r tQUANTUMQUANTUM DEVICEDEVICE
1ei
eiei
External parameters X(t)External parameters X(t)
ei originates from the unitary freedom in choosing the scattering states
How to observe scattering geometric phasesHow to observe scattering geometric phases[ H. -Q. Zhou, U. Lundin, S. Y. Cho, and R. H. McKenzie, cond-mat/0309096 (2003)]
[ Y. Ji, and coworkers, Science 290, 779 (2000)]
Geometric phase
Gauge potential
Time-reversedTime-reversed Scattering StatesScattering StatesTime-reversedTime-reversed Scattering StatesScattering States
x
r
r
t
tS=
EV(x(t))
r t
scattering statescattering state
x
E
t
time-reversedtime-reversed scattering state scattering state
rV(x(t))
ST=r
rt
t
At any given “frozen” time t
PumpingPumping Geometric Phase Geometric PhasePumpingPumping Geometric Phase Geometric Phase[P. W. Brouwer, Phys. Review B 58, R10135 (1998)]
For the time-reversed scattering states
Gauge potential
Pumped charge[c.f.] Brouwer formula for charge pumping
[H. -Q. Zhou, S. Y. Cho, and R. H. McKenzie, Phys. Rev. Lett. 91, 186803 (2003)]
[M. Switkes and coworkers, Science 283, 1905 (1999)]
Scattering states for Scattering states for spin pumpingspin pumpingScattering states for Scattering states for spin pumpingspin pumping
A+A-
G+G-
B+B-
F+F-
For spin dependent scatteringFor spin dependent scattering
At any given “frozen” time t
1
0
0
1+A+ A- eikx +
1
0
0
1+B+ B- e-ikx=L
A+
A-
G+
G-
B+
B-
F+
F-
S++ S+ -
S- + S- -
=
Magnetic atom
4 x 4 matrix
Magnetic atom
Adiabatic Spin Pumping CurrentAdiabatic Spin Pumping CurrentAdiabatic Spin Pumping CurrentAdiabatic Spin Pumping Current[H. -Q. Zhou, S. Y. Cho, and R. H. McKenzie, Phys. Rev. Lett. 91, 186803 (2003)]
ConclusionsConclusionsConclusionsConclusions
Adiabatic quantum pumping has a natural representation in terms of gauge fields defined on the space of system parameters.
We found a geometric phase accompanying scattering state in a cyclic and adiabatic variation of external parameters which
characterize an open system with a continuous energy spectrum.
Scattering geometric phase & pumping geometric phase are both sides of a coin !!