Transcript Yuval Oreg - Physics@Technion

Pumping in Interacting
Systems
Yuval Oreg
Department of Condensed Matter Physics
http://www.weizmann.ac.il/condmat/oreg_group.html
With Eran Sela
Outline
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What are pumps?
What are electron pumps?
Phase Coherent Pumps
Non coherent Pumps
General formula for interacting systems
The two channel Kondo system
Topological quantization of spin current
Effective magnetic field and Non Fermi liquid behavior
at finite T
• Conclusions
Heat pumps
• Sadi Nicholas Leonard
Carnot 1796-1832
• Work= Area
P
V
Single Electron Pumps –
Electron Turnstile
N+1
N+1
N+1
N
N
N
N+1
N
N+1
N+1
N
N
N+1
N
Single Electron Pumps
X2
X0
T
Pumps formulae
BPT [non interacting]
Hartree
X1
EC Brouwer
BPT
Interaction
Pumps formulae
T
Non coherent pumps
(Sela and YO PRB 2005)
EC Brouwer
BPT
Rate equations
Quantum - interacting
(Sela and YO PRL 2006)
Interaction
Non Coherent Pumps
With geometric interpretation
(Sela and YO PRB2005)
a
Asymmetry coefficient
Q charge on one of
the capacitor plates
Adiabatic limit
τ>RC
y
X0
x
Pure Spin Pumps
For 2DEG with area A
Prefers polarization
A=1μm2
When non coherent pumps
formula applies?
γ
L
δU
With dephasing
(using Buttiker’s model)
Classical non coherent result
With DOS ->1/C and
Transmission ->1/R
I /I
=
L kF =L/λF
Class
Coherent
T
Pumps formulae
Non coherent pumps
(Sela and YO PRB 2005)
EC Brouwer Rate equations
BPT
?
Interaction
Pumps (with interaction)
at low temp
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Kubo Formula
Aleiner and Matveev: Open dots (1998)
Sharma and Shamon: Lut-Liq (2001, 2003)
Citro et al: Lut – Liq (2003)
Cohen (2003): Applied to non interacting systems
Keldysh
• J. Splettstoesser et al.
(Average time approximation )
Central area may
depend on parameters
Left Lead
X1, X2
Right Lead
All parts (including leads) may have interactions
X2
X0
BPT (non interacting)
X1
Adiabatic Limit
O(δX2)
Relaxation
time
Curvature
X2
X0
X1
Geometric/Topologic
interpretation
Application to Dots
c
d
d
c
c
d
Average time Aprox.
εd
G
dQd=Adεd
A=#U2/(T2Γ)+U2/T3
-#U2/(T2Γ)
Infinite order in Γ second order in U,
Assume: U and Γ «T
Application to repulsive
quantum critical points
y
x
Spin pumps in
the two channel Kondo
x=Δ=J1-J2, y=h
At x=y=0 NFL point T1/2 sing.
Emery Kivelson Line
hГ
Δ=(J1 -J2)/Г=Cos( θ)
Kondo Temp
• Concentrated around r=1
• Integral over B=ћ
h0
Δ0
L2
1 Δ
Conclusions
• Non coherent pumps at high temp.
• A generic pumping formula for
interacting systems, with a
geometric interpretation.
• Application to two channel Kondo
physics with anomalous exponents
and interesting topology