Download THE WIRE AND THE PUMP

Spin and Charge Pumping
in an Interacting Quantum Wire
R. C., N. Andrei (Rutgers University, NJ), Q. Niu (The University
of Texas, Texas)
Quantum Pumping in the adiabatic limit
The (generic) system—The wire and the pump
-The LL fixed point and its neighborhood
- The pump: couples to electrons
- The wire: Luttinger Liquid, no fermionic excitations
==> anomalous response (in frequency, temperature, pump size)
Charge and spin currents
Current noise – Anomalous “coloured” noise
Quantum pump: A device that generates a dc
current by a periodic adiabatic variation of the system
characteristics-Thouless (83)
Quantization: integral of current over period is
quantized in system with full bands (robust against
disorder and interaction)-Niu and Thouless (84)
Mesoscopic systems: typically in quantum dots and
semiconductors- Sharma & Brouwer 03 (Theory), Switches (99),
Watson (03) (Experiments)
The oldest pump device:
Archimedean screw
B.L Altshuler & L.I. Glazman, Science
283 (1999)
Electron pump (Thouless 83)
One-dimensional electron gas in a sliding periodic
potential U(x-vt), with spatial period a
Interference-need interference of two waves to pump
U ( x  vt)  U1 (t ) sin( 2x / a )  U 2 (t ) cos( 2x / a )
U1, 2 (t )  U 0 cos( 2t / T  1, 2 )
Time-evolution-closed trajectory in the parameter
space U1,2, - the charge is the contour integral of some
“vector potential” along the contour
THE WIRE AND THE PUMP
The wire (exp. realization carbon nanotubes, organic conductor, ..)
The pump
The
Quantum
Pump-
a
spatially periodic potential (e.g.
meander line) acting on a segment
of finite length L oscillating in time
with frequency w0 and propagating
with momentum q0
THE WIRE AND THE PUMP-the
adiabatic description
The wire

R.C., Andrei, Niu, PRB, 68, 165312 (03)
THE WIRE-the adiabatic description
The RG effective low-energy Hamiltonian: Luttinger liquid
Gogolin, Nersesyan, Tsvelik,
T. Giamarchi, Quantum
Physics in one dimension,
2004
THE PUMP-the adiabatic description
Sum of the lattice Umklapp operators (transfer n electrons, ns
spin units from one Fermi point to the other)
Irrelevant
in the RG sense!
G=2/l
Lattice
momentum
Mirror symmetry breaking!!
Commensurability: Dkn,m=0
SPIN AND CHARGE CURRENTS
The currents
Keldysh formalism
Tc-time ordering operator along the Keldysh contour
L. Keldysh, JETP 20, 209 (79)
CHARGE CURRENTS-T=0
Pumping
area
Dynamic Stoner instability
SPIN CURRENTS-T=0
Spin current induced without magnetic field or spontaneous
symmetry breaking!!
Depending on n,n’, ns, ns’ we can have a pure spin current
Theoretical Proposals
Sharma, Chamon
Phys. Rev. Lett. 2001
Mucciolo, Chamon, Marcus
Phys. Rev. Lett. 2002
Tserkovnyak, Brataas, Bauer
Phys. Rev. Lett. 2002
Aono
Phys. Rev.B 2003
Governale, Taddei, Fazio
Phys. Rev. B 2003
Sharma, Brouwer
Phys. Rev. Lett. 2003
B-field
varying
Spin direction
tunable
constant
fixed
ferromagnet
fixed
varying
fixed
vary spin-orbit
fixed
spin orbit
tunable
The current boundary contribution (Sharma & Chamon 03):
PUMPED CURRENTS-T>0
Only the dynamical current factor is modified
Kn0n1n0s n1s=n0n1Kc/2+n0sn1s Ks/2
The non-interacting limit:
Ic=w0 max(w0,T)
NOISE SPECTRUM
Noise spectrum
Ohmic noise with interaction
dependent coefficient
Results
S(w)
New singularity at higher frequencies:
Pumping contribution
Coloured
noise
shot noise level
Small w
Similar to spectrum in
fractional Hall effect
(Chamon, PRB 1999)
R.C. & N. Andrei, in preparation
CONCLUSIONS
EFFICIENT PUMPING
charge or spin current
MECHANISM:
pure
GENERIC HAMILTONIAN: universal properties
CURRENTS:anomalous dependence on the frequency,
the temperature and the size of the pump L
EXPERIMENTAL REALIZATION: an oscillating
current flowing through a meander line on top of the
quantum wire
WORK IN PROGRESS
Noise in voltage spectrum
Rashba Spin-orbit interaction:investigate the role of
Rashba SO (quadratic interaction) in spin pump device