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
)/2cos()(
)/2cos()()/2sin()()(
2,102,1
21
TtUtU
axtUaxtUvtxU
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 PUMPThe 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 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 descriptionThe 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)
Mirror symmetry breaking!!
G=2/l
Lattice momentum
Irrelevant
in the RG sense!
Commensurability: kn,m=0
SPIN AND CHARGE CURRENTSThe 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 B-field Spin direction Sharma, Chamon Phys. Rev. Lett. 2001
varying tunable
Mucciolo, Chamon, Marcus Phys. Rev. Lett. 2002
constant fixed
Tserkovnyak, Brataas, Bauer Phys. Rev. Lett. 2002
ferromagnet fixed
Aono Phys. Rev.B 2003
varying fixed
Governale, Taddei, Fazio Phys. Rev. B 2003
vary spin-orbit fixed
Sharma, Brouwer Phys. Rev. Lett. 2003
spin orbit tunable
The current boundary contribution (Sharma & Chamon 03):
PUMPED CURRENTS-T>0Only the dynamical current factor is modified
The non-interacting limit:
Kn0n1n0s n1s=n0n1Kc/2+n0sn1s Ks/2
Ic=0 max(0,T)
NOISE SPECTRUMNoise spectrum
ResultsOhmic noise with interaction dependent coefficient
New singularity at higher frequencies: Pumping contribution
Small
S(
Coloured noise
shot noise level
Similar to spectrum in
fractional Hall effect (Chamon, PRB 1999)
R.C. & N. Andrei, in preparation
WORK IN PROGRESS
EFFICIENT PUMPING MECHANISM: pure charge or spin current
GENERIC HAMILTONIAN: universal properties
EXPERIMENTAL REALIZATION: an oscillating current flowing through a meander line on top of the quantum wire
CONCLUSIONS
Noise in voltage spectrum
Rashba Spin-orbit interaction:investigate the role of Rashba SO (quadratic interaction) in spin pump device
CURRENTS:anomalous dependence on the frequency, the temperature and the size of the pump L