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