1. 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

2. 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)

3. 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 Time-evolution-closed trajectory in the parameter space U 1,2, - the charge is the contour integral of some “vector potential” along the contour

4. 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   and propagating with momentum q 0

5. THE WIRE AND THE PUMP-the adiabatic description The wire R.C., Andrei, Niu, PRB, 68, 165312 (03) 

6. THE WIRE-the adiabatic description The RG effective low-energy Hamiltonian: Luttinger liquid Gogolin, Nersesyan, Tsvelik, T. Giamarchi, Quantum Physics in one dimension, 2004

7. 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 :  k n,m =0

8. SPIN AND CHARGE CURRENTS The currents Keldysh formalism Tc-time ordering operator along the Keldysh contour L. Keldysh, JETP 20, 209 (79)

9. CHARGE CURRENTS-T=0 Pumping area Dynamic Stoner instability

10. 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

11. The current boundary contribution ( Sharma & Chamon 03 ):

12. PUMPED CURRENTS-T>0 Only the dynamical current factor is modified The non-interacting limit: K n0n1 n0s n1s =n 0 n 1 Kc/2+n 0s n 1s Ks/2 Ic=  0 max(  0,T)

13. NOISE SPECTRUM Noise spectrum Results Ohmic 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

14. 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