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Spin and Charge Pumping in an Interacting Quantum Wire

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

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Spin and Charge Pumping in an Interacting Quantum Wire

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  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 U1,2, - 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 w0 and propagating with momentum q0

  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) Irrelevant in the RG sense! G=2p/l Lattice momentum Mirror symmetry breaking!! Commensurability: Dkn,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 Kn0n1n0s n1s=n0n1Kc/2+n0sn1s Ks/2 The non-interacting limit: Ic=w0 max(w0,T)

  13. NOISE SPECTRUM Noise spectrum Ohmic noise with interaction dependent coefficient Results New singularityat higher frequencies: Pumping contribution S(w) Similar to spectrum in fractional Hall effect (Chamon, PRB 1999) Coloured noise shot noise level R.C. & N. Andrei, in preparation Small w

  14. CONCLUSIONS EFFICIENT PUMPING MECHANISM:pure charge or spin current 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

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