Spin Incoherent Quantum Wires

1. Spin Incoherent Quantum Wires Leon Balents Greg Fiete Karyn Le Hur Frontiers of Science within Nanotechnology, BU August 2005

2. Atomic/molecular control many energy/length scales, individually controllable can access interesting physics with “emergent” or engineered separation of scales Small size = large Coulomb and large kinetic energy (» e2/r, ~2/mr2 ) Recurring theoretical problem: How to connect nano-structure to meso/macroscopic measuring devices? Nanoelectronics

3. Quantum Wires Theory: 1DEG Dimensionless gas parameter rs: rs¿ 1 log rs rsÀ 1 Quasi-Wigner crystal regime Luttinger liquid theory E F “phonons” ZB»F rs1/2 k spin exchange

4. Conductance Experiments Conductance (“0.7”) anomalies in quantum point contacts Thomas et al, 1996; widely reproduced since. • “plateau” better developed at intermediate temperatures • conductance moves toward G=0.5 (2 e^2/h) in longer constrictions Similar observations in gated nanotubes Biercuk et al, 2005

5. QPC = Low density wire? “Spin incoherent regime” Matveev (2004) argues: G = e2/h (one orbital channel) with ideal metallic leads Picture J(x) coherent incoherent coherent kBT - “hot” spin excitations in leads too energetic to penetrate into wire Competing scenarios: Kondo (Meir et al), Ferromagnetism (various) - try to distinguish by other properties?

6. Spectral Properties Cheianov+Zvonarev Greg Fiete+L.B. Introduce electron from outside via tunneling event A(k,) »2 »1/(4g)-1 k -kF kF -kF kF -kF kF 2kF Spin incoherent liquid Fermi liquid Luttinger liquid • Notable features: • No coherent single-particle propagation • Change kF! 2kF: spinless particles at total density • enhancement of local DOS: all spin states ¼ degenerate diverges for g>1/4

7. How to get these results? Our calculation Cheianov+Zvonarev • Basic idea: Feynmann world-line path integral - J ¿ T: no crossings of world lines in “time”  = ~/kBT all particles between initial and final point must have same spin action too costly: negligible weight Can be evaluated by a simple Gaussian integral prob. of aligned spins Fermi statistics create/annihilate particle

8. Some explicit formulae

9. Momentum Resolved Tunneling Experiment: Auslaender et al., Science 2002 Theory: Carpentier et al., PRB 2002 (submitted 2000!) Tserkovnyak et al., PRL 2002 Zulicke & Governale, PRB 2002 E= eV k=eB/mc Steinberg et al, cond-mat/0506812 More recent experiments with one wire gated to low density: » A(k,¼ 0) k • interplay of disorder and interactions complicated Detailed analysis specific to these experiments: Fiete et al, cond-mat/0501684. (no L.B.!) 2 lobes

10. Transport Properties • Suppose non-magnetic impurities/defects are introduced inside the spin incoherent wire. - General result: transport within the incoherent region is identical to that of a spinless Luttinger liquid with effective parameters G. Fiete, K. Le Hur, and LB (2005) geff = 2gc and kF,eff =2kF This can lead to interesting behavior with temperature e.g. Scattering from a single impurity with ½<gc<1 • increases with decreasing temperature for T¿ J • decreases with decreasing temperature for TÀ J Combination of coupling to coherent leads and defects is an open theoretical problem

11. Charge Correlations • Low temperature: “Luttinger theorems”: - power-law charge correlations at Q=2kF (LSM, Affleck, Oshikawa) “usually” gc>1/3 : 2kF oscillations longest-range they must disappear when TÀ J may have implications for drag and impurity scattering when T passes through J ? Why 2k_F correlations at all in the Wigner picture? • Heisenberg chain has 1/r staggereddimer fluctuations - spin-phonon coupling leads to period 2 density oscillations 2/(4kF)

12. Future Directions • Experiments to directly observe spin-incoherent physics? - Would like to see coherent spin transport “turn on/off” when T » J e.g very naïve geometry wire dot dot J À T: RKKY/2-impurity Kondo physics J ¿ T: no communication between spins of dots • Spin incoherent physics in ultracold fermions in 1d traps? - Measure hnki by expansion method hnki hnki T ¿ J TÀ J k 2kF k kF

13. Theoretical Issues • Dynamics at long times: • 0<J ¿ T: all spin configurations equally likely at any instant, in equilibrium • spins frozen for t < 1/J. • what do spins do for t>1/J? • Diffusion? naively guess spin flip rate » J • integrability of Heisenberg chain: no diffusion? • impact on charge transport, spectral properties? • Equilibration time? • How long does it take to sample full set of spin configurations? • Hyperfine interaction with nuclei important?

14. Thanks