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

2. Nanoelectronics 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 (» e 2 /r, ~ 2 /mr 2 ) Recurring theoretical problem: How to connect nano-structure to meso/macroscopic measuring devices?

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

4. Conductance Experiments Conductance (“0.7”) anomalies in quantum point contacts Similar observations in gated nanotubes Biercuk et al, 2005 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

5. QPC = Low density wire? Matveev (2004) argues: G = e 2 /h (one orbital channel) with ideal metallic leads “Spin incoherent regime” Picture J(x) kBTkBT coherent incoherent - “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 Introduce electron from outside via tunneling event kFkF -k F kFkF kFkF 2k F A(k,  ) k Fermi liquid » 2» 2 Luttinger liquid Spin incoherent liquid »  1/(4g)-1 Cheianov+Zvonarev Greg Fiete+L.B. Notable features: -No coherent single-particle propagation -Change k F ! 2k F : 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? Cheianov+Zvonarev Our calculation Basic idea: Feynmann world-line path integral - J ¿ T: no crossings of world lines in “time”  = ~/k B T action too costly: negligible weight all particles between initial and final point must have same spin prob. of aligned spinsFermi statisticscreate/annihilate particle Can be evaluated by a simple Gaussian integral

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 More recent experiments with one wire gated to low density: k » A(k,  ¼ 0) 2 lobes -interplay of disorder and interactions complicated Detailed analysis specific to these experiments: Fiete et al, cond-mat/0501684. (no L.B.!) Steinberg et al, cond-mat/0506812

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 eff = 2g c and k F,eff =2k F G. Fiete, K. Le Hur, and LB (2005) This can lead to interesting behavior with temperature e.g. Scattering from a single impurity with ½<g c <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=2k F (LSM, Affleck, Oshikawa) “usually” g c >1/3 : 2k F 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? 2  /(4k F ) Heisenberg chain has 1/r staggered dimer fluctuations - spin-phonon coupling leads to period 2 density oscillations

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 dot wire 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 hn k i by expansion method hnkihnki k kFkF hnkihnki k2k F T ¿ JTÀ J

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