Spin Incoherent Quantum Wires Leon Balents Greg Fiete

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

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?

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

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

QPC = Low density wire? • “Spin incoherent regime” • Matveev (2004) argues: G = e 2/h (one orbital channel) with ideal metallic leads • Picture J(x) k. BT 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?

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

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” = ~/k. BT 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

Some explicit formulae

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

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 G. Fiete, K. Le Hur, and LB (2005) effective parameters geff = 2 gc and k. F, eff =2 k. F • 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

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

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 dot • J À T: RKKY/2 -impurity Kondo physics • J ¿ T: no communication between spins of dots • Spin incoherent physics in ultracold fermions in 1 d traps? - Measure hnki by expansion method T¿J hnki k. F k TÀ J hnki 2 k. F k

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?

Thanks