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: 1DEG • Dimensionless gas parameter r s : r s ¿ 1 log r s Luttinger liquid theory r s À 1 Quasi-Wigner crystal regime E  F k • “phonons”  ZB »  F r s 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 B T coherent incoherent coherent “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 »  2 A(k,  ) »  1/(4g)-1

-k F k F

• Fermi liquid

k -k F k F

• Luttinger liquid

-k F k F 2k F

• Spin incoherent liquid • 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

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 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= eV  k=eB/mc Steinberg

et al

, cond-mat/0506812 » A(k,  ¼ 0) • More recent experiments with one wire gated to low density: k -interplay of disorder and 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 effective parameters G. Fiete, K. Le Hur, and LB (2005) g eff = 2g c and k F,eff =2k F • This can lead to interesting behavior with temperature e.g. Scattering from a single impurity with ½

and

defects is an open theoretical problem

Charge Correlations

• Low temperature: “Luttinger theorems”: (LSM, Affleck, Oshikawa) - power-law charge correlations at Q=2k F • “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? • Heisenberg chain has 1/r 2  /(4k F )

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 1d traps?

- Measure hn k i by expansion method hn k i hn k i T ¿ J T À J k F k 2k F k

Theoretical Issues

• Dynamics at long times: -0

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