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 (» e2/r, ~2/mr2 )• Recurring theoretical problem: How to connect

nano-structure to meso/macroscopic measuring devices?

Quantum Wires

• Theory: 1DEG

• Dimensionless gas parameter rs:

log rs rs À 1rs ¿ 1

Luttinger liquid theory

F

E

k

Quasi-Wigner crystal regime

• “phonons” ZB » F rs1/2

• spin exchange

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

QPC = Low density wire?

• Matveev (2004) argues: G = e2/h (one orbital channel) with ideal metallic leads

• “Spin incoherent regime”

• Picture J(x)

kBT coherent coherentincoherent

- “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• Introduce electron from outside via tunneling event

kF-kF kF-kF kF-kF 2kF

A(k,)

k

• Fermi liquid

» 2

• Luttinger liquid • Spin incoherent liquid

» 1/(4g)-1

Cheianov+ZvonarevGreg Fiete+L.B.

• 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

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” = ~/kBT

action too costly: negligible weight

all particles between initial and final point must have same spin

prob. of aligned spins Fermi statistics create/annihilate particle

Can be evaluated by a simple Gaussian integral

Some explicit formulae

Momentum Resolved TunnelingExperiment:Auslaender et al., Science 2002Theory:Carpentier et al., PRB 2002 (submitted 2000!)Tserkovnyak et al., PRL 2002Zulicke & 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

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

geff = 2gc and kF,eff =2kF

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<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”:

- 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?

2/(4kF)

• 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 dotwire

• 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 methodhnki

kkF

hnki

k2kF

T ¿ J TÀ J

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