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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