Download Spin Incoherent Quantum Wires

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:
rs ¿ 1
log rs
Luttinger liquid theory
F
rs À 1
Quasi-Wigner crystal regime
E
k
• “phonons” ZB » F rs1/2
• 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 = e2/h (one orbital channel)
with ideal metallic leads
• Picture
J(x)
kBT
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
A(k,)
» 1/(4g)-1
» 2
-kF
kF
• Fermi liquid
k
-kF
kF
• Luttinger liquid
-kF
kF
2kF
• Spin incoherent
liquid
• 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?
• Our calculation
• Cheianov+Zvonarev
• Basic idea: Feynmann world-line path integral
- J ¿ T: no crossings of world lines in “time”  = ~/kBT
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
• More recent experiments
with one wire gated to low
density:
k
» A(k,¼ 0)
-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
G. Fiete, K. Le Hur, and LB (2005)
effective parameters
geff = 2gc and kF,eff =2kF
• 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=2kF
• “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
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 hnki by expansion method
T¿J
hnki
hnki
kF
k
TÀ J
2kF
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