Transcript 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 ( » 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 • 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 • 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 • 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?Charge Correlations
Future Directions
Theoretical Issues
Thanks