Fermi-Luttinger Liquid Fermi-Luttinger Liquid Leonid Glazman, U Leonid Glazman, U of M Maxim Khodas, of M Maxim Khodas, U of M U of M Michael Pustilnik, Georgia Michael Pustilnik, Georgia Tech Tech Alex Kamenev Alex Kamenev in collaboration with PRL 96, 196405 (2006); arXiv:cond-mat/0702.505 arXiv:cond-mat/0705.2015 RPMBT14, Jul., 2007
Fermi-Luttinger Liquid. Alex Kamenev. in collaboration with. Leonid Glazman, U of M Maxim Khodas, U of M. Michael Pustilnik, Georgia Tech. PRL 96 , 196405 (2006); arXiv:cond-mat/0702.505 arXiv:cond-mat/0705.2015. RPMBT14, Jul., 2007. One-dimensional …. Dekker et al 1997. - PowerPoint PPT Presentation
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Fermi-Luttinger Liquid Fermi-Luttinger Liquid
Leonid Glazman, U of M Leonid Glazman, U of M Maxim Khodas, U of MMaxim Khodas, U of MMichael Pustilnik, Georgia Tech Michael Pustilnik, Georgia Tech
Alex KamenevAlex Kamenev
in collaboration with
PRL 96, 196405 (2006); arXiv:cond-mat/0702.505arXiv:cond-mat/0705.2015
RPMBT14, Jul., 2007
One-dimensional …One-dimensional …
M. Chang, et al 1996 Dekker et al 1997 Bockrath, et al 1997
Auslaender et al 2004 I. Bloch 2004
Spectral Function
d>1: Fermi Liquid
Energy relaxation rate:
interaction potential
Spectral density:
The same for holes
d=1d=1
Energy relaxation rate:
? ?
Spectral density:
Luttinger modelLuttinger model
Dzaloshinskii, Larkin 1973
Energy relaxation rate:
Spectral density:
Luttinger model (cont)Luttinger model (cont)
Haldane, 1983
1D with non-linear dispersion: Holes 1D with non-linear dispersion: Holes
1D with non-linear dispersion: Particles1D with non-linear dispersion: Particles
Energy relaxation rate:
interaction potential Does not work for integrable models
Particles (cont)Particles (cont)
Fermi head with the Luttinger tail
Spectral Edges Spectral Edges
Shake up or X-ray singularity
(cf. Mahan, Nozieres,…)
Structure Factor Structure Factor
Luttinger approximation Luttinger approximation
Linear dispersion
Exact result within the Luttinger approximation.
How does the dispersion curvature and interactions affect the structure factor ?