luttinger liquids n.
Skip this Video
Loading SlideShow in 5 Seconds..
Luttinger Liquids PowerPoint Presentation
Download Presentation
Luttinger Liquids

Loading in 2 Seconds...

play fullscreen
1 / 14

Luttinger Liquids - PowerPoint PPT Presentation

  • Uploaded on

Luttinger Liquids. Kevin Chan Cohen Group Meeting May 2, 2007. Introduction. Luttinger Liquid: system of 1D interacting fermions Reasons for interest: Strong correlations Real (quasi-)1D systems available experimentally Exactly solvable. Fermi Liquid Landau

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

Luttinger Liquids

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
luttinger liquids

Luttinger Liquids

Kevin Chan

Cohen Group Meeting

May 2, 2007

Cohen Group Meeting

  • Luttinger Liquid: system of 1D interacting fermions
  • Reasons for interest:
    • Strong correlations
    • Real (quasi-)1D systems available experimentally
    • Exactly solvable

Cohen Group Meeting

fermi vs luttinger liquid
Fermi Liquid


Elementary excitations are quasiparticles (fermions)

1-1 correspondence between quasiparticles and excitations of FEG

Weak correlations

Luttinger Liquid

Tomonaga, Luttinger

Elementary excitations are collective excitations (bosons)

Strong correlations

Fermi vs. Luttinger Liquid

Cohen Group Meeting

luttinger model
Noninteracting Hamiltonian:

Second quantization:

Spinless fermions

Two species

Linear dispersion

Luttinger Model

Cohen Group Meeting

Density operators:

Commutation relations:

Boson operators:


Cohen Group Meeting

interaction hamiltonian
Interaction Hamiltonian
  • Scattering of same species:
  • Different species:

Note: scattering must conserve momentum

Cohen Group Meeting

solution of model with spin
Solution of Model with Spin
  • Now include spin:
  • Define operators that obey Boson commutation relations:

Cohen Group Meeting

spin charge separation
Spin-Charge Separation
  • Hamiltonian separates into charge and spin parts:
  • Diagonalize charge density part:
  • For delta function potential:

Spin and charge have different speeds – spin-charge separation!

Cohen Group Meeting

1d versus 3d
1D versus 3D
  • Luttinger Liquids:
    • Charge and spin density waves (bosons)
    • Can show that Fermi surface is unstable to perturbation
  • Consider particle-hole excitation spectrum:



Cohen Group Meeting

experiment carbon nanotubes ropes
Experiment: Carbon Nanotubes (ropes)
  • For LL, conductance should follow power law:

Bockrath et al., Nature

Cohen Group Meeting

cnt junctions
CNT Junctions
  • Conductance measurements for two joined CNT segments


Yao et al., Nature


Cohen Group Meeting

spin charge separation in nanowires
Spin-Charge Separation in Nanowires
  • Observed in tunneling between parallel GaAs nanowires
  • Results not all explained by theory

Cohen Group Meeting

  • Luttinger model gives interesting phenomena
  • Some experimental evidence in CNTs, nanowires (also polymers)
  • Experimental situation not settled:
    • Spin-charge separation in CNTs?
    • Coulomb blockade?

Cohen Group Meeting

instability of fermi surface
Instability of Fermi Surface

Cohen Group Meeting