eliashberg function in arpes measurements

Eliashberg Function in ARPES measurements

Yu HeCuperates Meeting

Dec. 3, 2010

Content

Guidelines for extracting Eliashberg Function

Previous work

Our chances and challenges

E-p coupling in Pb

Be(1010)

Bi2212 and Pb-Bi2201

Eliashberg Function - Definition and background

Eliashberg Function - Definition and background

specific heatrenormalized density of statesmass enhancement factoreffective screening Coulomb potential Vcpseudopotential UcSuperconducting Tc

The total transition probability of a quasiparticle from/to the state by coupling to boson (phonon) modes of frequency ;k

Eliashberg Function - Definition

Junren Shi eet al., Phys. Rev. B 92, 186401(2004)

Eliashberg Function - Definition and backgroundEliashberg Function - Theory

W.L. McMillan and M.J. Rowell et al., Phys. Rev. Lett, 14, 108(1965)

Pb Pb In

sula

tor

Compare with actual electron DOS

Eliashberg Func Uc

Guess Eliashberg Func.

Solve gap Equ.

Vary Uc to fit Gap

Calculated electron DOS

Previous Work – Pb-I-Pb Junction

W.L. McMillan and M.J. Rowell et al., Phys. Rev. Lett, 14, 108(1965)

The ‘Kinkology’

v

T

Previous Work – the ‘Kinkology’

Previous work

Broad band at fermi surface (~80meV) - resolution

Linear fitting of bare band near F.S.

Introduce MEM for inverting the Integral

Previous Work – Be(1010)

Junren Shi eet al., Phys. Rev. B 92, 186401(2004)

Previous work

Bi2212

The angle independence of EliashbergFunc is consistent only with the fluctuation spectra at the short correlation length on the scale of the lattice constant

Previous Work – Bi2212

Lin Zhao et al., arXiv:0909.0762

Lin Zhao et al., arXiv:1002.0120v1

Previous Work – Pb-Bi2201

Dispersion

Self-energy

E-FunctionMultiple p-e peaks

Corresponding Raman and Infrared data

Guidelines for extracting Eliashberg Function

With k-dependence!

Reconstruct Dispersion

Real part of QP self-energy

Maximum Entropy Method

Take VERY nice cuts

Fit MDC

Eliashberg Function

General workflow to extract E-Func

Our chances and challenges

Narrow Band width or broad band width

Temperature control

MEM with Tom’s group

Provide more fundamental ways for quantitative analysis

Sensitive to self-energy extraction

Complementary ways for inelastic spectroscopy and transport

Right above Tc as little as possible – N(0) which is steep around gap

Complicated scenario in PG region

Chances and Challenges

The End