Thick wedged films:

excitations in insulating M.U. Gruninger, 1999 PhD Thesis YBa2Cu3O6 Weakly absorbing excitations in insulating No absorbtive features in R(w) Absorbtive features in T(w)

Plan parallel plates or films source detector

Optical Transmission

Thin films: NbN d=400 nm 9 K 13 K 18 K

SrTiO3 Sr Transmission 10 20 30 40 50

Direct measurement of the polariton w(q) relation 50 Transmission 10 20 30 40

THz time domain measurements Fabry-Perot etalon source detector

THz time domain measurements Fabry-Perot etalon source detector

THz transmission of SrTiO3 Time domain intensity (a.u.) 31 32 33 34 35 36 37 delay line (mm)

THz transmission of SrTiO3 Time domain Frequency domain 0.1 10-3 intensity (a.u.) transmission 10-5 31 32 33 34 35 36 37 10 20 30 40 50 delay line (mm) wavenumber (cm-1) Fourier transformation

What do we measure with optics ? Dipole transition from an occuped state  to an emtpy state 

KCl s1(w) measures the interacting electron-hole spectral function excitons KCl s(w) Charge transfer gap 7.5 8.5 ħw (eV)

Field operator Density operator Density operator Velocity operator

Interaction between light and matter Kubo formalism Velocity operator:

In the limit of linear response this becomes Finite temperature:

Finite temperature: The two delta-functions cancel exactly !

Drude-Lorentz expansion

Al has 13 electrons/atom

Glover Tinkham Ferrell: Optical conductivity Bi2Sr2CaCu2O8 T=20 K Tc=88K T=300K Glover Tinkham Ferrell:

Example, MgO:

f-sum rule Free charge spectral weight (Kubo, 1957)

Electron Energy Electron Momentum Electron Energy

E//ab Carbone, preprint ‘06 Molegraaf,Science’02

H.J.A.Molegraaf et al, Science 295, 2239 (2002)

Free charge spectral weight Nearest- neighbor tight-binding approximation Kinetic energy sum-rule

Calculated using BCS-model Molegraaf, Presura, vanderMarel, Kes, Li, Science 295, (2002). Loram, Luo, Cooper, Liang, Tallon, J. Phys. Chem. Solids (2001). Experiments

Special case: diatomic molecule Hopping parameter: t

  1 electron:

d Hopping parameter: t 1 electron:

a’-NaV2O5 Topview: 4 V-atoms c average: V4.5+ 2 valence electrons per unit cell c Topview: unit cell b a

b a t^ t^>> t||  

E ^ chain E // chain