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Optical excitations of Peierls-Mott insulators with bond disorder

Optical excitations of Peierls-Mott insulators with bond disorder. Jörg Rissler, Philipps-Universität Marburg cond-mat/0405180. Introduction: The absorption of p -conjugated Polymers

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Optical excitations of Peierls-Mott insulators with bond disorder

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  1. Optical excitations of Peierls-Mott insulators with bond disorder Jörg Rissler, Philipps-Universität Marburg cond-mat/0405180 • Introduction: The absorption of p-conjugated Polymers • Theoretical description: The extended Peierls-Hubbard model, Analysis of wavefunctions • Ordered chains • Disordered chainstwo cases with different disorder • Summary and outlook

  2. - + Light emitting diode (OLED) S1 Solar Cell hn hn Key Question:Description of the lowest optically excited states Introduction: Experimental situation Examples of p-conjugated polymers: Fabrication of electro-optical devices: • molecular glas • subject to disorder

  3. a b c E increasing n a E 1/n Problems: • Explanation of 1/n dependence? • Length scales? • Effect of disorder? • Electron-hole states? Introduction: Absorption The oligomer approach: a: large oligomers - saturation b: medium sizes - linear c: small - deviation

  4. D U V t extended Peierls -Hubbard Theory: ordered oligomers Generic system: Polyacetylene 1d lattice Hamiltonian Microscopic model: • Parameters:D=0.38 U=3 V=1 D=0.2 U=3 V=1.2 D=11 U=2.5 V=0.625 • (S. Pleutin, J.-L. Fave, J. Phys. Condens. Matter10, 3941 (1998). M. Bowan, R.J. Bursill, Phys. Rev. B57, 15167 (1998). E. Jeckelmann, Phys. Rev. B57, 11838 (1998).) • Density-Matrix Renormaliza-tion Group (DMRG) • L<200 (n<100), m=400 DMRG states model

  5. Statistical model: hard disorder Polymer film is an ensemble of ordered chain segments of length n. • Nominal length unlikely • Typical length increases slowly • Saturation of excitation energies(B.E. Kohler, J.C. Woehl, J. Chem. Phys. 103, 6253 (1995).) P(n) n Statistical model: soft disorder Ordered chain segments are bend randomly: • Typical length ls. • Excitation energies E~1/n.(G. Rossi, R.R. Chance, R. Silbey, J. Chem. Phys. 103, 7594 (1989).) ls Theory: disordered oligomers

  6. P(L) L • Replace every ts with a random • number from the interval [tsmin,ts] • Use a constant probability distri- bution. • Calculate 20 realisations for each chain length. t‘s ta tb tc td hard disorder: n‘ • Average spectra for • n‘=7,14,19,25 28 56 76 100 Theory: Combination soft disorder: td td ts

  7. Theory: wave-function analysis This is the probabilityto find a hole on site i and an electron on site j.

  8. Egap = E(N+1) + E(N-1) - 2E(N)Eex = ES1 – EGS a b c E 1/L Bound quasi-particle in a box! Ordered chains: Energies D=0.38 U=3 V=1 D=0.2 U=3 V=1.2 D=11 U=2.5 V=0.625 • Eex=A0+A1 1/L2 • mqp~ 0.2me

  9. Egap Ordered chains: wave function • Bound particle-hole pair • Necessary size L»28

  10. a b c E 1/L Intrinsic length scale: <reh> a <reh> < Lb<reh> »Lc <reh> > L Ordered chains: length scale <reh>»5 length scale due to electron-electron interaction

  11. Soft disorder: Energies D=0.38 U=3 V=10.79<ts<0.81 (J=9°)0.71<ts<0.81 (J=21°) L=100 Gaussian lines h= O (10-3) • Energy increase • Broadening O (10-3) - O (10-2) • Eex=B0+B11/L+B2 1/L2 • Redistribution of spectral weight (symmetry breaking)

  12. Soft disorder: length scale <reh> decreases with increasing disorder: J = 9° <reh>= 4.9 J = 21° <reh> = 4.4 New length scale due to disorder?

  13. Soft disorder: length scale D=0.38 U=3 V=1 0.79<ts<0.81 (J=9°) 0.71<ts<0.81 (J=21°) With increasing disorder more localisation and less deformation Segment length Lseg=72 (J=9°) and Lseg=47 (J=21°)

  14. Eex(seg)=2.319329 Segments represent the whole chain. segment Soft disorder: length scale How meaningful is Lseg? Eex=2.319274

  15. a b c E 1/L a: Eex(L>28) »Eex(L=28) saturation induced by hard disorder b: combination of intrinsic and soft-disorder behaviour c: deviation due to <reh> > L Soft + hard disorder: Energies D=0.38 U=3 V=10.71<ts<0.81 (J=21°) Ltyp=28,56,76,100

  16. <reh> Lseg Ltyp Disordered chains - summary Soft disorder Hard disorder • Ensemble of chains is dominated by the small chains. • Typical chain length Ltyp increases slowly with nominal length L.

  17. a b c E 1/L <reh> Lseg Ltyp Summary • Length scales? • Effects of disorder?All the expected ones. • Consistent microscopic description of disorder, electron-electron correlation and Peierls distortion. • Explanation of 1/L dependence? • Blend of order and disorder effects.

  18. Outlook • Comparison with experiment • Intramolecular transfer • Electro absorption • Discussion Collaborators F. Gebhard, E. Jeckelmann Financial support:

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