Theoretical and computational studies of excitons in conjugated polymers

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 11, 2002, Pages 1152051-11520512

  Barford, William ^a   Bursill, Robert J ^b   Smith, Richard W ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

POLYACETYLENE; POLYMER;

ANALYTIC METHOD; ARTICLE; CALCULATION; DIMERIZATION; MODEL; MOLECULAR INTERACTION; PARTICLE SIZE; PHASE SEPARATION; POLYMERIZATION; SEMICONDUCTOR;

EID: 0037105168     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.66.115205     Document Type: Article

References (36)

1. See, for example, R. S. Knox Solid State Physics (Academic, New York, 1963), Suppl. 5.
2. A. Abe, J. Yu, W. P. Su, Phys. Rev. B 45, 8264 (1992).
3. D. Yaron and R. Silbey, Phys. Rev. B 45, 11 655 (1992).
4. D. Yaron, Phys. Rev. B 54, 4609 (1996).
5. R. Loudon, Am. J. Phys. 27, 649 (1959).
6. F. Gebhard, K. Bott, M. Scheidler, P. Thomas, and S. W. Koch, Philos. Mag. B 75, 13 (1997); F. H. L. Essler, F. Gebhard, and J. Jeckelmann, Phys. Rev. B 64, 12 5119 (2001).
7. F. Gebhard, K. Bott, M. Scheidler, P. Thomas, and S. W. Koch, Philos. Mag. B 75, 13 (1997); F. H. L. Essler, F. Gebhard, and J. Jeckelmann, Phys. Rev. B 64, 12 5119 (2001).
8. F. B. Gallagher and S. Mazumdar, Phys. Rev. B 56, 15 025 (1997).
9. W. Barford, Phys. Rev. B 65, 205118 (2002).
10. More correctly, we should define the weak-coupling limit when the noninteracting band gap is larger than the correlation gap, and vice versa for the strong-coupling limit. However, as no general expression exists for the correlation gap as a function of U/W we prefer our more qualitative definition.
11. S. R. White, Phys. Rev. Lett. 69, 2863 (1992); Density Matrix Renormalization, edited by I. Peschel, X. Wang, M. Kaulke, and K. Hallberg (Springer, Berlin 1999).
12. S. R. White, Phys. Rev. Lett. 69, 2863 (1992); Density Matrix Renormalization, edited by I. Peschel, X. Wang, M. Kaulke, and K. Hallberg (Springer, Berlin 1999).
13. W. Barford, R. J. Bursill, and M. Yu Lavrentiev, J. Phys.: Condens. Matter 10, 6429 (1998).
14. S. N. Dixit, D. Guo, and S. Mazumdar, Phys. Rev. B 43, 6781 (1991); D. Guo, S. Mazumdar, S. N. Dixit, F. Kajzar, F. Jarka, Y. Kawabe, and N. Peyghambarian, ibid. 48, 1433 (1993).
15. S. N. Dixit, D. Guo, and S. Mazumdar, Phys. Rev. B 43, 6781 (1991); D. Guo, S. Mazumdar, S. N. Dixit, F. Kajzar, F. Jarka, Y. Kawabe, and N. Peyghambarian, ibid. 48, 1433 (1993).
16. e>
17. The amplitude for the Wannier molecular orbital to overlap a neighboring dimer is very small. For δ=0.2 this amplitude is 0.16, resulting in nearest-, next-nearest-, and next-next-nearest-neighbor hopping terms to be in the ratio of 1:0.17:0.06. Neglecting the longer range hopping terms means that the approximate single-particle bands differ from the exact single-particle bands, resulting in different effective masses and qualitatively different binding energies. Also, the two-electron parameters will be different. Thus, using the Wannier molecular orbitals rather than the local molecular orbitals will give a more accurate, but more complicated effective-particle theory; see Ref. 18.
18. The general recipe for mapping between atomic orbital and molecular orbital Hamiltonians is given in R. J. Bursill, W. Barford, and H. Daly, Chem. Phys. 243, 35 (1999).
19. The molecular orbital Hamiltonian also contains terms that change the occupancy of the valence and conduction bands. However, as such terms do not connect basis states within the exciton sub-basis, they are neglected.
20. D. C. Mattis, The Theory of Magnetism (Springer-Verlag, Berlin, 1981), p. 147.
21. n(m).
22. 2 operator reflects both the center-of-mass and relative coordinates, and hence exchanges the electron and hole.
23. The binding energy is defined as the excitation energy relative to the charge gap, and the charge gap = E(N+1)+E(N-1) -2E(N). Although the charge gap is only truly meaningful for infinite chains, where the highest exciton energies become closely spaced and their particle-hole separations diverge, it is still a qualitatively useful concept for finite length chains, as it marks the energy above which a particle-hole excitation has more energy than an uncorrelated particle-hole pair.
24. nj, and hence this is a measure of the exciton wave function.
25. The anticrossings between a higher j of a lower n with the j = 1 state of a higher n, shown in Fig. 3, can lead to spurious "essential states," as oscillator strength is transferred from the j = 1 state of higher n to the higher j state of the lower n. These other essential states, arising from the accidental degeneracies, are quite different from the competing essential states seen in the intermediate-coupling regime, as discussed in Sec. IV.
26. K. Schulten and M. Karpus, Chem. Phys. Lett. 14, 299 (1972).
27. P. Tavan and K. Schulten, Phys. Rev. B 36, 4337 (1987).
28. D. Mukhopadhyay, G. W. Hayden, and Z. G. Soos, Phys. Rev. B 51, 9476 (1995).
29. R. J. Bursill and W. Barford (unpublished).
30. R. J. Bursill and W. Barford, Phys. Rev. Lett. 82, 1514 (1999); W. Barford, R. J. Bursill, and M. Yu. Lavrentiev, Phys. Rev. B 63, 195108 (2001).
31. R. J. Bursill and W. Barford, Phys. Rev. Lett. 82, 1514 (1999); W. Barford, R. J. Bursill, and M. Yu. Lavrentiev, Phys. Rev. B 63, 195108 (2001).
32. A. Race, W. Barford, and R. J. Bursill, Phys. Rev. B 64, 035208 (2001).
33. A. Race, W. Barford and R. J. Bursill (unpublished).
34. E. Moore, B. Gherman, and D. Yaron, J. Chem. Phys. 106, 4216 (1997); E. Moore and D. Yaron, ibid. 109, 6147 (1998).
35. E. Moore, B. Gherman, and D. Yaron, J. Chem. Phys. 106, 4216 (1997); E. Moore and D. Yaron, ibid. 109, 6147 (1998).
36. In the continuum limit the exchange term diverges, leading to a diverging on-site repulsion for the singlet states. This reduces the binding energy of the even parity singlet states, so that each even parity state becomes degenerate with the higher-lying odd parity state. The onset of such behavior is seen in Fig. 1(a) for large U.