Quantum Lattice Fluctuations and Nonlinear Optics of Conducting Polymers
- PDF / 287,671 Bytes
- 6 Pages / 420.48 x 639 pts Page_size
- 68 Downloads / 193 Views
QUANTUM LATTICE FLUCTUATIONS AND NONLINEAR OPTICS OF CONDUCTING POLYMERS J. YU, B. FRIEDMAN AND W.P. SU Department of Physics, University of Houston, Houston, Texas 77204-5504
ABSTRACT Quantum lattice fluctuations of conjugated polymers in the form of virtual soliton-antisoliton pairs have important effects on the nonlinear optical properties. Quantitative calculations of nonlinear susceptibilities based on the solitonic molecular model are presented. INTRODUCTION Recent experimental interest on the nonlinear optical properties of conducting polymers calls for a detailed theoretical understanding of the underlying microscopic mechanism(1]. For frozen lattices, the X(3) due to -noninteracting electrons has been calculated[2,31 and shows good agreement with experiment[4]. There are, however, important discrepancies. The existence of a pronounced two-photon resonance peak in the X( spectrum is especially acute. We address this problem by taking into account the quantum motion of the lattice. Among all possible fluctuations of the lattice in the ground state, we single out those anharmonic components which can be regarded as virtual soliton-antisoliton pairs. A single virtual soliton-antisoliton pair behaves very much like a diatomic molecule (hence solitonic molecule) as far as photophysics is concerned. In this article we give a brief description of a solitonic molecule. Some linear optical properties of such a molecule are described. The nonlinear optical properties of this molecule are then discussed. CONFIGURATIONAL COORDINATE AND VIRTUAL SS PAIRS For quantitative discussions on trans-polyacetylene we take the SSH model[5]. In the adiabatic approximation the electronic spectrum is completely determined by any given lattice configuration {uJ}. The total energy is the sum of nuclear kinetic energies plus an effective potential energy V({u,}), which in turn comprises the elastic energies of the oa-bonds and the energies of the occupied electronic states
H _ E 2n
=2+
u,,1U.1(1)
2 V({u,}) = K-D(un - Un-1_) + E nc,o,,
(2)
The effective Hamiltonian in (1) describes a group of atoms interacting through a complicated interatomic potential. Static classical solutions are obtained by minimizing V
with respect to {u,}. Thus a uniform dimerization u, = (-1)nu. is found to exist in the ground state of an undoped chain. Correspondingly there is a gap at the center of the electronic energy band separating the conduction band from the valence band. Experimentally a strong smearing in the absorption curve is seen near the edge of the gap. This seems to be an intrinsic property. To explain such a subgap absorption tail we imagine the presence of virtual SS pairs in the ground state due to quantum fluctuaMat. Res. Soc. Symp. Proc. Vol. 173. @1990 Materials Research Society
672
tion of nuclear motion. An S3 pair represents a local depression of the bond alternation order and thus is accompanied by some localized electronic gap states. These states can induce subgap optical absorption. Here we are assuming a dilute gas of vi
Data Loading...
