Semiclassical Formalism of Optical Absorption and Breathers in Polyacetylene

Abstract

A formalism for the optical absorption in a coupled electron-ion system is developed. The formalism assumes an initial trajectory with frequency much lower than electronic energy scales, and a shortmemory condition, i.e., the excited-state trajectories diverge away from the initial trajectory within one period. The result shows nonadiabatic features such as level broadening, sidebands, and tails in nonclassical regimes. We apply the formalism to breather modes in polyacetylene and show that they can account for the intragap absorption tail and for the observed photoinduced absorption at 1.35 eV. PACS numbers: 71.38.+i, 33.10.Cs, 36.20.Kd, 78.20.Bh The semiclassical description of many-body theory has been a useful approach in the study of molecules, 1 " 4 solid state, 5,6 nuclear matter, 7 elementary particles, 8 and more. 9 A coupled electron-ion system is a natural application, since the heavier ions allow for "adiabatic dynamics," 3,5 i.e., the ions obey classical dynamics while the electrons follow the ions instantaneously. The presence of an external electromagnetic field poses, however, new difficulties for this formalism by allowance of nonadiabatic effects. In particular, we consider photoexcited states for which the adiabatic potential, as a function of the ion coordinates, is near a maximum (turning point) while the minimum is far, or even infinitely far, from that of the ground state. Such unstable excitations occur in photoinduced fission of molecules or nuclei, photoexcitation during molecular collisions or photoexcitation of a well-separated electron-hole pair in semiconductors.We note that the conventional Franck-Condon 10 approximation is not sufficient to handle these cases; in particular, it leads to spurious divergences at the turning points. Nonadiabatic absorption may also be inferred from precise derivations of electron density of states. 11,12 Since such derivations are, in general, not feasible for many-body systems, we focus instead on deriving the leading semiclassical behavior. Furthermore, our direct evaluation of the absorption itself manifests the essential role of interference near classical turning points.Consider a periodic initial state with frequency COB <o>, where the external field frequency co is comparable to the gap in the electronic spectrum. The external field leads to excited states whose ion trajectories are assumed to deviate strongly from the initial trajectory within one period. We show that this "short memory" condition, together with adiabatic conditions (e.g., co ^>COB), lead to a simple yet powerful expression for the real part of the conductivity Recr(w). We apply the formalism to the polyacetylene model 5 and find that it describes the observed intragap absorption tail 13,14 and that nonlinear localized ion oscillators, i.e., breathers, 6 can account for the unusual photoinduced absorption data. 15 " 18 A general Hamiltonian for an electron-ion system isHere q^iquqi,.. .), p = (pupi,. . .), M and V(q) are the coordinates, momenta, mass and potential energy o...

Intrinsic localized modes in the charge-transfer solid PtCl

“…Therefore, the amplitude of Peierls distortion should be well described in the adiabatic approximation. On the other hand, as was shown in [9], the purely adiabatic theory fails to describe dynamic optical absorption attributed to breathers. This is related to the fact that, although the adiabatic approximation may well describe the A minimal phenomenological model to describe qualitative features of P tCl is the twoband Peierls-Hubbard model, introduced for this purpose in [2].…”