Quantum Tunneling of an Acoustic Polaron in One-Dimensional Electron-Lattice System

Abstract

More than two decades ago, Donovan and Wilson [1] found peculiar charge carriers with an anomalously high mobility in photo-conduction experiments on polydiacetylene which belongs to conjugated polymers and could be regarded as a quasi-one-dimensional system; for example, in the single crystal of polydiacetylene toluene sulphonate, one of typical polydiacetylene, the minimum distance between neighboring polymer chains is 0.75 nm [2] which is much larger than the bond length between carbon atoms (˜ 0.13 nm). The characteristics of the photo-excited charge carriers are summarized as follows; (1) they have a rather high mobility which is estimated to be no less than 20 m²/(sec·V), and (2) their drift velocity shows saturation at a value of the order of the sound velocity v _s of the system in the applied electric field with the strength 10² to 10⁶ V/m. For a possible explanation of this charge carrier, Wilson [3] proposed an acoustic polaron which is a composite of an electron near the conduction band bottom and lattice distortions induced by the presence of the electron and giving rise to an effective attractive potential confining the electron to a locally distorted lattice region. In fact, starting from Su, Schrieffer and Heeger's (SSH) model [4] which is one of the standard theoretical models for one-dimensional coupled electron-lattice systems, Wilson [3] could derive theoretically the following properties of an acoustic polaron within the continuum approximation which is justified in the weak coupling limit; (1) the polaron has a saturation velocity equal to the sound velocity of the system, (2) the extent of the polaron (referred to as “width” in the following) decreases with increasing velocity and tends to vanish as the velocity v approaches the saturation velocity (= the sound velocity, ), and (3) the energy of the moving polaron diverges as (v _s -v)^-3 when the polaron velocity v approaches v _s . These properties of the acoustic polaron were confirmed later by numerical simulations [5] treating the SSH model as it is without assuming the weak coupling limit; details of these simulations will be explained in the following section.