Electronic oscillations in paired polyacetylene chains

Abstract

An interacting pair of polyacetylene chains are initially modeled as a couple of undimerized polymers described by a Hamiltonian based on the tight-binding model representing the electronic behavior along the linear chain, plus a Dirac's potential double well representing the interaction between the chains. A theoretical field formalism is employed, and we find that the system exhibits a gap in its energy band due to the presence of a mass-matrix term in the Dirac's Lagrangian that describes the system. The Peierls instability is introduced in the chains by coupling a scalar field to the fermions of the theory via spontaneous symmetry breaking, to obtain a kink-like soliton, which separates two vacuum regions, i.e., two spacial configurations (enantiomers) of the each molecule. Since that mass-matrix and the pseudo-spin operator do not commute in the same quantum representation, we demonstrate that there is a particle oscillation phenomenon with a periodicity equivalent to the Bloch oscillations. Quantum mechanical particles moving under the influence of a constant electric field and submitted to a periodic potential oscillate instead of moving with uniform acceleration. This phenomenon is called Bloch oscillations and were predicted theoretically by F. Bloch in 1928 [1]. Such oscillations have never been observed in a natural lattice because the characteristic times of the electrons scattering by the lattice defects, or impurities, are much shorter than the Bloch period. As a consequence, during a long time these oscillations were seen like a mere theoretical curiosity to demonstrate the strange properties of matter, according to quantum mechanics principles. However, they have been recently observed experimentally in semiconductor superlattices [2,[4][5][6]8] and with larger periods, of the order of ten seconds, in strontium atoms trapped by laser beams, cooled at temperatures close to absolute zero. In the former case, the dependence of the Bloch frequency on the electric field makes the oscillations tunable, yielding a potential source of coherent high frequency radiation and, in latter case, the constant external force was the terrestrial gravitational field itself [3].These oscillations can play an effective and important role in quantum electronics, due to development of the physics of quasi-unidimensional molecular structures, as polyacetylene [9] and graphene ribbons [10,11]. Polyacetylene consists of a linear chain of carbon atoms, coupled to each other with alternating simple and double chemical bonds, that can be obtained via acetylene polymerization. It is an organic polymer with special electronic properties. Thin films of this polymer produced under special doping conditions are excellent conductors that can be used to develop electronic devices in the nanometer scale [14]. Due to its dimensionality we can model the undimerized polyacetylene as a linear chain of carbon atoms with periodic boundary conditions and a Hamiltonian based on the tight binding model. In this approach, the valence electron...