Adiabatic self-trapped states in zigzag nanotubes

Abstract

We study the polaron (soliton) states of a quasiparticle (electron, hole, exciton) in aquasi-one-dimensional (quasi-1D) model which describes a carbon-type zigzag nanotubestructure. In the Hamiltonian of the system we include the electron–phonon interactionthat arises from the dependence of both the on-site and the hopping interaction energies onthe lattice deformation. We derive, in the adiabatic approximation, the equations for theself-trapped states of a quasiparticle in a zigzag nanotube. We show that the ground stateof such a system depends on the strength of the electron–phonon coupling and we findpolaron-type solutions with different symmetries. Namely, at a relatively weakcoupling a quasiparticle is self-trapped in a quasi-1D polaron state which has anazimuthal symmetry. When the coupling constant exceeds some critical value, theazimuthal symmetry breaks down and the quasiparticle state can be described as atwo-dimensional small polaron on the nanotube surface. In the crossover regionbetween the two solutions there is a range of intermediate couplings, in whichthe two structures, the quasi-1D polaron and the strongly localized 2D polaron,coexist as their energies are very close together. We note that the results of thisanalytical study are in quantitative agreement with what has recently been observednumerically.