Adiabatic self-trapped states in zigzag nanotubes

• Published in: Journal of physics. Condensed matter Vol. 19; no. 30; pp. 306205 - 306205 (22)
• Main Authors: Brizhik, L S, Eremko, A A, Piette, B M A G, Zakrzewski, W J
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.08.2007; Institute of Physics
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Electronic structure of nanoscale materials : clusters, nanoparticles, nanotubes, and nanocrystals; Exact sciences and technology; Physics; Quasiparticles; Adiabatic approximation; Self trapping; Excitons; Ground states; Hamiltonians; Solitons; Carbon nanotubes; Electron-phonon interactions; Interaction energy; Polarons
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/19/30/306205

We study the polaron (soliton) states of a quasiparticle (electron, hole, exciton) in a quasi-one-dimensional (quasi-1D) model which describes a carbon-type zigzag nanotube structure. In the Hamiltonian of the system we include the electron-phonon interaction that arises from the dependence of both the on-site and the hopping interaction energies on the lattice deformation. We derive, in the adiabatic approximation, the equations for the self-trapped states of a quasiparticle in a zigzag nanotube. We show that the ground state of such a system depends on the strength of the electron-phonon coupling and we find polaron-type solutions with different symmetries. Namely, at a relatively weak coupling a quasiparticle is self-trapped in a quasi-1D polaron state which has an azimuthal symmetry. When the coupling constant exceeds some critical value, the azimuthal symmetry breaks down and the quasiparticle state can be described as a two-dimensional small polaron on the nanotube surface. In the crossover region between the two solutions there is a range of intermediate couplings, in which the 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 this analytical study are in quantitative agreement with what has recently been observed numerically.