Theory of libron effects on the electron spectrum of one-dimensional conductors

The Peierls instability has been studied for a one-dimensional conductor in which the rotational degree of freedom of the molecules plays a role. The rotational motion is described in terms of a pseudospin $S=1\mathrm{}$ Hamiltonian in which the electrostatic quadrupole-quadrupole and dipole-dipole interactions are included. The Hamiltonian also takes account of the conduction-electron-band motion as well as the coupling of the conduction band to the rotation of the molecules. The electron Green's function is evaluated in the meanfield approximation and the libron Green's function in a self-consistent field theory. It is found that the derived expressions for both the electron and libron Green's functions give a simple recursion formula for the Peierls transition temperature $T_c$ which is driven by the loss of librons from the Peierls condensate through thermal excitation. The recursion formula is solved numerically for a half-filled tight-binding conduction band and the dependence of $T_c$ on the values of the different parameters involved in the problem is studied. An expression for the electrical conductivity is derived which describes the collective contribution arising from the phase oscillations of the lattice distortion. This expression is compared with the corresponding one for the Fröhlich Hamiltonian which describes the translational degree of freedom of the molecules but ignores their rotational motion.