Using the Feynman path-integral formalism, we study the polaron effects in quantum wires above a liquid-helium film. The electron interacts with two-dimensional (2D) surface phonons, i.e., ripplons, and is confined in one dimension (1D) by a harmonic potential. The obtained results are valid for arbitrary temperature (T), electron-phonon coupling strength (α), and lateral confinement $\left({\omega }_0\right).\mathrm{}$ Analytical and numerical results are obtained for limiting cases of T, α, and ${\omega }_0.$ We found the surprising result that reducing the electron motion from 2D to quasi-1D makes the self-trapping transition more continuous.

• Received 19 April 2001

DOI:https://doi.org/10.1103/PhysRevB.64.104301