Ground state and optical conductivity of interacting polarons in a quantum dot

Abstract

The ground-state energy, the addition energies and the optical absorption spectra are derived for interacting polarons in parabolic quantum dots in three and two dimensions. A path integral formalism for identical particles is used in order to take into account the fermion statistics. The approach is applied to both closed-shell and open-shell systems of interacting polarons. Using a generalization of the Jensen-Feynman variational principle, the ground-state energy of a confined N-polaron system is analyzed as a function of N and of the electron-phonon coupling constant. As distinct from the few-electron systems without the electron-phonon interaction, three types of spin polarization are possible for the ground state of the few-polaron systems: (i) a spin-polarized state, (ii) a state where the spin is determined by Hund's rule, (iii) a state with the minimal possible spin. A transition from a state fulfilling Hund's rule, to a spin-polarized state occurs when decreasing the electron density. In the strong-coupling limit, the system of interacting polarons turns into a state with the minimal possible spin. These transitions should be experimentally observable in the optical absorption spectra of quantum dots.

33 pages, 9 figures, E-mail addresses: [email protected], [email protected], [email protected], [email protected], accepted for Phys. Rev. B

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• Variational path-integral treatment of a translation invariant many-polaron system
• Intermolecular forces and correlations mediated by a phonon bath
• Path-integral approach to the thermodynamics of bosons with memory: Partition function and specific heat
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