Bipolaron formation in 1D-3D quantum dots: A lattice quantum Monte Carlo approach

TL;DR

This study uses unbiased quantum Monte Carlo simulations to explore how polaron and bipolaron formations depend on various parameters in quantum dot structures across one to three dimensions.

Contribution

It introduces a lattice quantum Monte Carlo approach that fully accounts for lattice discreteness and quantum phonon effects in modeling polaron phenomena in quantum dots.

Findings

Confinement reduces polaron and bipolaron sizes at fixed coupling.

Confinement lowers the critical coupling needed for bipolaron formation.

Confinement increases polaron binding energy, especially in lower dimensions.

Abstract

Polaron and bipolaron formation in the Holstein-Hubbard model with harmonic confinement potential, relevant to quantum dot structures, is investigated in one to three dimensions by means of unbiased quantum Monte Carlo simulations. The discrete nature of the lattice and quantum phonon effects are fully taken into account. The dependence on phonon frequency, Coulomb repulsion, confinement strength (dot size) and electron-phonon interaction strength is studied over a wide range of parameter values. Confinement is found to reduce the size of (bi-)polarons at a given coupling strength, to reduce the critical coupling for small-(bi-)polaron formation, to increase the polaron binding energy, and to be more important in lower dimensions. The present method also permits to consider models with dispersive phonons, anharmonic confinement, or long-range interactions.