Mott transitions of exciton-polaritons and indirect excitons in a periodic potential

TL;DR

This paper develops an effective Bose-Hubbard model to predict phase transitions from Bose-Einstein condensates to Mott insulators in exciton-polariton and indirect exciton systems under periodic potentials, including a crossover to Fermi-Hubbard behavior.

Contribution

It derives a unified Bose-Hubbard model for both systems and analyzes the conditions for observing Mott insulator phases, including a crossover to Fermi-Hubbard models with increasing bilayer separation.

Findings

Effective Bose-Hubbard model predicts phase transition conditions.

Strong periodic potentials and large excitonic components are necessary.

Crossover from Bose-Hubbard to Fermi-Hubbard model with bilayer separation.

Abstract

We derive an effective Bose-Hubbard model that predicts a phase transition from Bose-Einstein condensate to Mott insulator in two different systems subject to applied periodic potentials: microcavity exciton-polaritons and indirect excitons. Starting from a microscopic Hamiltonian of electrons and holes, we derive an effective Bose-Hubbard model for both systems and evaluate the on-site Coulomb interaction U and hopping transition amplitudes t. Experimental parameters required for observing a phase transition between a Bose-Einstein condensate and a Mott insulator are discussed. Our results suggest that strong periodic potentials and polaritons with a very large excitonic component are required for observing the phase transition. The form of the indirect exciton interaction is derived including direct and exchange components of the Coulomb interaction. For indirect excitons, the system crosses over from a Bose-Hubbard model into a double layer Fermi-Hubbard model as a function of increasing bilayer separation. The Fermi-Hubbard model parameters are calculated, and the criteria for the location of this crossover are derived. We conjecture that a crossover between a Bose Mott insulator to a Fermi Mott insulator should occur with increasing bilayer separation.