Exact solution for two interacting electrons on artificial atoms and molecules in solids

TL;DR

This paper develops an exact method to find eigenstates of two interacting electrons in artificial atoms and molecules within solids, revealing limits of Coulomb blockade and exploring quantum delocalization and magnetic transitions.

Contribution

It introduces a general scheme for exact solutions of two-electron systems with on-site interactions in impurity models, applicable to doped semiconductors and quantum dots.

Findings

Energy cost for adding two electrons is bounded, not diverging with U_i.

Analytic results show quantum delocalization in one-dimensional chains.

Magnetic transitions are identified in the model.

Abstract

We present a general scheme for finding the exact eigenstates of two electrons, with on-site repulsive potentials U_i, on I impurities in a macroscopic crystal. The model describes impurities in doped semiconductors and artificial molecules in quantum dots. For quantum dots, the energy cost for adding two electrons is bounded by the single-electron spectrum, and does not diverge when U_i approaches infinity, implying limitations on the validity of the Coulomb blockade picture. Analytic applications on a one-dimensional chain yield quantum delocalization and magnetic transitions.