Geometric and Orbital Control of Correlated States in Small Hubbard Clusters

TL;DR

This paper develops a framework for controlling electron pairing in quantum dot arrays by manipulating geometry, orbital hybridization, and electric fields, revealing fundamental principles for designing correlated quantum states.

Contribution

It introduces a systematic approach combining geometry, orbital hybridization, and electric fields to engineer local electron pairing in quantum dot clusters, supported by Hartree-Fock simulations.

Findings

Coordination number Z influences resilience to Coulomb repulsion.

Orbital hybridization can enhance double occupancy at moderate U.

Electric fields induce pairing by charge localization, especially in low-connectivity clusters.

Abstract

Arrays of semiconductor quantum dots provide a powerful platform to design correlated quantum matter from the bottom up. We establish a predictive framework for engineering local electron pairing in these artificial molecules by systematically deploying three control levers: lattice geometry, orbital hybridization, and external electric fields. Using Hartree-Fock simulations on canonical 3D clusters from the tetrahedron (Z = 3) to the FCC lattice (Z = 12), at and near half-filling, we uncover three fundamental design principles. (i) Geometric Hierarchy: The resilience to Coulomb repulsion U is dictated by the coordination number Z, which controls kinetic delocalization. (ii) Orbital Hybridization: Counter-intuitively, inter-orbital hopping t_orb acts not as a simple suppressor of pairing, but as a sophisticated control knob that enhances double occupancy at moderate U by engineering the on-site energy landscape. (iii) Field Squeezing: An electric field robustly induces pairing by forcing charge localization, an effect most potent in low-connectivity clusters. These principles form a blueprint for deterministically targeting charge and spin correlations in quantum-dot-based quantum hardware.