Extended Hubbard model for mesoscopic transport in donor arrays in silicon

TL;DR

This paper demonstrates that for donor arrays in silicon, a comprehensive Hubbard model including intersite interactions is necessary, and it explores how resonant tunneling can reveal Hubbard physics, with localization effects influencing transport.

Contribution

It introduces an extended Hubbard model for silicon donor arrays that accounts for strong intersite interactions and investigates transport phenomena and localization effects.

Findings

Intersite interactions are crucial for accurate modeling.

Resonant tunneling reveals Hubbard bands and Mott gap.

Localization mechanisms significantly suppress transport in one-dimensional arrays.

Abstract

Arrays of dopants in silicon are promising platforms for the quantum simulation of the Fermi-Hubbard model. We show that the simplest model with only on-site interaction is insufficient to describe the physics of an array of phosphorous donors in silicon due to the strong intersite interaction in the system. We also study the resonant tunneling transport in the array at low temperature as a mean of probing the features of the Hubbard physics, such as the Hubbard bands and the Mott gap. Two mechanisms of localization which suppresses transport in the array are investigated: The first arises from the electron-ion core attraction and is significant at low filling; the second is due to the sharp oscillation in the tunnel coupling caused by the intervalley interference of the donor electron's wavefunction. This disorder in the tunnel coupling leads to a steep exponential decay of conductance with channel length in one-dimensional arrays, but its effect is less prominent in two-dimensional ones. Hence, it is possible to observe resonant tunneling transport in a relatively large array in two dimensions.