Extended Hubbard model for mesoscopic transport in donor arrays in silicon

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 wave function. 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.

Excited states of defect linear arrays in silicon: A first-principles study based on hydrogen cluster analogs

“…There has also been growing experimental interest in performing quantum simulations [9,23] in donor clusters. Arrays of dopants in silicon [9] and quantum dots [23] have been fabricated for the quantum simulation of the Fermi-Hubbard model; the freedom to position the atoms arbitrarily enables tuning of correlations by varying the interdonor distance [24]. Such a platform could be enhanced by the ability to probe the state of the electrons using optical absorption.…”

Radii of Rydberg states of isolated silicon donors

“…Without knowledge of the wave-function extent we cannot engineer the contact of the impurity with readout electronics [5], external leads (source, drain, gates etc.) or know how much control is required to construct a dimer [4], a chain [6] or a lattice [3]. The questions we raise here are closely analogous to those for cold Rydberg atoms in magnetic traps, where the excited states are large and highly susceptible to magnetic fields (as in our case), and so are the dipole moments and interactions with neighboring atoms that affect both the spectra [17] and the formation of condensates [18], though in this case the ion is fixed, and we have the extra complication of an anisotropic effective mass.…”

Using non-homogeneous point process statistics to find multi-species event clusters in an implanted semiconductor

“…Previously, clusters of impurities with homogeneous density have been discussed in terms of the distribution of neighbour-neighbour distance [15]. In order to put our discussion into this context we give the nonhomogeneous case, which follows immediately from equation (2). We define the probability d…”

“…Individual interacting impurity atoms can be important for donor qubit gates, such as that proposed by Stoneham et al [1], while an important class of theoretical physics problems is produced by the Hubbard model, which relies on hopping and magnetic interactions between neighbours in chains [2]. In the case of donor impurities in a semiconductor, deterministic placement using scanning probe tips has improved greatly in recent years, but is currently limited to a small number of species of impurity (principally phosphorus and arsenic [3] in silicon [4,5] and germanium [6], and Mn in GaAs [7]).…”