Experimental realization of an extended Fermi-Hubbard model using a 2D lattice of dopant-based quantum dots

Abstract

The Hubbard model is an essential tool for understanding many-body physics in condensed matter systems. Artificial lattices of dopants in silicon are a promising method for the analog quantum simulation of extended Fermi-Hubbard Hamiltonians in the strong interaction regime. However, complex atom-based device fabrication requirements have meant emulating a tunable two-dimensional Fermi-Hubbard Hamiltonian in silicon has not been achieved. Here, we fabricate 3 × 3 arrays of single/few-dopant quantum dots with finite disorder and demonstrate tuning of the electron ensemble using gates and probe the many-body states using quantum transport measurements. By controlling the lattice constants, we tune the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from metallic to Mott insulating behavior. We simulate thermally activated hopping and Hubbard band formation using increased temperatures. As atomically precise fabrication continues to improve, these results enable a new class of engineered artificial lattices to simulate interactive fermionic models.

Quantifying the Variation in the Number of Donors in Quantum Dots Created Using Atomic Precision Advanced Manufacturing

“…In Figure 5a, the soft transition from 0 to 1 over a range of about 1 nm in any direction indicates lithographic roughness that is typical in HDL. 7,23,25 While techniques such as feedback lithography could be used to improve the sharpness of the defined lithographic window, 41−43 this represents a reasonable STM lithography run that is similar to recent works utilized to fabricate quantum electronics. 7,23,25 Using our kinetic model, we predict that these observed errors in depassivation do not lead to significant deviations in the total number of incorporations for a given window.…”

“…7,23,25 While techniques such as feedback lithography could be used to improve the sharpness of the defined lithographic window, 41−43 this represents a reasonable STM lithography run that is similar to recent works utilized to fabricate quantum electronics. 7,23,25 Using our kinetic model, we predict that these observed errors in depassivation do not lead to significant deviations in the total number of incorporations for a given window. We investigate this by creating 500 depassivation patterns for our kinetic model based on the empirical probability map in Figure 5a.…”

Enhanced Atomic Precision Fabrication by Adsorption of Phosphine into Engineered Dangling Bonds on H–Si Using STM and DFT

“…As HDL techniques develop toward greater device complexity, it will become increasingly important to also control the number of P atoms at each site to be greater than one (e.g., ensuring exactly two P atoms incorporate); knowing where to place the tip and what manipulations to perform will require the precision identification enabled by the simulated image catalog. Some examples of devices that would benefit are singlet−triplet qubits 27 consisting of a single P atom at one site within tunneling range of a second site with two P atoms and AQS arrays 17 where selected sites have a predetermined number of P atoms intended to induce a different chemical potential than sites with precisely one P atom. In this study, we have presented a pathway to use HDL fabrication in development of devices and materials where the details of the Hamiltonian are engineered with absolute precision based on the number and placement of atoms in quantum structures.…”

“…However, it will ultimately be necessary to move beyond the level of control currently available to the HDL method and develop ways to achieve greater precision. A case where this has become particularly apparent is in the use of donor arrays for analogue quantum simulation (AQS) where we have been able to make significant progress with devices that include some disorder . Such AQS systems can be qualitatively linked to an extended Hubbard model, but in order for them to be effective as a quantitative tool, the chemical potential and on-site interactions at each array element will need to be precisely defined.…”

“…A case where this has become particularly apparent is in the use of donor arrays for analogue quantum simulation (AQS) where we have been able to make significant progress with devices that include some disorder. 17 Such AQS systems can be qualitatively linked to an extended Hubbard model, but in order for them to be effective as a quantitative tool, the chemical potential and on-site interactions at each array element will need to be precisely defined. This can only be done by fixing the number of P atoms exactly.…”