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



Richard M. Silver, Jonathan Wyrick, Xiqiao Wang, Ranjit Kashid, Garnett W. Bryant, Albert Rigosi, Pradeep Namboodiri, Ehsan Khatami


The Hubbard model is one of the primary models for understanding the essential many-body physics in condensed matter systems such as Mott insulators and cuprate high-Tc superconductors. Due to the long-range Coulomb interactions, accessible low-temperatures, and atomic-scale nature, an artificial lattice of dopant-based quantum dots in silicon, consisting of one or a few dopant atoms per site, makes possible the analog quantum simulation of many-body problems that can be modeled by an extended Fermi-Hubbard Hamiltonian, particularly in the strong interaction regime. Effective control of tunable parameters in a dopant-based Hubbard simulator relies on the controlled placement of dopant atoms with atomic-scale precision. Recent advances in atomically precise fabrication in silicon using scanning tunneling microscopy (STM) have made possible atom-by-atom fabrication of single and few-dopant quantum dots and atomic-scale control of tunneling in dopant-based devices. However, the complex fabrication requirements of multi-component devices have meant that emulating two-dimensional (2D) Fermi-Hubbard physics using these systems has not been demonstrated. Here, we overcome these challenges by integrating the latest developments in atomic fabrication and demonstrate the analog quantum simulation of a 2D extended Fermi-Hubbard Hamiltonian using STM-fabricated 3×3 arrays of single/few-dopant quantum dots. We demonstrate low-temperature quantum transport and tune the chemical potential landscape using in-plane gates as efficient probes to characterize the many-body properties, such as charge addition, tunnel coupling, and the impact of disorder within the array. By controlling the array lattice constants with sub-nm precision, we demonstrate tuning of the hopping amplitude and long-range interactions and observe a transition from Mott insulating to metallic behavior in the array. By increasing the measurement temperature, we simulate the effect of thermally activated hopping and Hubbard band formation in transport spectroscopy. We compare the analog quantum simulations with numerically simulated results to help understand the energy spectrum and resonant tunneling within the array. As atomically precise control of dopant-based quantum dots continues to improve, the results demonstrated in this study serve as a launching point for a new class of engineered artificial lattices to simulate the extended Fermi-Hubbard model of strongly correlated materials.
Nature Communications


Hubbard model, analog quantum simulation, Coulomb interactions, hoppnig amplitude


Silver, R. , Wyrick, J. , Wang, X. , Kashid, R. , Bryant, G. , Rigosi, A. , Namboodiri, P. and Khatami, E. (2022), Experimental realization of an extended Fermi-Hubbard model using a 2D lattice of dopant-based quantum dots, Nature Communications, [online],, (Accessed April 18, 2024)
Created November 11, 2022, Updated March 16, 2023