Quantum simulations of the Su–Schrieffer–Heeger model in P-doped silicon devices

The atomic precision of impurity placement in dopant-based silicon devices makes them ideal for use in analog quantum simulation. Recently, the Simmons group reported analog simulations of the Su-Schrieffer-Heeger (SSH) model (Nature 606, p.694 (2022)) in an array of silicon quantum dots, each consisting of about 25 P atoms, demonstrating trivial and topological phases. Here, we explore the possibility of realizing an SSH system in zig-zag arrays of single P-atom quantum dots in Si. We implement atomistic tight-binding, configuration-interaction calculations for systems with 6 to 10 phosphorus atoms and modulate the electron hopping and intersite Coulomb interactions by varying the staggered distribution and separation of the impurities. Our fully atomistic calculations for trivial and topological arrays reveal the differences in the single and many-particle states that arise due to geometry, valley splitting, and interaction. In particular, we resolve from the energy spectrum and charge distribution effects of valley splitting, that go beyond the SSH model, and characterize the formation of the topological phases and edge states at half-filling as a function of P-P distance.