Engineering topological states in atom-based semiconductor quantum dots

Analogue quantum simulators have long promised the ability to simulate emergent microscopic phenomena in physics beyond the capability of classical computers. Recent results in semiconductor quantum dots have demonstrated simulation of the Fermi-Hubbard model and Nagaoka ferromagnetism, the simplest one-dimensional model of strongly correlated topological insulators, the many body Su-Schrieffer-Heeger (SSH) model has remained elusive. Realising strong quantum correlations in interacting Fermionic systems is difficult due to the challenge of precisely engineering long-range interactions between electrons such that the system is not destroyed. Here, we show that for precision placed atoms in silicon with strong Coulomb confinement we can engineer a minimum of 6 all-epitaxial in-plane gates to tune the electrochemical potential across the chain to realise both the trivial and topological phases of the many-body SSH model in a linear array of 10 quantum dots. The strong on-site energies (U ~ 30 meV) and unique staggered device design allow us to tune the ratio between inter- and intracell electron transport to observe clear signatures of a topological phase with 2 conductance peaks at quarter-filling compared to the 10 conductance peaks of the trivial phase. The demonstration of the SSH model in a Fermionic system designed with sub-nanometre precision and low-gate densities, isomorphic to qubits, has identified a highly controllable quantum system that can be used for future simulations of strongly interacting electrons.