Simulating topological insulators with donors and quantum dots*

We explore the possibilities of simulating the Su-Schrieffer–Heeger (SSH) model of topological insulators with a one dimensional chain of donors or quantum dots. A measurement of the transverse tunneling current through one end of the chain is proposed for confirming the existence of the edge state in the topologically non-trivial phase. For donors and quantum dots the electron-electron interaction is typically larger than the hopping amplitude, resulting in strong correlation in the ground state. We investigate the effect of interaction on the spin correlation, entanglement, excitation energy spectrum and the Zak phase. We discuss bulk-edge correspondence between the Zak phase and the edge state in the correlated case. An external magnetic field can be used to induce a transition to the well-understood limit of the non interacting SSH model. This transition is accompanied by a strong enhancement of the edge state's spatial localization, and hence can be identified by observing a sharp increase in the conductance signal.