Quantum spin compass models in two-dimensional electronic topological metasurfaces

We consider a metasurface consisting of a square lattice of cylindrical antidots in a two-dimensional topological insulator (2DTI). Each antidot supports a degenerate Kramer's pair of eigenstates formed by the helical topological edge states. We show that the on-site Coulomb repulsion leads to the onset of the Mott insulator phase in the system in a certain range of experimentally relevant parameters. Intrinsic strong spin-orbit coupling characteristic for the 2DTI supports a rich class of the emerging low-energy spin Hamiltonians that can be emulated in the considered system, which makes it an appealing solid-state platform for quantum simulations of strongly correlated electron systems.

Figure 1

A 2D array of antidots (holes) in 2DTI. Blue (dark) and red (light) arrows show topologically protected counterpropagating edge states with opposite spin directions.

Figure 2

Energies of in-gap edge states circulating around an antidot as functions of the antidot radius $a$; $m$ is the quantum number defining z projection of the total angular momentum of the circulating edge states.

Figure 3

(a) The dependence of the ${\left|\psi \left(r\right)\right|}^2$ of the edge state of an antidot with the radius $a=15\mathrm{nm}$ vs distance from the center of the antidot, $\left|m\right|=1/2$. (b) Spin density of the edge state near a single antidot.

Figure 4

(a) The dependence of the tunneling amplitude (black curve) and $\alpha \left(\beta \right)$ parameter (dashed blue curve) vs distance between centers of antidots R (in units of the dot radius $a$, taken to be 15 nm). The gray area of the plot denotes Mott insulating regime of the system at half filling. (b) The dependence of the on-site interaction energy vs radius of the antidot