Simulation of higher-order topological phases in 2D spin-phononic crystal networks

Abstract: We propose and analyse an efficient scheme for simulating higher-order topological phases of matter in two dimensional (2D) spin-phononic crystal networks. We show that, through a specially designed periodic driving, one can selectively control and enhance the bipartite silicon-vacancy (SiV) center arrays, so as to obtain the chiral symmetry-protected spin-spin couplings. More importantly, the Floquet engineering spin-spin interactions support rich quantum phases associated with topological invariants. In momentum space, we analyze and simulate the topological nontrivial properties of the one- and two-dimensional system, and show that higher-order topological phases can be achieved under the appropriate periodic driving parameters. As an application in quantum information processing, we study the robust quantum state transfer via topologically protected edge states. This work opens up new prospects for studying quantum acoustic, and offers an experimentally feasible platform for the study of higher-order topological phases of matter.