Quantized electromagnetic response of three-dimensional chiral topological insulators

Protected by the chiral symmetry, three-dimensional chiral topological insulators are characterized by an integer-valued topological invariant. How this invariant could emerge in physical observables is an important question. Here, we show that the magnetoelectric polarization can identify the integer-valued invariant if we gap the system without coating a quantum Hall layer on the surface. The quantized response is demonstrated to be robust against weak perturbations. We also study the topological properties by adiabatically coupling two nontrivial phases, and find that gapless states appear and are localized at the boundary region. Finally, an experimental scheme is proposed to realize the Hamiltonian and measure the quantized response with ultracold atoms in optical lattices.