Ferroelectric polarizations of Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ nanotube array

Ferroelectric polarization and structural properties are determined for the Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ (PZT) nanotube array embedded in matrix materials of different polarizability, by means of first-principles derived effective Hamiltonian and finite-temperature Monte Carlo simulations. The polarizability of the matrix is controlled by the on-site $\kappa_2$ quantity. We found three drastically different structural phases in PZT nanotubes, depending on the polarizability of the matrix. Microscopic insight for these structural phases will be revealed.