Floquet generation of higher order topological phases and its quenching dynamics

We discuss a non-equilibrum Floquet scheme to generate the higher-order topological (HOT) phases. In particular, we find that if a d-dimensional regular topological phase involves m Hermitian matrices then a kick in the discrete symmetry breaking Wilsonian mass term, which is composed of additional p-1 anti-commuting matrices, can give rise to n^th order Floquet HOT phases (with n=1,...,p). We demonstrate explicitly this mechanism in the cases of three-dimensional spin-1/2 Dirac semimetal, 2^nd order topological insulator and nodal loop semimetal. We give analytical support for the numerical findings by using the Floquet effective Hamiltonian. Additionally, we study the relaxation dynamics of the above phases by calculating the survival probability for a topological phase followed by a sudden quench. Our results suggest that survival probability for quenching from a higher-order to a lower-order phase depends on the system size while the reverse quenching does not show any system size dependence.