Floquet engineering offers a unique approach to generate nonequilibrium topological phases in which the unbounded nature of a quasienergy band allows two kinds of topological edge modes, one of them traversing the 0 gap and another one traversing the $\ensuremath{\pi}$ gap. Characterizing of these two modes is the main topic of Floquet topological insulators, where they are usually characterized by different topological invariants. However, in this paper, for a specific protocol of Floquet engineering where the Dirac mass term of the Chern insulator is periodically kicked, its topological phases are characterized with the Floquet Chern number ${C}_{F}$ . Specifically, in our illustrative example, the periodically kicked Qi-Wu-Zhang model, there are six different topological phases in total, denoted as ${C}_{F}={\ensuremath{-}{1}_{0},\ensuremath{-}2,\ensuremath{-}{1}_{\ensuremath{\pi}},{1}_{\ensuremath{\pi}},2,{1}_{0}}$. Topological phases with larger topological number are observed, i.e., ${C}_{F}=\ifmmode\pm\else\textpm\fi{}2$, where the chiral edge modes traversing the 0 gap and those traversing $\ensuremath{\pi}$ gap have the opposite chirality. The mechanism of its topology is revealed by studying the corresponding low-energy effective Dirac Hamiltonian, and the phase boundaries between different topological phases are explicitly found. Additionally, we investigate the orders of phase transitions between different topological phases by studying the von Neumann entropy of the Floquet steady state (FSS), where the FSS corresponds to a stationary state of the Floquet system that is coupled to a Markovian environment. The hallmark of a periodically kicked Dirac mass term is uncovered in this paper, which may inspire further explorations of the physical effects of periodically kicked Dirac mass terms in other systems.Floquet engineering offers a unique approach to generate nonequilibrium topological phases in which the unbounded nature of a quasienergy band allows two kinds of topological edge modes, one of them traversing the 0 gap and another one traversing the $\ensuremath{\pi}$ gap. Characterizing of these two modes is the main topic of Floquet topological insulators, where they are usually characterized by different topological invariants. However, in this paper, for a specific protocol of Floquet engineering where the Dirac mass term of the Chern insulator is periodically kicked, its topological phases are characterized with the Floquet Chern number ${C}_{F}$. Specifically, in our illustrative example, the periodically kicked Qi-Wu-Zhang model, there are six different topological phases in total, denoted as ${C}_{F}={\ensuremath{-}{1}_{0},\ensuremath{-}2,\ensuremath{-}{1}_{\ensuremath{\pi}},{1}_{\ensuremath{\pi}},2,{1}_{0}}$. Topological phases with larger topological number are observed, i.e., ${C}_{F}=\ifmmode\pm\else\textpm\fi{}2$, where the chiral edge modes traversing the 0 gap and those traversing $\ensuremath{\pi}$ gap have the opposite chirality. The mechanism of its topology is revealed by studying the corresponding low-energy effective Dirac Hamiltonian, and the phase boundaries between different topological phases are explicitly found. Additionally, we investigate the orders of phase transitions between different topological phases by studying the von Neumann entropy of the Floquet steady state (FSS), where the FSS corresponds to a stationary state of the Floquet system that is coupled to a Markovian environment. The hallmark of a periodically kicked Dirac mass term is uncovered in this paper, which may inspire further explorations of the physical effects of periodically kicked Dirac mass terms in other systems.

Physical review. B./Physical review. BMay 7, 20242 citations

{C}_{F}

. Specifically, in our illustrative example, the periodically kicked Qi-Wu-Zhang model, there are six different topological phases in total, denoted as ${C}_{F}={\ensuremath{-}{1}_{0},\ensuremath{-}2,\ensuremath{-}{1}_{\ensuremath{\pi}},{1}_{\ensuremath{\pi}},2,{1}_{0}}$. Topological phases with larger topological number are observed, i.e., ${C}_{F}=\ifmmode\pm\else\textpm\fi{}2$, where the chiral edge modes traversing the 0 gap and those traversing $\ensuremath{\pi}$ gap have the opposite chirality. The mechanism of its topology is revealed by studying the corresponding low-energy effective Dirac Hamiltonian, and the phase boundaries between different topological phases are explicitly found. Additionally, we investigate the orders of phase transitions between different topological phases by studying the von Neumann entropy of the Floquet steady state (FSS), where the FSS corresponds to a stationary state of the Floquet system that is coupled to a Markovian environment. The hallmark of a periodically kicked Dirac mass term is uncovered in this paper, which may inspire further explorations of the physical effects of periodically kicked Dirac mass terms in other systems.