Floquet topological phases in parity-time symmetric lattices

Selma Franca, Fabian Hassler, Ion Cosma Fulga

Tian Chen, Bo Wang, Xiangdong Zhang

We present a method to detect topological invariants in nonunitary parity-time-symmetric (PT-symmetric) quantum walks (QWs). The topological phases of a PT-symmetric QW can be characterized by the mean position of the walk, which is an experimentally observable quantity. This method can also be applied to reveal topological phases in the unitary split-step QW and lattice model. We also explore the selection of topological interface modes in the PT-symmetric QW. The introduction of nonunitarity into the PT-symmetric QW can render the eigenvalue of the topological interface mode larger than the bulk region modes, which leads to the selective excitation of the corresponding topological interface mode during the evolution. Contrary to the Su--Schrieffer--Heeger (SSH) lattice model, in the PT-symmetric QW, the transition between the amplification and the suppression of the topological interface mode may not occur. Our study of the selection of topological interface modes in the PT-symmetric QW provides a route to realize the lasing of specific modes within the system.

Kaixiang Su, Po-Wei Lo, Michael J. Lawler

Takahiro Morimoto, Hoi Chun Po, Ashvin Vishwanath

Nonequilibrium systems under periodic driving realize novel topological phases that cannot be achieved in equilibrium systems. One unique feature of periodically driven systems is that they can host a purely dynamical symmetry that involves time translation. This work explores a new class of Floquet topological phases protected by one realization of such dynamical symmetry, i.e., ``time glide symmetry'', which is defined by a combination of reflection and time translation. Lattice models with time glide symmetric driving that are introduced show stable gapless surface states along with nontrivial topological numbers defined with time glide symmetry. In addition, a general classification theory of time glide symmetric topological phases is obtained by using a Clifford algebra approach.

Szabolcs Vajna, B. Horovitz

Haiming Deng, Zhenjiang Shen, Qiongtao Xie

Abstract We investigate a type of periodically driven non-Hermitian two-level model with parity-time (PT) symmetry. It is shown that in a wide range of the model parameters, this model supports exact Floquet solutions. In particular, under certain parameter conditions, these exact Floquet solutions can characterize the transition from the unbroken PT-symmetric phase to the broken PT-symmetric phase.