Activating non-Hermitian skin modes by parity-time symmetry breaking

Parity-time (PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{\mathcal{PT}}}}}}}}$$\end{document}) symmetry is a cornerstone of non-Hermitian physics as it ensures real energies for stable experimental realization of non-Hermitian phenomena. In this work, we propose PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{\mathcal{PT}}}}}}}}$$\end{document} symmetry as a paradigm for designing rich families of higher-dimensional non-Hermitian states with unique bulk, surface, hinge or corner dynamics. Through systematically breaking or restoring PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{\mathcal{PT}}}}}}}}$$\end{document} symmetry in different sectors of a system, we can selectively activate or manipulate the non-Hermitian skin effect (NHSE) in both the bulk and topological boundary states. Some fascinating phenomena include the directional toggling of the NHSE, and the flow of boundary states without chiral or dynamical pumping, developed from selective boundary NHSE. Our results extend richly into 3D or higher, with more sophisticated interplay with selective bulk and boundary NHSE and charge-parity (CP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{\mathcal{CP}}}}}}}}$$\end{document}) symmetry. Based on non-interacting lattices, PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{\mathcal{PT}}}}}}}}$$\end{document}-activated NHSEs can be observed in various optical, photonic, electric and quantum platforms that admit gain/loss and non-reciprocity. PT-symmetric non-Hermitian systems possess real and complex eigenenergies in the symmetry unbroken and broken phases, respectively. Based on these spectral features and non-Hermitian band theory, the authors provide a framework to generate localized states and dynamics at different sectors of non-Hermitian systems, which can be selectively activated/deactivated by breaking/restoring PT symmetry.