Fig. 4: Non-Hermitian skin effect (NHSE) selectively activated by parity-time (\({{{{{{{\mathcal{PT}}}}}}}}\)) or charge-conjugation-parity (\({{{{{{{\mathcal{CP}}}}}}}}\)) symmetry breaking for three-dimensional (3D) models.
From: Activating non-Hermitian skin modes by parity-time symmetry breaking
In most panels [except for c with periodic boundary conditions (PBCs) along x], colored dots represent the bulk, surface or hinge spectra under full OBCs, and gray dots represent the spectra with xz-OBCs and PBCs along y direction. Insets of 3D cubes display the average spatial distribution of eigenstates of the respective color. a–e and f, g pertain to Hγ,3D, Hg,3D, \({H}_{g,3{{{{{{{\rm{D}}}}}}}}}^{{\prime} }\), and \({H}_{3{{{{{{{\rm{D}}}}}}}}}^{{\prime} }\) respectively. In a–c (001) and \((00\bar{1})\)-surface states (blue) experience corner pumping from \({{{{{{{\mathcal{CP}}}}}}}}\)-breaking b or x to y-NHSE directional toggling a, c. In d, e, hinge states (red) can have \({{{{{{{\mathcal{CP}}}}}}}}\) symmetry selectively broken (unbroken), respectively resulting in corner (red) or hinge (green) localization. In f, g, on-demand switching of 1st and 2nd-order 3D bulk NHSE (black surface and edges) through \({{{{{{{\mathcal{PT}}}}}}}}\) breaking leaves other states (green,blue) invariant. In a to c, parameters are v = 1, \({u}^{{\prime} }=0.6\), \({v}^{{\prime} }=3\) and t1 = t2 = 0.1, with u = 0.6 and γ = 0.4 for a and c; u = 0.5 and γ = 1.4 for b. In d and e, parameters are u = 0.2, v = 1, \({u}^{{\prime} }=0.4\), \({v}^{{\prime} }=2\), g = 0.3, t1 = 0.3 and t2 = 0.1. In f and g, parameters are \({u}^{{\prime} }=0.2\), \({v}^{{\prime} }=1\), v = 3, γ = 1.4 and t1 = t2 = 0.1, with u = 0.9 for f and u = 0.5 for g.
