Fig. 4: Non-Hermitian bulk and surface bands of the zigzag boundary.
From: Experimental probe of point gap topology from non-Hermitian Fermi-arcs
a–c Calculated eigenfrequencies under the configuration with the 3D periodic boundary conditions (PBCs) (\({E}^{{{\rm{P}}}}\)) and the \(y\)-open boundary condition (OBC) and \({xz}\)-PBCs (\({E}^{y-{\mbox{O}}}\)) by fixing \({k}_{z}=0.5\pi\). The gray area in (a) and (c) represents \({E}^{{{\rm{P}}}}\) for \({k}_{y}\in \left[-\pi ,\pi \right]\) and \({k}_{x}\in \left[-\pi ,\pi \right]\), while the solid blue arcs in (a) highlight \({E}^{{{\rm{P}}}}\) by further fixing \({k}_{x}=0.5\pi\). The black (cyan and red) markers in (a) are the bulk (surface) states in \({E}^{y-{\mbox{O}}}\) with \({k}_{x}=0.5\pi\). The spatial distributions of two surface states are shown in (b). The blue markers in (c) represent \({E}^{y-{\mbox{O}}}\) for \({k}_{x}\in \left[-\pi ,\pi \right]\). d \({\mbox{Re}}\left({E}^{y-{\mbox{O}}}\right)\) as functions of \({k}_{x}\) and \({k}_{z}\) with the color displaying \({{\rm{Im}}}\left({E}^{y-{\mbox{O}}}\right)\). A bulk \({L}_{r}\) gap is seen when \({k}_{z}\in \left[-0.85\pi ,-0.15\pi \right]\cup \left[0.15\pi ,0.85\pi \right]\), wherein two topological surface states survive but with separate lifetimes \(\tau\).
