Fig. 4: Spectral localizer.

a–c Spatial distributions \(| {\bar{\psi }}_{x}| =| \hat{S}{\psi }_{x}|\) of topological zero modes. d–f Eigenvalues of \({\tilde{L}}_{\zeta }\), labeled by \(\sigma ({\tilde{L}}_{\zeta })\), versus x for different I = ∑_j(∣a_j∣² + ∣b_j∣²), with η = 0.2 and \(\bar{\omega }=0\). g–i Site-resolved topological invariant \({C}_{\zeta }=\,{\mbox{Sig}}\,({\tilde{L}}_{\zeta })/2\), and local band gap \({\mu }_{\zeta }=| {\sigma }_{\min }({\tilde{L}}_{\zeta })|\) for different I. The distributions \({\tilde{t}}_{j}\) and \({\tilde{\lambda }}_{j}\), along with the other parameters, are chosen to be the same as in the case δ = 1 and β = 0.05 shown in Fig. 3.