$B$}}}=\hat{{\mbox{\boldmath $z$}}}$, $L=200$, $(\Gamma, \alpha, V_\mathrm{Q}) = (0.2, 0.3, 0.5)$, $\Delta = 0.1$. Eigenstates for $n_\mathrm{B} = 100$ are plotted for (b) $\mu = -0.28$ (only the right side of the system is single band), (c) $\mu = 0$ (both sides are single band), and (d) $\mu = 0.1$ (only the left side is single band). []{data-label="fig:partialModulation"}](Full_Fig8_200){width="8.66cm"}

The view above is further confirmed when we remove the lattice modulation from some part of the system, by having $$\epsilon_l = \left\{
\begin{array}{cc}
0, & (0 \leq l < n_\mathrm{B})\\
V_\mathrm{Q} \cos(\kappa(l - l_c)). & (n_\mathrm{B} \leq l < L)
\end{array}
\right.$$ In Fig. \[fig:partialModulation\] (a) we plot the value of $\epsilon^+$ for different values of $n_\mathrm{B}$ for the case in which the part of the system to the left of site $n_\mathrm{B}$ has the same parameter as in Fig. \[fig:localization\] (a), whereas the right part has the same parameter as in Fig. \[fig:localization\] (b). For $n_\mathrm{B} = L/2 = 100$ we observe that $\epsilon^+$ vanishes when it vanishes either in Fig. \[fig:localization\] (a) with $V_\mathrm{Q} = 0$ or (b) with $V_\mathrm{Q} = 0.5$. In Fig. \[fig:partialModulation\] (b–d) we have plotted the spatial distribution of eigenvectors of (\[eqn:BdG\]) corresponding to $\epsilon^+$. In 