Special modes induced by inter-chain coupling in a non-Hermitian ladder system

Rong Huang,Yu Yan,Zhi-Xu Zhang,Lu Qi,Hong-Fu Wang,Shou Zhang

Figure 14. The spectra of a general non-Hermitian SSH chain with on-site potential energy under the OBC. In (a) and (b), α = 1.5, β = 1.5; in (c) and (d), α = −1.5, β = 1.5; in (e) and (f), $\alpha =1.5{\rm{i}},\,\beta =1.5{\rm{i}};$ in (g) and (h) $\alpha =-1.5{\rm{i}},\,\beta =1.5{\rm{i}};$ in (i) and (j), $\alpha =3,\,\beta =3,{\alpha }^{{\prime} }=-3,\,{\beta }^{{\prime} }=-3;$ in (k) and (l), $\alpha =3,\,\beta =-3,\,{\alpha }^{{\prime} }=-3,\,{\beta }^{{\prime} }=3;$ in (m) and (n) $\alpha =4.5,\,\beta =0,\,{\alpha }^{{\prime} }=-4.5,\,{\beta }^{{\prime} }=0;$ in (o) and (p), $\alpha =0,\,\beta =5,\,{\alpha }^{{\prime} }=0,\,{\beta }^{{\prime} }=-5;$ in (q) and (r), $\alpha =3{\rm{i}},\,\beta =3{\rm{i}},\,{\alpha }^{{\prime} }=-3{\rm{i}},\,{\beta }^{{\prime} }=-3{\rm{i}};$ in (s) and (t) $\alpha =3{\rm{i}},\,\beta =-3{\rm{i}},\,{\alpha }^{{\prime} }=-3{\rm{i}},{\beta }^{{\prime} }=3{\rm{i}}$. The other parameters are ${\rm{\Delta }}=2/3$, t1 = 1, and N = 21. N is the number of lattice sites of one chain. The bands of the two non-Hermitian chains are marked with solid red and dashed green lines, respectively.