Controllable Emergence of Multiple Topological Anderson Insulator Phases in Photonic Su-Schrieffer-Heeger Lattices

Abstract

We investigate the emergence and control of multiple topological Anderson insulator (TAI) phases in a one-dimensional Su-Schrieffer-Heeger (SSH) waveguide lattice with generalized Bernoulli-type disorder introduced in the intradimer couplings. By systematically varying the disorder configuration -- including the values and probabilities of the multivariate distribution -- we demonstrate that both the number and width of TAI phases can be precisely engineered. Analytical determination of topological phase boundaries via the inverse localization length shows excellent agreement with numerical simulations. Our results reveal a rich landscape of disorder-induced topological phase transitions, including multiple reentrant TAI phases that arise as the disorder amplitude increases. Furthermore, we show that the mean chiral displacement serves as a sensitive probe for detecting these topological transitions, providing a practical route for experimental realization in photonic waveguide lattices. This work establishes a versatile framework for designing quantum and photonic materials with customizable topological properties driven by tailored disorder.

Figures (5)

• Figure 1: (a) Topological phase diagram characterized by the disorder-averaged topological invariant $\overline{Q}$, as a function of intradimer hopping amplitude $t_1$ and disorder amplitude $\lambda$ for $p_1=2/5$ and $p_2=3/5$. Orange, white, and black dashed lines indicate $t_1=0.5$, $2.0$, and $3.3$, respectively; blue dashed lines mark the analytical phase boundaries. (b1)-(b3) Disorder-average central energies $\overline{E}_N$, $\overline{E}_{N+1}$ and topological number $\overline{Q}$ versus $\lambda$ under OBC for $t_1=0.5$, $2.0$, and $3.3$, respectively. (c1)-(c4) Density distributions of the $N$-th and $N+1$-th eigenstates under OBCs for $\lambda=0.80$, $1.71$, $2.60$, and $3.27$ (marked by red squares in (a)). All data averaged over $N_c=200$ disorder realizations, $N=400$ and $\xi^{(1)}=\lambda$, $\xi^{(2)}=2\lambda$.
• Figure 2: (a) Widths of the first and second TAI phases as a function of probability distribution for $t_1=3.3$ with $\xi^{(1)}=\lambda$ and $\xi^{(2)}=2\lambda$. (b) Widths of the first and second TAI phases versus $\xi^{(2)}/\xi^{(2)}$ for $t_1=3.3$ with $\xi^{(1)}=\lambda$, $p_1=2/5$, and $p_2=3/5$.
• Figure 3: (a) Topological phase diagram characterized by the disorder-averaged topological invariant $\overline{Q}$, as a function of intradimer hopping $t_1$ and disorder amplitude $\lambda$ ($p_1=1/2$, $p_2=p_3=1/4$). Orange, white, and black dashed lines indicate $t_1=0.5$, $2.0$, and $3.3$; blue dashed lines mark analytical phase boundaries. (b1)-(b3) Disorder-averaged central energies $\overline{E}_N$, $\overline{E}_{N+1}$, and topological number $\overline{Q}$ versus $\lambda$ under OBC for $t_1=0.5$, $2.0$, and $3.3$, respectively. (c) Widths of TAI phases for different $p_2$ ($\xi^{(1)}=\lambda$, $\xi^{(2)}=2\lambda$, $\xi^{(3)}=3\lambda$, $p_1=1/2$). (d) Widths of TAI phases versus $\xi^{(2)}/\xi^{(1)}$ ($\xi^{(1)}=\lambda$, $\xi^{(3)}=3\lambda$, $p_1=1/2$, $p_2=p_3=1/4$). All data averaged over $N_c=200$ disorder realizations, and $N=400$.
• Figure 4: Disorder-averaged mean chiral displacement operator $\overline{C}(t)$ versus time $t$ for various disorder amplitudes $\lambda$ ($N=200$ and $N_c=300$) for (a) $M=2$ and (c) $M=3$. Time-averaged chiral displacement $\langle\overline{C}\rangle$ as a function of $\lambda$ ($N=100$ and $N_c=300$), averaged over time steps from $0$ to $100$ (step size $0.5$), for (b) $M=2$ and (d) $M=3$. The pink regions indicate topologically nontrivial phase. Parameters: (a), (b) $\xi^{(1)}=\lambda, \xi^{(2)}=2\lambda, p_1=2/5, p_2=3/5$; (c), (d) $\xi^{(1)}=\lambda,\xi^{(2)}=2\lambda,\xi^{(3)}=3\lambda, p_1=1/2, p_2=p_3=1/4$.
• Figure A1: The disorder-average topological phase diagram as a function of the intradimer hopping amplitude $t_1$ and the disorder strength $\lambda$ for (a) $\xi^{(m)}=m\lambda$, $(m=1,2,3,4)$, $p_1=7/20$, $p_2=1/4$, $p_3=p_4=1/5$ and (b) $\xi^{(m)}=m\lambda$, $(m=1,2,3,4,5)$, $p_1=p_2=1/4$, $p_3=p_4=p_5=1/6$. The blue dashed lines correspond to the topological phase boundaries. Here, all the data are averaged by $N_c=200$ disorder realizations.