Topological Anderson insulator and reentrant topological transitions in a mosaic trimer lattice

Abstract

We study the topological properties of a one-dimensional quasiperiodic-potential-modulated mosaic trimer lattice. To begin with, we first investigate the topological properties of the model in the clean limit free of quasiperiodic disorder based on analytical derivation and numerical calculations of the Zak phase $Z$ and the polarization $P$. Two nontrivial topological phases corresponding to the $1/3$ filling and $2/3$ filling, respectively, are revealed. Then we incorporate the mosaic modulation and investigate the influence of quasiperiodic disorder on the two existing topological phases. Interestingly, it turns out that quasiperiodic disorder gives rise to multiple distinct effects for different fillings. At $2/3$ filling, the topological phase is significantly enhanced by the quasiperiodic disorder and topological Anderson insulator emerges. Based on the calculations of polarization and energy gap, we explicitly present corresponding topological phase diagram in the $λ-J$ plane. While for the $1/3$ filling case, % the topological phase is dramatically suppressed by the same quasiperiodic disorder. the quasiperiodic disorder dramatically compresses the topological phase, and strikingly, further induces the emergence of reentrant topological phase transitions instead. Furthermore, we verify the topological phase diagrams by computing the many-body ground state fidelity susceptibility for both the $1/3$ filling and $2/3$ filling cases. Our work exemplifies the diverse roles of quasiperiodic disorder in the modulation of topological properties, and will further inspire more research on the competitive and cooperative interplay between topological properties and quasiperiodic disorder.

Figures (9)

• Figure 1: Sketch of the one-dimensional mosaic trimer lattice. Each small circle represents a lattice site. Black solid line represents intra-cell hopping $t$, blue solid line denotes inter-cell hopping $J$, and the quasi-periodic potential $V_j$ exists only at $b$ sites.
• Figure 2: Energy spectra as a function of the inter-cell hopping strength $J$ for the trimer lattice model in Eq. (\ref{['Htrimer']}) with open boundary condition (OBC) in its clean limit. The topological edge states are highlighted with magenta color. Other parameters are $L=3N=699$, $t=1$.
• Figure 3: The total Zak phase $Z$ and polarization $P$ of the clean trimer lattice in Eq. (\ref{['Htrimer']}) under different filling conditions. (a) The two lower bands are filled. (b) Only the lowest band is filled. The red dots represent the Zak phase $Z$ and the blue circles represent polarization $P$. The Zak phase $Z$ is calculated in momentum space and the polarization $P$ is calculated in real space under periodic boundary condition (PBC) with $L=3N=699$. Common parameter $t=1$.
• Figure 4: The topological phase diagram of the mosaic trimer lattice of Eq. (\ref{['Htrimer']}) in the $\lambda-J$ plane at $2/3$ filling. (a) The polarization $P$ as a function of $\lambda$ and $J$. Values of $P$ in the phase diagram are marked with different colors. The green dashed line corresponds to $\lambda=4$. (b) The energy gap $\Delta E_{2/3}$ as a function of $\lambda$ and $J$. The color denotes the value of $\log \Delta E_{2/3}$. Both the polarization $P$ and the energy gap $\Delta E_{2/3}$ are calculated under periodic boundary conditions (PBCs) with $L=3N=1830$. Common parameter $t=1$.
• Figure 5: (a) The eigenenergy spectra $E$ around 2/3 filling as a function of $J$ with $\lambda=4$ and open boundary conditions (OBCs). The emergence of topological edge states is highlighted with magenta lines. (b) The polarization $P$ as a function of $J$ with $\lambda=4$. Both the eigenenergy spectrum $E$ and the polarization $P$ are calculated with $L=3N=1131$. Common parameter $t=1$. The green dashed lines in (a) and (b) both correspond to $J = 1.12$, marking the topological phase transition point.