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Topological Anderson insulators represent a class of disorder-induced, nontrivial topological states. In this study, we propose a feasible strategy to unveil and design the latent-symmetry protected topological Anderson insulators. By employing the isospectral reduction approach from graph theory, we reduce a family of the disordered multi-atomic chains to the disordered dimerized chain characterized by energy-dependent potentials and hoppings, which exhibits the chiral symmetry or inversion symmetry. According to the topological invariants, bulk polarization, and the divergence of localization length of the topological bound edge states in the reduced disordered system, the gapped and ungapped topological Anderson states with latent symmetry could be identified in the original disordered multi-atomic systems. The concept of topological Anderson insulating phases protected by the geometric symmetries and tenfold-way classification is thus extended to the various types of latent symmetry cases. This work paves the way for exploiting topological Anderson insulators in terms of latent symmetries., Comment: 9 pages, 5 figures, Comments are welcome

A different type of topological phase dubbed topological inverse Anderson insulators is proposed, which is characterized by the disorder-induced extended bulk states from the flat-band localization and topological edge states. Based on the topological invariant, the behaviors of the localization length of the zero-energy modes, and quantum transport, we identify its existence in several all-band-flat models with the disordered potentials or hopping including the $\pi$-flux Creutz ladder, the fully dimerized Su-Schrieffer-Heeger chain, and $\pi$-flux diamond chain. Unlike the topological Anderson insulator, where disorder induces localization and exponential suppression of transport, the disorder-assisted quantum ballistic coherent transport can appear in the topological inverse Anderson insulator. In addition, our proposal and results could be realized by the current experimental techniques., Comment: 9 pages, 5 figures

The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques., Comment: 11 pages, 8 figures