arXiv subjects

Jing-Run Lin

Publications and source records attributed to Jing-Run Lin.

4 recordsLinked to original sources

arXiv2025

Topological band insulators without translational symmetry

In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here we propose a systematic method of constructing the topological band insulators without translational symmetry in the amorphous systems. By way of the isospectral reduction approach from spectral graph theory, we reduce the structural-disordered systems formed by different multi-atomic cells into the isospectral effective periodic systems with the energy-dependent hoppings and potentials. We identify the topological band insulating phases with extended bulk states and topological in-gap edge states by the topological invariants of the reduced systems, density of states, and the commutation of the transfer matrix. In addition, when the building blocks of the two multi-atomic cells have different number of the lattice sites, our numerical calculations demonstrate that the existences of the flat band and the macroscopic bound states in the continuum in the amorphous systems. Our findings uncover an arena for the exploration of the topological band states beyond translational symmetry systems paradigm.

cond-mat.dis-nn↗

arXiv2025

Topological Anderson insulators by latent symmetry

Topological Anderson insulators represent a class of disorder-induced, nontrivial topological states of matter. In this study, we propose a feasible strategy to unveil and design topological Anderson insulators protected by latent symmetries. These are not visible in the original system, but become obvious after performing an isospectral reduction. Using this technique, we design a family of disordered multi-atomic chains that exhibit latent chiral symmetry or mirror (inversion) symmetry. Using topological invariants, bulk polarization, and the divergence of localization length of the topological bound edge states in the reduced disordered system, we show how to identify the gapped and ungapped topological Anderson states in the original systems. Our work thus extends the concept of topological Anderson insulating phases protected by geometric symmetries and tenfold-way classification to the various types of latent symmetry cases. Overall, our work paves the way for exploiting topological Anderson insulators in terms of latent symmetries.

cond-mat.dis-nn↗

arXiv2024

Topological inverse Anderson insulator

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.

cond-mat.mes-hall↗

arXiv2024

Topological states constructed by two different trivial quantum wires

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.

cond-mat.mes-hall↗