Related papers: Topological tight-binding models from non-trivial …

We propose topological semimetals generated by the square-root operation for tight-binding models in two and three dimensions, which we call square-root topological semimetals. The square-root topological semimetals host topological band…

Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…

A topological mechanism is a zero elastic-energy deformation of a mechanical structure that is robust against smooth changes in system parameters. Here, we map the nonlinear elasticity of a paradigmatic class of topological mechanisms onto…

Topological photonic edge states, protected by chiral symmetry, are attractive for guiding wave energy as they can allow for more robust guiding and greater control of light than alternatives; however, for photonics, chiral symmetry is…

It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be…

This is the second of two papers devoted to tight-binding electronic spectra on graphs with the topology of the sphere. We investigate the problem of an electron subject to a spin-orbit interaction generated by the radial electric field of…

Justification of tight-binding model from Schroedinger formalism for various topologies of position-based semiconductor qubits is presented in this work. Simplistic tight-binding model allows for description of single-electron devices at…

The non-trivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature, unique to non-Hermitian…

Square-root topological insulators are recently-proposed intriguing topological insulators, where the topologically nontrivial nature of Bloch wave functions is inherited from the square of the Hamiltonian. In this paper, we propose that…

Square-root topology is one of the newest additions to the ever expanding field of topological insulators (TIs). It characterizes systems that relate to their parent TI through the squaring of their Hamiltonians. Extensions to $2^n$-root…

We introduce a novel class of low-dimensional topological tight-binding models that allow for bound states that are fractionally charged fermions and exhibit non-Abelian braiding statistics. The proposed model consists of a double (single)…

Braiding has attracted significant attention in physics because of its important role in describing the fundamental exchange of particles. Infusing the braiding with topological protection will make it robust against imperfections and…

We consider non-Hermitian dynamics of a quantum particle hopping on a one-dimensional tight-binding lattice made of $N$ sites with asymmetric hopping rates induced by a time-periodic oscillating imaginary gauge field. A deeply different…

We classify Hermitian tight-binding models describing noninteracting electrons on a one-dimensional periodic lattice with two energy bands. To do this, we write a generalized Rice-Mele model with two orbitals per unit cell, including all…

Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of…

The complex energy bands of non-Hermitian systems braid in momentum space even in one dimension. Here, we reveal that the non-Hermitian braiding underlies the Hermitian topological physics with chiral symmetry under a general framework that…

We establish a connection between an arbitrary Hermitian tight-binding model with chiral (C) symmetry and its non-Hermitian counterpart with chiral-time (CT ) symmetry.We show that such a non-Hermitian Hamiltonian is pseudo-Hermitian. The…

Symmetry plays an important role in the topological band theory. In contrary, study on the topological properties of the asymmetric systems is rather limited, especially in higher-dimensional systems. In this work, we explore a new theory…

In this Letter, we study a previously unexplored class of topological states protected by hidden chiral symmetries that are local, that is, that protect against any off-diagonal disorder. We derive their related topological invariant for…

The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…