Related papers: Topological properties in one-dimensional periodic…
The ground states of noninteracting fermions in one-dimension with chiral symmetry form a class of topological band insulators, described by a topological invariant that can be related to the Zak phase. Recently, a generalization of this…
We investigate the topological properties of a generalized Dirac--Kronig--Penney model, a continuum one-dimensional model for a relativistic quantum chain. By tuning the coupling parameters this model can accommodate five…
We discuss the relation between bulk topological invariants and the spectrum of surface states in three dimensional non-interacting topological insulators. By studying particular models, and considering general boundary conditions for the…
Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize…
Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…
Unlike a Chern number in $2$D and $3$D topological system, Zak phase takes a subtle role to characterize the topological phase in $1$D. On the one hand, it is not a gauge invariant, on the other hand, the Zak phase difference between two…
We present comparatively simple two-dimensional and three-dimensional checkerboard-like optical lattices possessing nontrivial topological properties. By simple tuning of the parameters these lattices can have a topological insulating…
Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs),…
Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider…
Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of…
Topological concepts have been introduced into electronic, photonic, and phononic systems, but have not been studied in surface-water-wave systems. Here we study a one-dimensional periodic resonant surface-water-wave system and demonstrate…
Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal…
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…
As energy dissipation and gain are ubiquitous in the real world, such phenomena demand the generalization of Hermitian methods such as the analysis of topological properties for non-Hermitian systems. However, as non-Hermitian systems…
Discrete-time quantum walks have been shown to simulate all known topological phases in one and two dimensions. Being periodically driven quantum systems, their topological description, however, is more complex than that of closed…
Continuum grid-like frames composed of rigidly jointed beams are classic subjects in the field of structural mechanics, whose topological dynamical properties have only recently been revealed. For two-dimensional frames, higher-order…
We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…
A topological measure characterizing symmetry-protected topological phases in one-dimensional open fermionic systems is proposed. It is built upon the kinematic approach to the geometric phase of mixed states and facilitates the extension…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
In crystalline systems, charge polarization is related to Zak's phase determined by bulk band topology. Nontrivial charge polarization induces robust edge states accompanied with fractional charge. In Su-Schrieffer-Heeger (SSH) model, it is…