Related papers: Automorphic Bloch theorems for hyperbolic lattices
The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept…
We prove a theorem describing the limiting fine-scale statistics of orbits of a point in hyperbolic space under the action of a discrete subgroup. Similar results have been proved only in the lattice case, with two recent infinite-volume…
Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a…
Topologically protected edge states have been extensively studied in systems characterized by the topological invariants in band gaps (also called line gaps). In this study, we unveil a whole new form of edge states that transcends the…
The discovery of novel topological states has served as a major branch in physics and material science. However, to date, most of the established topological states of matter have been employed in Euclidean systems, where the interplay…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
While the landscape of free-fermion phases has drastically been expanded in the last decades, recently novel multi-gap topological phases were proposed where groups of bands can acquire new invariants such as Euler class. As in conventional…
Band formation in periodic media is a central topic in undergraduate solid-state physics, typically introduced through Bloch's theorem as an eigenvalue problem in reciprocal space for infinitely periodic systems. While mathematically…
There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key…
We study topological properties of one-dimensional nonlinear bichromatic superlattices and unveil the effect of nonlinearity on topological states. We find the existence of nontrivial edge solitions, which distribute on the boundaries of…
We investigate the dispersion topology of elastic lattices characterized by spatial stiffness modulation. The modulation is defined by the sampling of a two-dimensional surface, which provides the lattices with topological properties that…
A systematic framework for realizing $\mathbb{Z}_2$ gauge extensions of hyperbolic lattices within the nearest-neighbor tight-binding formalism is developed. Using the triangle group $\Delta(2,8,8)$ as an example, we classify all…
The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…
The discovery of hyperbolic lattice, a discretized regularization of non-Euclidean space with constant negative curvature, has provided an unprecedented platform to extend topological phases of matter from Euclidean to non-Euclidean spaces.…
Non-Hermitian systems exhibit diverse graph patterns of energy spectra under open boundary conditions. Here we present an algebraic framework to comprehensively characterize the spectral geometry and graph topology of non-Bloch bands. Using…
Electronic flat bands have localized Wannier-like orbitals as zero modes. In the Lieb or the kagome models, the localized orbitals satisfy a topological condition that entails two non-contractible loop eigenstates along $x/y$-axis in real…
This article provides a synopsis of our recent experimental work exploring Bose-Einstein condensation in metastable higher Bloch bands of optical lattices. Bipartite lattice geometries have allowed us to implement appropriate band…
Theoretical studies and experiments in the last six years have revealed the potential for novel behaviours and functionalities in device physics through the synthetic engineering of negatively-curved spaces. For instance, recent…
Topological properties of solid-state materials arise when crossings occur in their band-structure eigenvalues, which give rise to discontinuities in the associated Bloch-function eigenvectors once these are mapped over the whole Brillouin…
To realize band structures with non-trivial topological properties in an optical lattice is an exciting topic in current studies on ultra cold atoms. Here we point out that this lofty goal can be achieved by using a simple scheme of shaking…