Related papers: Automorphic Bloch theorems for hyperbolic lattices
Bloch's theorem is the centerpiece of topological band theory, which itself has defined an era of quantum materials research. However, Bloch's theorem is broken by a perpendicular magnetic field, making it difficult to study topological…
We investigate the dynamic properties of elastic lattices defined by tessellations of a curved hyperbolic space. The lattices are obtained by projecting nodes of a regular hyperbolic tessellation onto a flat disk and then connecting those…
We investigate the nonlinear Bloch dynamics and Landau-Zener tunneling of quantum droplets in optical lattices, where the interplay between mean-field repulsion and beyond-mean-field attraction from Lee-Huang-Yang corrections introduces a…
Two-dimensional van der Waals heterostructures can be engineered into artificial superlattices that host flat bands with significant Berry curvature and provide a favorable environment for the emergence of novel electron dynamics. In…
Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they…
We develop a comprehensive theory for the effective dynamics of Bloch electrons based on symmetry. We begin with a scheme to systematically derive the irreducible representations (IRs) characterizing the Bloch functions. Starting from a…
Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the…
The static and high-frequency differential conductivity of a one-dimensional superlattice with parabolic miniband, in which the dispersion law is assumed to be parabolic up to the Brillouin zone edge, are investigated theoretically. Unlike…
The vacuum of a band system, with respect to particles or holes, can become topologically nontrivial when the exceptional points of the non-hermitian Hamiltonian spread over the whole Brillouin zone. The coalescence of the eigenstates…
Bloch oscillations refer to the periodic oscillation of a wavepacket in a lattice under a constant force. Typically, the oscillation has a fundamental period that corresponds to the wavepacket traversing the first Brillouin zone once. Here…
Recently, it has been observed that the Floquet-Bloch transform with real quasiperiodicities fails to capture the spectral properties of non-reciprocal systems. The aim of this paper is to introduce the notion of a generalised Brillouin…
A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of…
Using a hyperbolic complex plane, we study the realization of the underlying hyperbolic symmetry as an internal symmetry that enables the unification of scalar fields of cosmological and particle physics interest. Such an unification is…
The intra-band tunneling of a Bose-Einstein condensate between three degenerate high-symmetry X-points of the Brillouin zone of a cubic optical lattice is studied in the quantum regime by reduction to a three-mode model. The mean-field…
Topological phases like topological insulators or superconductors are fascinating quantum states of matter, featuring novel properties such as emergent chiral edge states or Majorana fermions with non-Abelian braiding statistics. The recent…
In this paper, we classify completely hyperbolic 3-manifolds corresponding to geometric limits of Kleinian surface groups isomorphic to $\pi_1(S)$ for a finite-type hyperbolic surface $S$. In the first of the three main theorems, we…
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…
Motivated by recent experimental breakthroughs in realizing hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. By utilizing large hyperbolic lattices…
Being dispersionless, flat bands on periodic lattices are solely characterized by their macroscopically degenerate eigenstates: compact localized states (CLSs) in real space and Bloch states in reciprocal space. Based on this property, this…
We establish a non-Bloch band theory for one-dimensional(1D) non-Hermitian topological superconductors. The universal physical properties of non-Hermitian topological superconductors are revealed based on the theory. According to the…