Related papers: A bulk-interface correspondence for equatorial wav…
Topology sheds new light on the emergence of unidirectional edge waves in a variety of physical systems, from condensed matter to artificial lattices. Waves observed in geophysical flows are also robust to perturbations, which suggests a…
Inhomogeneous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. When they are robust against continuous deformations of parameters, such waves are said to be of…
Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes…
The bulk-edge correspondence is a fundamental principle of topological wave physics, which states that the difference in gap Chern numbers between the interfaced materials is equal to the net number of topological edge modes. Although this…
Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is an…
We show that topological waves at the interface between two magnetic domains in a graphene device are possible. First, we consider the case of a linear relation between the applied gate voltage and local density in the channel and,…
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary…
We study the two-dimensional rotating shallow-water model describing Earth's oceanic layers. It is formally analogue to a Schr\"odinger equation where the tools from topological insulators are relevant. Once regularized at small scale by an…
Topological properties of the spectrum of shallow-water waves on a rotating spherical body are established. Particular attention is paid to its spectral flow, i.e. the modes whose frequencies transit between the Rossby and inertia-gravity…
A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting…
Many-body topological quantum states host exotic quantum phenomena and lie at the forefront of developing next-generation quantum technologies. Recently emerged neural network wavefunction methods have established themselves as a powerful…
Atmospheric and oceanic mass transport near the equator display a well-studied asymmetry characterized by two modes moving eastward. This asymmetric edge transport is characteristic of interfaces separating two-dimensional topological…
We investigate the topological phase transition with large Chern number in a coupled layer system. The topological transitions between different topological superfluids can be realized by controlling the binding energy, interlay tunneling…
This tutorial is divided into two parts: the first examines the application of topology to problems in wave physics. The origins of the Chern number are reviewed, where it is shown that this counts the number of critical points of a complex…
We consider topologically non-trivial interface Hamiltonians, which find several applications in materials science and geophysical fluid flows. The non-trivial topology manifests itself in the existence of topologically protected,…
The topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional…
Topology plays an increasing role in physics beyond the realm of topological insulators in condensed mater. From geophysical fluids to active matter, acoustics or photonics, a growing family of systems presents topologically protected…
In 2D Chern insulators (2D CI), the topology of the bulk states is captured by a topological invariant, the Chern number. The scalar bulk-boundary correspondence (sBBC) relates the change in Chern number across an interface with the number…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but…