arXiv subjects

Pierre Delplace

Publications and source records attributed to Pierre Delplace.

At least 19 recordsLinked to original sources

arXiv2026

Accessing Chern Numbers From Bloch Eigenstates Singularities

We propose two methods to extract the Chern numbers of the Bloch bands of a two dimensional insulator, and apply them to a photonic lattice experiment. These two methods require the knowledge of the complex-valued components of the Bloch eigenvectors, or their ratios. Unlike other tomography methods relying on the approximate reconstruction of the Berry curvature and its integration over the Brillouin zone, our methods boil down to the observation of phase vorticities in the eigensates structure. Those measurements, robust to experimental noise, yield exactly quantized values. One of the two methods exploits the non-normalization of the eigenmodes, making it particularly relevant for classical wave systems.

cond-mat.mes-hall↗

arXiv2025

A core-sensitive mixed $f$/$g$ mode of the Sun predicted by wave topology and hydrodynamical simulation

Helioseismology has revolutionized our understanding of the Sun by analyzing its global oscillation modes. However, the solar core remains elusive, limiting a full understanding of its evolution. In this work, we study a previously unnoticed global oscillation mode of the Sun using a fully compressible, hydrodynamical simulation of the solar interior, and assess that it is a mixed $f$/$g$ mode with a period of about one hour. This is the first global stellar hydrodynamics simulation that successfuly couple compressible and gravity modes. To understand this coupling, we invoke a recent theory on the nature of $f$-modes seen through the prism of wave topology, characterizing their ability to propagate deep into stellar interiors. We demonstrate that the mixed $f$/$g$ mode is highly sensitive to the core's rotation rate, providing a new promising pathway to explore the Sun's core.

astro-ph.SR↗

arXiv2025

Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants

The mode-shell correspondence relates the number $I_M$ of gapless modes in phase space to a topological \textit{shell invariant} $\Ish$ defined on a close surface -- the shell -- surrounding those modes, namely $I_M=I_S$. In part I, we introduced the mode-shell correspondence for zero-modes of chiral symmetric Hamiltonians (class AIII). In this part II, we extend the correspondence to arbitrary dimension and to both symmetry classes A and AIII. This allows us to include, in particular, $1D$-unidirectional edge modes of Chern insulators, massless $2D$-Dirac and $3D$-Weyl cones, within the same formalism. We provide an expression of $I_M$ that only depends on the dimension of the dispersion relation of the gapless mode, and does not require a translation invariance. Then, we show that the topology of the shell (a circle, a sphere, a torus), that must account for the spreading of the gapless mode in phase space, yields specific expressions of the shell index. Semi-classical expressions of those shell indices are also derived and reduce to either Chern or winding numbers depending on the parity of the mode's dimension. In that way, the mode-shell correspondence provides a unified and systematic topological description of both bulk and boundary gapless modes in any dimension, and in particular includes the bulk-boundary correspondence. We illustrate the generality of the theory by analyzing several models of semimetals and insulators, both on lattices and in the continuum, and also discuss weak and higher-order topological phases within this framework. Although this paper is a continuation of Part I, the content remains sufficiently independent to be mostly read separately.

cond-mat.mes-hall↗

arXiv2024

Observation of extrinsic topological phases in Floquet photonic lattices

Discrete-step walks describe the dynamics of particles in a lattice subject to hopping or splitting events at discrete times. Despite being of primordial interest to the physics of quantum walks, the topological properties arising from their discrete-step nature have been hardly explored. Here we report the observation of topological phases unique to discrete-step walks. We use light pulses in a double-fibre ring setup whose dynamics maps into a two-dimensional lattice subject to discrete splitting events. We show that the number of edge states is not simply described by the bulk invariants of the lattice (i.e., the Chern number and the Floquet winding number) as would be the case in static lattices and in lattices subject to smooth modulations. The number of edge states is also determined by a topological invariant associated to the discrete-step unitary operators acting at the edges of the lattice. This situation goes beyond the usual bulk-edge correspondence and allows manipulating the number of edge states without the need to go through a gap closing transition. Our work opens new perspectives for the engineering of topological modes for particles subject to quantum walks.

quant-ph↗

arXiv2024

Topology of shallow-water waves on the rotating sphere

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 wavebands as the zonal wave number is varied. Organising the modes according to the number of zeros of their meridional velocity, we conclude that the net number of modes transiting between the shallow-water wavebands on the sphere is null, in contrast with the Matsuno spectrum. This difference can be explained by a miscount of zeros under the $\beta$-plane approximation. We corroborate this result with the analysis of Delplace et al (2017) by showing that the curved metric discloses a pair of degeneracy points in the Weyl symbol of the wave operator, non-existent under the $\beta$-plane approximation, each of them bearing a Chern number $-1$.

physics.flu-dyn↗

arXiv2024

Practical realization of chiral nonlinearity for strong topological protection

Nonlinear topology has been much less inquired compared to its linear counterpart. Existing advances have focused on nonlinearities of limited magnitudes and fairly homogeneous types. As such, the realizations have rarely been concerned with the requirements for nonlinearity. Here we explore nonlinear topological protection by determining nonlinear rules and demonstrate their relevance in real-world experiments. We take advantage of chiral symmetry and identify the condition for its continuation in general nonlinear environments. Applying it to one-dimensional topological lattices, we show possible evolution paths for zero-energy edge states that preserve topologically nontrivial phases regardless of the specifics of the chiral nonlinearities. Based on an acoustic prototype design with non-local nonlinearities, we theoretically, numerically, and experimentally implement the nonlinear topological edge states that persist in all nonlinear degrees and directions without any frequency shift. Our findings unveil a broad family of nonlinearities compatible with topological non-triviality, establishing a solid ground for future drilling in the emergent field of nonlinear topology.

cond-mat.mes-hall↗

arXiv2023

Bulk-Edge Correspondence Recovered in Incompressible Geophysical Flows

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 in parameter space. In continuous media, violation of this correspondence has been reported when some of the frequency wavebands are unbounded, resulting in weak topological protection of chiral edge states. Here, we propose a strategy to reestablish strong bulk-edge correspondence in incompressible rotating stratified flows, taking advantage of a natural cutoff frequency provided by density stratification. The key idea involves the introduction of an auxiliary field to handle the divergence-free constraint. This approach highlights the resilience of internal coastal Kelvin waves near vertical walls under varying boundary conditions.

cond-mat.other↗

arXiv2023

Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks

Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the existence of a bulk invariant known as the winding number. However, in lattices subject to periodic discrete-step walks the existence of edge states does not only depend on bulk invariants but also on the boundary. This is a consequence of the absence of an intrinsic time-dependence or micromotion in discrete-step walks. We report the observation of edge states and a simultaneous measurement of the bulk invariants in anomalous topological phases in a two-dimensional synthetic photonic lattice subject to discrete-step walks. The lattice is implemented using time multiplexing of light pulses in two coupled fibre rings, in which one of the dimensions displays real space dynamics and the other one is parametric. The presence of edge states is inherent to the periodic driving and depends on the properties of the boundary in the implemented two-band model with zero Chern number. We provide a suitable expression for the topological invariants whose calculation does not rely on micromotion dynamics.

cond-mat.mes-hall↗

arXiv2023

The Exceptional Ring of buoyancy instability in stars

We reveal properties of global modes of linear buoyancy instability in stars, characterised by the celebrated Schwarzschild criterion, using non-Hermitian topology. We identify a ring of Exceptional Points of order 4 that originates from the pseudo-Hermitian and pseudo-chiral symmetries of the system. The ring results from the merging of a dipole of degeneracy points in the Hermitian stablystratified counterpart of the problem. Its existence is related to spherically symmetric unstable modes. We obtain the conditions for which convection grows over such radial modes. Those are met at early stages of low-mass stars formation. We finally show that a topological wave is robust to the presence of convective regions by reporting the presence of a mode transiting between the wavebands in the non-Hermitian problem, strengthening their relevance for asteroseismology.

astro-ph.SR↗

arXiv2023

Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes

We propose a theory, that we call the \textit{mode-shell correspondence}, which relates the topological zero-modes localised in phase space to a \textit{shell} invariant defined on the surface forming a shell enclosing these zero-modes. We show that the mode-shell formalism provides a general framework unifying important results of topological physics, such as the bulk-edge correspondence, higher-order topological insulators, but also the Atiyah-Singer and the Callias index theories. In this paper, we discuss the already rich phenomenology of chiral symmetric Hamiltonians where the topological quantity is the chiral number of zero-dimensionial zero-energy modes. We explain how, in a lot of cases, the shell-invariant has a semi-classical limit expressed as a generalised winding number on the shell, which makes it accessible to analytical computations.

cond-mat.mes-hall↗

arXiv2023

Topological properties of Floquet winding bands in a photonic lattice

The engineering of synthetic materials characterised by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a two-coupled ring system we engineer an anomalous Floquet metal that is gapless in the bulk and shows simultaneously two different topological properties. On the one hand, this synthetic lattice presents bands characterised by a winding number. The winding emerges from the breakup of inversion symmetry and it directly relates to the appearance of Bloch suboscillations within its bulk. On the other hand, the Floquet nature of the lattice results in well-known anomalous insulating phases with topological edge states. The combination of broken inversion symmetry and periodic time modulation studied here enrich the variety of topological phases available in lattices subject to Floquet driving and suggest the possible emergence of novel phases when periodic modulation is combined with the breakup of spatial symmetries.

physics.optics↗

arXiv2022

Anomalous topological waves in strongly amorphous scattering networks

Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects or local disorder, and can even survive some random deformations of their crystalline structures. However, they always break down when the level of disorder or amorphism gets too large, transitioning to a topologically trivial Anderson insulating phase. Here, we demonstrate a two-dimensional amorphous topological regime that survives arbitrarily strong levels of amorphism. We implement it for electromagnetic waves in a non-reciprocal scattering network and experimentally demonstrate the existence of unidirectional edge transport in the strong amorphous limit. This edge transport is shown to be mediated by an anomalous edge state whose topological origin is evidenced by direct topological invariant measurements. Our findings extend the reach of topological physics to a new class of systems in which strong amorphism can induce, enhance and guarantee the topological edge transport instead of impeding it.

physics.app-ph↗

arXiv2022

Estimating bulk and edge topological indices in finite open chiral chains

We develop a formalism to extend, simultaneously, the usual definition of bulk and edge indices from topological insulators to the case of a finite sample with open boundary conditions, and provide a physical interpretation of these quantities. We then show that they converge exponentially fast to an integer value when we increase the system size, and also that bulk and edge quantities coincide at finite size. The theorem applies to any non-homogeneous system such as disordered or defect configurations. We focus on one-dimensional chains with chiral symmetry, such as the Su-Schrieffer-Heeger model, but the proof actually only requires the Hamiltonian to be short-range and with a spectral gap in the bulk. The definition of bulk and edge indices relies on a finite-size version of the switch-function formalism where the Fermi projector is smoothed in energy using a carefully chosen regularization parameter.

math-ph↗

arXiv2022

Topological modes in stellar oscillations

Stellar oscillations can be of topological origin. We reveal this deep and so-far hidden property of stars by establishing a novel parallel between stars and topological insulators. We construct an hermitian problem to derive the expression of the stellar $\mathrm{\textit{acoustic-buoyant}}$ frequency $S$ of non-radial adiabatic pulsations. A topological analysis then connects the changes of sign of the acoustic-buoyant frequency to the existence of Lamb-like waves within the star. These topological modes cross the frequency gap and behave as gravity modes at low harmonic degree $\ell$ and as pressure modes at high $\ell$. $S$ is found to change sign at least once in the bulk of most stellar objects, making topological modes ubiquitous across the Hertzsprung-Russel diagram. Some topological modes are also expected to be trapped in regions where the internal structure varies strongly locally.

astro-ph.SR↗

arXiv2022

Non-Hermitian spectral flows and Berry-Chern monopoles

We propose a non-Hermitian generalization of the correspondence between the spectral flow and the topological charges of band crossing points (Berry-Chern monopoles). A class of non-Hermitian Hamiltonians that display a complex-valued spectral flow is built by deforming an Hermitian model while preserving its analytical index. We relate those spectral flows to a generalized Chern number that we show to be equal to that of the Hermitian case, provided a line gap exists. We demonstrate the homotopic invariance of both the non-Hermitian Chern number and the spectral flow index, making explicit their topological nature. In the absence of a line gap, our system still displays a spectral flow whose topology can be captured by exploiting an emergent pseudo-Hermitian symmetry.

cond-mat.mes-hall↗

arXiv2022

Unidirectional modes induced by nontraditional Coriolis force in stratified fluids

Using topology, we unveil the existence of new unidirectional modes in compressible rotating stratified fluids. We relate their emergence to the breaking of time-reversal symmetry by rotation and vertical mirror symmetry by stratification and gravity. We stress the role of the Coriolis force's nontraditional part, induced by a rotation field tangent to the surface. In contrast with horizontally trapped equatorial waves induced by the traditional component of Coriolis force perpendicular to the surface, we find vertically trapped modes that are trapped along interfaces between regions with distinct stratification properties. We show that such modes are generalized atmospheric Lamb waves whose direction of propagation can be selected by the nontraditional component of the Coriolis force.

physics.flu-dyn↗

arXiv2022

Floquet Winding Metals

We propose a generic scattering matrix model implementable in photonics to engineer a new Floquet metallic phase that combines two distinct topological properties: the winding of the bulk bands and the existence of robust chiral edge states. The winding of the bulk bands gives rise to a wavepacket oscillations in real space while conserving its initial momentum. Our findings open the way to the study of a new class of winding Floquet systems.

cond-mat.mes-hall↗

arXiv2022

Topological power pumping in quantum circuits

In this article, we develop a description of topological pumps as slow classical dynamical variables coupled by a quantum system. We discuss the cases of quantum Hall pumps, Thouless pumps, and the more recent Floquet pumps based frequency converters. This last case corresponds to a quantum topological coupling between classical modes described by action-angle variables on which we focus. We propose a realization of such a topological coupler based on a superconducting qutrit suitably driven by three modulated drives. A detailed experimental protocol allowing to measure the quantized topological power transfer between the different modes of a superconducting circuit is discussed.

cond-mat.mes-hall↗