Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits

Abstract Robust boundary states epitomize how deep physics can give rise to concrete experimental signatures with technological promise. Of late, much attention has focused on two distinct mechanisms for boundary robustness - topological protection, as well as the non-Hermitian skin effect. In this work, we report the first experimental realizations of hybrid higher-order skin-topological effect, in which the skin effect selectively acts only on the topological boundary modes, not the bulk modes. Our experiments, which are performed on specially designed non-reciprocal 2D and 3D topolectrical circuit lattices, showcases how non-reciprocal pumping and topological localization dynamically interplays to form various novel states like 2D skin-topological, 3D skin-topological-topological hybrid states, as well as 2D and 3D higher-order non-Hermitian skin states. Realized through our highly versatile and scalable circuit platform, theses states have no Hermitian nor lower-dimensional analog, and pave the way for new applications in topological switching and sensing through the simultaneous non-trivial interplay of skin and topological boundary localizations.

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Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits

Nature Communications ◽

10.1038/s41467-021-26414-5 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Deyuan Zou ◽

Tian Chen ◽

Wenjing He ◽

Jiacheng Bao ◽

Ching Hua Lee ◽

...

Keyword(s):

Skin Effect ◽

Higher Order ◽

Boundary States ◽

Topological Localization ◽

Topological Effect ◽

2D And 3D ◽

3D Skin ◽

Lower Dimensional ◽

Topological Boundary ◽

The Way

AbstractRobust boundary states epitomize how deep physics can give rise to concrete experimental signatures with technological promise. Of late, much attention has focused on two distinct mechanisms for boundary robustness—topological protection, as well as the non-Hermitian skin effect. In this work, we report the experimental realizations of hybrid higher-order skin-topological effect, in which the skin effect selectively acts only on the topological boundary modes, not the bulk modes. Our experiments, which are performed on specially designed non-reciprocal 2D and 3D topolectrical circuit lattices, showcases how non-reciprocal pumping and topological localization dynamically interplays to form various states like 2D skin-topological, 3D skin-topological-topological hybrid states, as well as 2D and 3D higher-order non-Hermitian skin states. Realized through our highly versatile and scalable circuit platform, theses states have no Hermitian nor lower-dimensional analog, and pave the way for applications in topological switching and sensing through the simultaneous non-trivial interplay of skin and topological boundary localizations.

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Higher Order Turbulence Model Predictions for Complex 2D and 3D Flowfields

Engineering Turbulence Modelling and Experiments ◽

10.1016/b978-0-444-89802-9.50026-5 ◽

1993 ◽

pp. 229-238

Author(s):

Florian R. Menter

Keyword(s):

Turbulence Model ◽

Higher Order ◽

Model Predictions ◽

2D And 3D

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Points as Higher-Order Constructs

The History of Continua ◽

10.1093/oso/9780198809647.003.0015 ◽

2020 ◽

pp. 347-378

Author(s):

Achille C. Varzi

Keyword(s):

20Th Century ◽

Higher Order ◽

General Idea ◽

Natural Knowledge ◽

Full Development ◽

Classical Geometry ◽

Definition Of ◽

Lower Dimensional

Euclid’s definition of a point as “that which has no part” has been a major source of controversy in relation to the epistemological and ontological presuppositions of classical geometry, from the medieval and modern disputes on indivisibilism to the full development of point-free geometries in the 20th century. Such theories stem from the general idea that all talk of points as putative lower-dimensional entities must and can be recovered in terms of suitable higher-order constructs involving only extended regions (or bodies). This chapter focuses on what is arguably the first thorough proposal of this sort, Whitehead’s theory of “extensive abstraction”, offering a critical reconstruction of the theory through its successive installments: from the purely mereological version of ‘La théorie relationniste de l’espace’ (1916) to the refined versions presented in An Enquiry Concerning the Principles of Natural Knowledge (1919) and in The Concept of Nature (1920) to the last, mereotopological version of Process and Reality (1929).

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Topological boundary states in 1D: An effective Fabry-Perot model

The European Physical Journal Special Topics ◽

10.1140/epjst/e2016-60341-8 ◽

2017 ◽

Vol 226 (7) ◽

pp. 1563-1582 ◽

Cited By ~ 3

Author(s):

E. Levy ◽

E. Akkermans

Keyword(s):

Fabry Perot ◽

Boundary States ◽

Topological Boundary

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A Dynamic Continuation-Passing Style for Dynamic Delimited Continuations

BRICS Report Series ◽

10.7146/brics.v13i15.21920 ◽

2006 ◽

Vol 13 (15) ◽

Cited By ~ 4

Author(s):

Dariusz Biernacki ◽

Olivier Danvy ◽

Kevin Millikin

Keyword(s):

Higher Order ◽

Evaluation Function ◽

Abstract Machine ◽

Delimited Continuations ◽

New Applications

We put a pre-existing definitional abstract machine for dynamic delimited continuations in defunctionalized form, and we present the consequences of this adjustment.<br /> <br />We first prove the correctness of the adjusted abstract machine. Because it is in defunctionalized form, we can refunctionalize it into a higher-order evaluation function. This evaluation function, which is compositional, is in continuation+state passing style and threads a trail of delimited continuations and a meta-continuation. Since this style accounts for dynamic delimited continuations, we refer to it as `dynamic continuation-passing style' and we present the corresponding dynamic CPS transformation. We show that the notion of computation induced by dynamic CPS takes the form of a continuation monad with a recursive answer type and we present a new simulation of dynamic delimited continuations in terms of static ones as well as new applications of dynamic delimited continuations.<br /> <br />The significance of the present work is that the computational artifacts surrounding dynamic CPS are not independent designs: they are mechanical consequences of having put the definitional abstract machine in defunctionalized form.

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Observation of higher-order non-Hermitian skin effect

10.21203/rs.3.rs-182126/v1 ◽

2021 ◽

Author(s):

Xiujuan Zhang ◽

Yuan Tian ◽

Jian-Hua Jiang ◽

Ming-Hui Lu ◽

Yan-Feng Chen

Keyword(s):

Degrees Of Freedom ◽

Skin Effect ◽

Higher Order ◽

Dependent Manner ◽

Acoustic Metamaterials ◽

Opposite Edge ◽

Band Theory ◽

Acoustic Resonators ◽

Fermi Arcs ◽

Spin Polarized

Abstract Hermitian theories play a major role in understanding the physics of most phenomena. It has been found only in the past decade that non-Hermiticity enables unprecedented effects such as exceptional points, spectral singularities and bulk Fermi arcs. Recent studies further show that non-Hermiticity can fundamentally change the topological band theory, leading to the non-Hermitian band topology and non-Hermitian skin effect, as confirmed in one-dimensional (1D) systems. However, in higher dimensions, these non-Hermitian effects remain unexplored in experiments. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional (2D) acoustic metamaterials. Using a lattice of coupled whisper-gallery acoustic resonators, we realize a spinful 2D higher-order topological insulator (HOTI) where the spin-up and spin-down states are emulated by the anti-clockwise and clockwise modes, respectively. We find that the non-Hermiticity drives wave localizations toward opposite edge boundaries depending on the spin polarizations. More interestingly, for finite systems with both edge and corner boundaries, the higher-order non-Hermitian skin effect leads to wave localizations toward two corner boundaries for the bulk, edge and corner states in a spin-dependent manner. We further show that such a non-Hermitian skin effect enables rich wave manipulation through the loss configuration in each unit-cell. The reported spin-dependent, higher-order non-Hermitian skin effect reveals the interplay between higher-order topology and non-Hermiticity, which is further enriched by the spin degrees of freedom. This unveils a new horizon in the study of non-Hermitian physics and the design of non-Hermitian metamaterials.

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Observation of higher-order non-Hermitian skin effect

Nature Communications ◽

10.1038/s41467-021-25716-y ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Xiujuan Zhang ◽

Yuan Tian ◽

Jian-Hua Jiang ◽

Ming-Hui Lu ◽

Yan-Feng Chen

Keyword(s):

Topological Insulators ◽

Skin Effect ◽

Higher Dimensions ◽

Higher Order ◽

Dependent Manner ◽

Two Dimensional ◽

Band Theory ◽

One Dimensional ◽

Finite Systems ◽

Spin Polarized

AbstractBeyond the scope of Hermitian physics, non-Hermiticity fundamentally changes the topological band theory, leading to interesting phenomena, e.g., non-Hermitian skin effect, as confirmed in one-dimensional systems. However, in higher dimensions, these effects remain elusive. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional acoustic higher-order topological insulators. We find that non-Hermiticity drives wave localizations toward opposite edges upon different spin polarizations. More interestingly, for finite systems with both edges and corners, the higher-order non-Hermitian skin effect leads to wave localizations toward two opposite corners for all the bulk, edge and corner states in a spin-dependent manner. We further show that such a skin effect enables rich wave manipulation by configuring the non-Hermiticity. Our study reveals the intriguing interplay between higher-order topology and non-Hermiticity, which is further enriched by the pseudospin degree of freedom, unveiling a horizon in the study of non-Hermitian physics.

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On the topological immunity of corner states in two-dimensional crystalline insulators

npj Quantum Materials ◽

10.1038/s41535-020-00265-7 ◽

2020 ◽

Vol 5 (1) ◽

Author(s):

Guido van Miert ◽

Carmine Ortix

Keyword(s):

Topological Insulator ◽

Rotational Symmetry ◽

Higher Order ◽

Two Dimensions ◽

Edge States ◽

Kagome Lattice ◽

Kagomé Lattice ◽

Mistaken Identity ◽

Boundary States ◽

Charge Mode

Abstract A higher-order topological insulator (HOTI) in two dimensions is an insulator without metallic edge states but with robust zero-dimensional topological boundary modes localized at its corners. Yet, these corner modes do not carry a clear signature of their topology as they lack the anomalous nature of helical or chiral boundary states. Here, we demonstrate using immunity tests that the corner modes found in the breathing kagome lattice represent a prime example of a mistaken identity. Contrary to previous theoretical and experimental claims, we show that these corner modes are inherently fragile: the kagome lattice does not realize a higher-order topological insulator. We support this finding by introducing a criterion based on a corner charge-mode correspondence for the presence of topological midgap corner modes in n-fold rotational symmetric chiral insulators that explicitly precludes the existence of a HOTI protected by a threefold rotational symmetry.

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