Second-order topological non-Hermitian skin effects

Okugawa, Ryo; Takahashi, Ryo; Yokomizo, Kazuki

doi:10.48550/arxiv.2008.03721

Cited by 7 publications

(24 citation statements)

References 35 publications

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“…In the Supplementary Information A we show that this invariant is equivalent to that in Ref. [5], and that it signals a second-order skin-effect as follows. First, Ŵ has inversion symmetry, and a point gap spectrum in which corner modes appear only for open-boundary conditions in both directions (Figs.…”

Section: Corner Accumulation From Second-order Non-hermitian Skin Effectmentioning

confidence: 53%

“…when t 1 /t 2 > 1), these display a non-Hermitian skin effect with open boundary conditions in the x direction, resulting in an accumulation of active particles at the corners. This effect is a second-order non-Hermitian skin-effect [5][6][7], which exists when the topological number…”

Section: Edge Modesmentioning

confidence: 99%

“…Recently, a more elusive second-order non-Hermitian skin effect was predicted only in out-of-equilibrium systems in two dimensions (2D) [5][6][7]. It differs from the first-order skin effect because (i) it can occur in inversion symmetric systems, accumulating modes at opposing corners rather than edges [24,27], and (ii) the number of accumulated modes is of order of the system boundary L, rather than its area L 2 .…”

mentioning

confidence: 99%

“…It differs from the first-order skin effect because (i) it can occur in inversion symmetric systems, accumulating modes at opposing corners rather than edges [24,27], and (ii) the number of accumulated modes is of order of the system boundary L, rather than its area L 2 . Its emergence is guaranteed by the presence of certain symmetries [5,6], but predicting it is challenging in general. Moreover, it remains unobserved, partially because dissipation, which drives a system out of equilibrium, is hard to control experimentally.…”

mentioning

confidence: 99%

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Guided accumulation of active particles by topological design of a second-order skin effect

Palacios,

Tchoumakov,

Guix

et al. 2020

Preprint

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Collective guidance of out-of-equilibrium systems without using external fields is a challenge of paramount importance in active matter, ranging from bacterial colonies to swarms of self-propelled particles. Designing strategies to guide active matter using microfabricated circuits will provide insights for applications from sensing, drug delivery to water remediation [1-3]. However, achieving directed motion without breaking detailed balance, for example by asymmetric topographical patterning, is challenging. Here we engineer a two-dimensional periodic topographical design with detailed balance in its unit cell where we observe spontaneous particle edge guidance and corner accumulation of self-propelled particles. This emergent behaviour is guaranteed by a second-order [4-7] non-Hermitian skin effect [8-12], a so far unobserved topologically robust non-equilibrium phenomenon, that we use to dynamically break detailed balance. Our stochastic circuit model predicts, without fitting parameters, how guidance and accumulation can be controlled and enhanced by design: a device guides particles more efficiently if the topological invariant characterizing it is non-zero. Our work establishes a fruitful bridge between active and topological matter, and our design principles offer a broad blueprint to design devices that display spontaneous, robust and predictable guided motion and accumulation, guaranteed by out-of-equilibrium topology.

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Section: Corner Accumulation From Second-order Non-hermitian Skin Effectmentioning

confidence: 53%

Section: Edge Modesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Guided accumulation of active particles by topological design of a second-order skin effect

Palacios,

Tchoumakov,

Guix

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…In particular, the non-reciprocity induces skin modes which are a large number of localized states around the edge due to the finite winding number in the bulk. This remarkable topological phenomenon in non-Hermitian systems is further extended by taking into account symmetry [49,[78][79][80][81]. In particular, it turned out that mirror symmetry protects a type of non-Hermitian crystalline symmetry inducing the mirror skin effect [82].…”

mentioning

confidence: 98%

Machine Learning of Mirror Skin Effects in the Presence of Disorder

2021

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Non-Hermitian systems with mirror symmetry may exhibit mirror skin effect which is the extreme sensitivity of the spectrum and eigenstates on the boundary condition due to the non-Hermitian topology protected by mirror symmetry. In this paper, we report that the mirror skin effect survives even against disorder which breaks the mirror symmetry. Specifically, we demonstrate the robustness of the skin effect by employing the neural network which systematically predicts the presence/absence of the skin modes, a large number of localized states around the edge. The trained neural network detects skin effects in high accuracy, which allows us to obtain the phase diagram. We also calculate the probability by the neural network for each of states. The above results are also confirmed by calculating the inversed participation ratio.

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Real-space dynamical mean field theory study of non-Hermitian skin effect for correlated systems: Analysis based on pseudospectrum

Yoshida

2021

Phys. Rev. B

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We analyze a correlated system in equilibrium with special emphasis on non-Hermitian topology inducing a skin effect. The pseudo-spectrum, computed by the real-space dynamical mean-field theory, elucidates that additional pseudo-eigenstates emerge for the open boundary condition in contrast to the dependence of the density of states on the boundary condition. We further discuss how the line-gap topology, another type of non-Hermitian topology, affects the pseudo-spectrum. Our numerical simulation clarifies that while the damping of the quasi-particles induces the nontrivial point-gap topology, it destroys the non-trivial line-gap topology. The above two effects are also reflected in the temperature dependence of the local pseudo-spectral weight.

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Second-order topological non-Hermitian skin effects

Cited by 7 publications

References 35 publications

Guided accumulation of active particles by topological design of a second-order skin effect

Guided accumulation of active particles by topological design of a second-order skin effect

Machine Learning of Mirror Skin Effects in the Presence of Disorder

Real-space dynamical mean field theory study of non-Hermitian skin effect for correlated systems: Analysis based on pseudospectrum

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