Second-order topological non-Hermitian skin effects

Okugawa, Ryo; Takahashi, Rohta; Yokomizo, Kazuki

doi:10.1103/physrevb.102.241202

Cited by 129 publications

(50 citation statements)

References 101 publications

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“…In Supplementary Discussion 1 .F, we show that this invariant is equivalent to that in ref. 33 , and that it signals a second-order skin effect as follows. First, has inversion symmetry, and a point gap spectrum in which corner modes appear only for open-boundary conditions in both directions (Fig.…”

Section: Resultsmentioning

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 20 , 37 , and (ii) the number of accumulated modes is of the order of the system boundary L , rather than its area L 2 . While the first-order non-Hermitian skin effect requires inversion to be broken, e.g., due to an applied field, the emergence of the second-order non-Hermitian skin effect is guaranteed by the presence of certain symmetries 33 , 34 . However, predicting the second-order non-Hermitian skin effect is challenging in general, and it remains unobserved.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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 and exploiting enhanced diffusion associated to its motion will provide insights for application from sensing, drug delivery to water remediation. 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 non-Hermitian skin effect, a 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 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: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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“…For example, the analysis could be extended by considerning inhomogeneous (space-dependent) imaginary gauge fields, as well as other kinds of non-Hermitian terms in the continuous Schrödinger equation [106]. Also, continuous models of non-Hermitian two-dimensional systems could be considered, where the second-order NHSE and corner states are observed within the tight-binding models [22,56,58]. Finally, the continuous non-Hermitian Schrödinger equation could be of relevance to investigate dual Hermitian systems in curved spaces [107].…”

Section: Discussionmentioning

confidence: 99%

Non-Hermitian skin effect beyond the tight-binding models

Longhi

2021

Preprint

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The energy bands of non-Hermitian systems exhibit nontrivial topological features that arise from the complex nature of the energy spectrum. Under periodic boundary conditions (PBC), the energy spectrum describes rather generally closed loops in complex plane, characterized by integer nonzero winding numbers. Such nontrivial winding provides the topological signature of the non-Hermitian skin effect (NHSE), i.e. the macroscopic condensation of bulk states at the lattice edges under open boundary conditions (OBC). In spite of the great relevance of band winding in the non-Hermitian topological band theory and the related NHSE, most of current results rely on tight-binding models of non-Hermitian systems, while exact Bloch wave function analysis of the NHSE and related topological band theory is still lacking. While tight-binding models can correctly describe narrow-band electronic states with a relatively weak degree non-Hermiticity, they are not suited to describe high-energy wide-band electronic states and/or regimes corresponding to strong non-Hermiticity. Here we consider the single-particle continuous Schrödinger equation in a periodic potential, in which non-Hermiticity is introduced by an imaginary vector potential in the equation, and show that the NHSE is ubiquitous under OBC and characterized by a non-vanishing integer winding number, even thought the energy spectrum under PBC always comprises an open curve, corresponding to high-energy electronic states. We also show that the interior of the PBC energy spectrum corresponds to the complex eigenenergies sustaining localized (edge) states under semiinfinite boundary conditions.

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“…Non-Hermitian phenomena [1][2][3][4] are one of the most exciting topics that have emerged in condensed matter physics. In general, the breaking of Hermiticity by non-reciprocal couplings between lattice sites or onsite gain/loss terms [5][6][7] can induce a plethora of unusual phenomena that include exceptional points [5,8,9], nodal rings [10], and the extensive localization of eigenstates [11][12][13][14][15], also known as the non-Hermitian skin effect (NHSE). The NHSE can be exploited for ultra-sensitive sensors [16,17], unidirectional transport [18], and the amplification and attenuation of quantum signals [19,20].…”

Section: Introductionmentioning

confidence: 99%

Critical non-Hermitian Skin Effect in a Single Closed non-Hermitian Chain

Siu

Rafi-Ul-Islam

Jalil

2022

Preprint

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A critical non-Hermitian skin effect (CNHSE) was recently discovered in which the eigenenergy spectrum of a coupled system comprising two 1D non-Hermitian (NH) chains exhibits an abrupt change when the length of the system increases beyond a critical length. Here, we overturn the conventional wisdom that multiple chains are required for the CNHSE by showing that a similar abrupt transition in the eigenenergy spectrum occurs with increasing length in a single finite 1D chain when the two ends of the chain are connected by a weak terminal coupling to form a closed loop. We illustrate this phenomenon using the classic Hatano-Nelson and Su-Schrieffer-Heeger NH systems, and show that it can co-exist with the conventional CNHSE in coupled NH loops.

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Second-order topological non-Hermitian skin effects

Cited by 129 publications

References 101 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

Non-Hermitian skin effect beyond the tight-binding models

Critical non-Hermitian Skin Effect in a Single Closed non-Hermitian Chain

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