Probing non-Hermitian skin effect and non-Bloch phase transitions

Longhi, Stefano

doi:10.1103/physrevresearch.1.023013

Cited by 332 publications

(202 citation statements)

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“…Hence, the feedback control interactions define distinct phases characterized by winding numbers which exhibit opposite behaviors for lattices with γ c = 0.1 and γ c = −0.1. These behaviors manifest as localized bulk Eigen modes in finite lattices, a phenomenon known as non-Hermitian skin-effect (NHSE) [65][66][67][68][69][70][71]. As an illustration, the Eigen frequencies of a finite lattice with N = 100 masses under free-free boundary conditions are displayed as black dots in figures 4(b) and (h), while representative Eigen modes marked by the blue circles are displayed in figures 4(c) and (i).…”

Section: Bulk Topology and Non-hermitian Skin Effectmentioning

confidence: 99%

“…Further observations of a seemingly breakdown of the bulk-boundary correspondence principle [62,63] has led to proposals for a general classification of the topological phases of non-Hermitian systems [55,56,64]. A particular point of interest is the observation of the non-Hermitian skin effect [65][66][67][68][69][70][71], whereby all Eigen states of one-dimensional (1D) systems are localized at a boundary, in sharp contrast with the extend Bloch modes of Hermitian counterparts. This intriguing feature of non-Hermitian lattices has recently been experimentally demonstrated using topo electrical circuits [72] and quantum walks of single photons [73].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Rosa

Ruzzene

2020

New J. Phys.

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We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems.

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Section: Bulk Topology and Non-hermitian Skin Effectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Rosa

Ruzzene

2020

New J. Phys.

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“…Specifically, no systematic understanding of the shape, location, and topology of non-Hermitian NKM surface state regions currently exists beyond isolated numerical results [24,28,29]. This conceptual gap has endured until today, because non-Hermiticity modifies the topological bulk-boundary correspondence in subtle complex-analytic ways, which so far have not been studied beyond 1D [30][31][32][33][34][35][36][37][38].…”

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confidence: 99%

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Lee

Li²,

Liu

et al. 2020

Preprint

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The paradigm of metals has undergone a revision and diversification from the viewpoint of topology. Non-Hermitian nodal knot metals (NKMs) constitute a class of matter without Hermitian analog, where the intricate structure of complex-valued energy bands gives rise to knotted lines of exceptional points and new topological surface state phenomena. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their underlying parent knots, and complement our results by an optimized constructive ansatz that provides tight-binding models for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization range. In particular, we identify the surface state boundaries as ``tidal' intersections of the complex band structure in a marine landscape analogy. We further find these tidal surface states to be intimately connected to the band vorticity and the layer structure of their dual Seifert surface, and as such provide a fingerprint for non-Hermitian NKMs.

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“…* stefano.longhi@polimi.it tening near an exceptional point (EP) can be observed for non-Bloch bands, while ordinary Bloch bands remain dispersive [38,56,66]. As BOs and ZT in non-Hermitian lattices have been investigated in some recent works [69][70][71][72][73][74], the implications of non-Bloch band theory to particle Bloch dynamics remain obscure.…”

mentioning

confidence: 99%

“…An example of non-Bloch band collapse is shown in Fig.1 for a lattice model which is a variant of the Hamiltonian earlier introduced in Ref. [35] (see also [29,38,56]). The model corresponds to the following non-vanishing values of couplings [ Fig.1(a)]: ρ 0 = ∆, θ 0 = ϕ 0 = t 0 , θ 1 = t + δ, and ϕ −1 = t − δ, with ∆, t 0 , t and δ real showing skin effect.…”

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confidence: 99%

Non-Bloch-Band Collapse and Chiral Zener Tunneling

Longhi¹

2020

Phys. Rev. Lett.

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146

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Non-Bloch band theory describes bulk energy spectra and topological invariants in non-Hermitian crystals with open boundaries, where the bulk eigenstates are squeezed toward the edges (skin effect). However, the interplay of non-Bloch band theory, skin effect and coherent Bloch dynamics is so far unexplored. In two-band non-Hermitian lattices, it is shown here that collapse of non-Bloch bands and skin modes deeply changes the Bloch dynamics under an external force. In particular, for resonance forcing non-Bloch band collapse results in Wannier-Stark ladder coalescence and chiral Zener tunneling between the two dispersive Bloch bands.Introduction. Bloch band theory is the fundamental tool to describe electronic states in crystals [1]. Under the action of a weak dc electric field, Bloch theory predicts that electrons undergo an oscillatory motion, the famous Bloch oscillations (BOs) [1], which can be explained from the formation of a Wannier-Stark (WS) ladder energy spectrum [2]. Transitions among different bands occur for stronger fields because of Zener tunneling (ZT) [3]. BOs and ZT are ubiquitous phenomena of coherent wave transport in periodic media and have been observed in a wide variety of physical systems [4][5][6][7][8][9][10][11][12][13][14]. It is remarkable that, after one century from the seminal paper by Felix Bloch [1], there are still treasures to be uncovered within Bloch band theory. For example, Bloch band theory is central in the understanding of topological insulators [15][16][17] and in the description of flat band systems showing unconventional localization, anomalous phases, and strongly correlated states of matter [18][19][20][21][22][23][24][25][26][27][28]. Recently, a great interest is devoted to extend Bloch band theory and topological order to non-Hermitian lattices . In Bloch band theory, an electronic state is defined by the quasi-momentum k, which spans the first Brillouin zone, and is delocalized all along the crystal, regardless periodic boundary conditions (PBC) or open boundary conditions (OBC) are assumed. However, in non-Hermitian crystals something strange happens: energy bands in crystals with OBC are described by non-Bloch bands that deviate from ordinary Bloch bands; bulk eigenstates cease to be delocalized and get squeezed toward the edges (non-Hermitian skin effect); and the bulk-boundary correspondence based on Bloch topological invariants generally fails to correctly predict the existence of topological zero-energy modes [29, 33-39, 45, 56, 59]. Recent seminal works [35,37,45] showed that to correctly describe energy spectra and topological invariants in crystals with OBC one needs to extend Bloch band theory so as the quasi-momentum k becomes complex and varies on a generalized Brillouin zone. Bloch and non-Bloch bands can show different symmetry breaking phase transitions and, interestingly, band flat-

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Probing non-Hermitian skin effect and non-Bloch phase transitions

Cited by 332 publications

References 70 publications

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Non-Bloch-Band Collapse and Chiral Zener Tunneling

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