Non-Hermitian dislocation modes: Stability and melting across exceptional points

Archisman, Panigrahi,; Moessner, Roderich; Roy, Bitan

doi:10.1103/physrevb.106.l041302

Cited by 23 publications

(7 citation statements)

References 66 publications

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“…Dislocations. To further corroborate the topological nature of the 1D projected brains, we study their response to the bulkdislocation defects, known to be sensitive to the electronic topology [34][35][36][37][38][39] . In particular, despite supporting robust gapless edge modes, the Γ and M phases are distinguishable by the first Chern number.…”

Section: Resultsmentioning

confidence: 99%

Projected topological branes

2022

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Nature harbors crystals of dimensionality (d) only up to three. Here we introduce the notion of projected topological branes (PTBs): Lower-dimensional branes embedded in higher-dimensional parent topological crystals, constructed via a geometric cut-and-project procedure on the Hilbert space of the parent lattice Hamiltonian. When such a brane is inclined at a rational or an irrational slope, either a new lattice periodicity or a quasicrystal emerges. The latter gives birth to topoquasicrystals within the landscape of PTBs. As such PTBs are shown to inherit the hallmarks, such as the bulk-boundary and bulk-dislocation correspondences, and topological invariant, of the parent topological crystals. We exemplify these outcomes by focusing on two-dimensional parent Chern insulators, leaving its signatures on projected one-dimensional (1D) topological branes in terms of localized endpoint modes, dislocation modes and the local Chern number. Finally, by stacking 1D projected Chern insulators, we showcase the imprints of three-dimensional Weyl semimetals in d = 2, namely the Fermi arc surface states and bulk chiral zeroth Landau level, responsible for the chiral anomaly. Altogether, the proposed PTBs open a realistic avenue to harness higher-dimensional (d > 3) topological phases in laboratory.

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Section: Resultsmentioning

confidence: 99%

Projected topological branes

2022

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“…The proposed ISEs on periodic fractal lattices should be contrasted with dislocation NH skin effect with PBC [46][47][48] . Dislocation NH skin effect crucially depends on the relative orientation between the associated Burgers vector and the direction of the skin effect at outer boundaries with open geometry.…”

Section: Discussionmentioning

confidence: 99%

“…Dislocation NH skin effect crucially depends on the relative orientation between the associated Burgers vector and the direction of the skin effect at outer boundaries with open geometry. A skin effect appears at the defect core under PBC only when they are orthogonal to each other 46 . Furthermore, such dislocation skin effects can be masked by localized dislocation bound states, making it challenging to detect in experiments.…”

Section: Discussionmentioning

confidence: 99%

Inner skin effects on non-Hermitian topological fractals

Manna

Roy

2023

Commun Phys

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Non-Hermitian (NH) crystals, quasicrystals, and amorphous network display an accumulation of a macroscopic number of states near one of its specific interfaces with vacuum, such as edge, surface, hinge, or corner. This phenomenon is known as the NH skin effect, which can only be observed with open boundary condition. In this regard self-similar fractals, manifesting inner boundaries in the interior of the system, harbor a novel phenomenon, the inner skin effect (ISE). Then the NH skin effect appears at the inner boundaries of the fractal lattice with periodic boundary condition. We showcase this observation by implementing prominent models for NH insulators and superconductors on representative planar Sierpinski carpet fractal lattices. They accommodate both first-order and second-order ISEs at inner edges and corners, respectively, for charged as well as neutral Majorana fermions. Furthermore, over extended parameter regimes ISEs are tied with nontrivial bulk topological invariants, yielding intrinsic ISEs. With the recent success in engineering NH topological phases on highly tunable metamaterial platforms, such as photonic and phononic lattices, as well as topolectric circuits, the proposed ISEs can be observed experimentally at least on fractal metamaterials with periodic boundary condition.

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“…Here, crystal defects in the form of 'dislocations' can act as terminal points within the lattice and cause the localization of eigenstates in their vicinity. This has been termed the dislocation NHSE (DNHSE) [224][225][226]. Bhargava et al [227] recently made an interesting discovery that in a two-dimensional system with two dislocation sites, there not only arises a dislocation-induced skin effect at one site, but there occurs an 'anti-skin effect' at the other site.…”

Section: Internal Symmetries Of the Underlying Non-hermitianmentioning

confidence: 99%

Non-Hermitian topological phases: principles and prospects

Banerjee

Sarkar

Dey

et al. 2023

J. Phys.: Condens. Matter

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The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models -- Hatano-Helson, non-Hermitian Su-Schrieffer-Heeger and non-Hermitian Chern insulator -- we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future.

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Non-Hermitian dislocation modes: Stability and melting across exceptional points

Cited by 23 publications

References 66 publications

Projected topological branes

Projected topological branes

Inner skin effects on non-Hermitian topological fractals

Non-Hermitian topological phases: principles and prospects

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