Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges

Cerjan, Alexander; Xiao, Meng; Yuan, Luqi; Fan, Shanhui

doi:10.1103/physrevb.97.075128

Cited by 137 publications

(104 citation statements)

References 76 publications

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“…These periodic tables specify exceptional points and non-Hermitian topological semimetals in a general manner and describe their unconventional nodal structures. In fact, they corroborate previous works [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]100]. For example, stable exceptional points in two dimensions [28,60,68,72] are explained by the Z index in Table I with no symmetry, p = 2, and point (P) gap; symmetry-protected exceptional rings in two dimensions [54,62,63,65,67] are explained by the Z or Z 2 index in Table I with chiral or PT symmetry, p = 1, and point (P) gap.…”

supporting

confidence: 92%

“…We also elucidate that exceptional points generally possess multiple topological structures due to the two types of complex-energy gaps. Our theory provides the unified understanding of non-Hermitian topological semimetals studied in previous works [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. Furthermore, it systematically predicts novel non-Hermitian topological materials unnoticed in the literature; we construct as an illustration a topological dumbbell of exceptional points [ Fig.…”

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confidence: 98%

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Classification of Exceptional Points and Non-Hermitian Topological Semimetals

2019

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Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic topologically stable exceptional points according to two types of complex-energy gaps and fundamental symmetries of charge conjugation, parity, and time reversal. This classification reveals unique non-Hermitian gapless structures with no Hermitian analogs and systematically predicts unknown non-Hermitian semimetals and nodal superconductors; a topological dumbbell of exceptional points in three dimensions is constructed as an illustration. Our work paves the way toward richer phenomena and functionalities of exceptional points and non-Hermitian topological semimetals.Topology plays a pivotal role in the understanding of phases of matter [1]. In gapless systems such as semimetals and nodal superconductors, topology guarantees stable degeneracies accompanying distinctive excitations [2][3][4][5][6][7]. A prime example is the Weyl semimetal in three dimensions, where each gapless point is topologically protected by the Chern number defined on the enclosing surface. Symmetry further brings about diverse types of topological semimetals. Their unified understanding is developed as the classification theory according to fundamental symmetries such as PT and CP symmetries [8][9][10][11][12][13][14][15].Recently, the interplay between topology and non-Hermiticity has attracted widespread interest in a non-Hermitian extension of topological insulators and semimetals [54-72]. Non-Hermiticity ubiquitously appears, for instance, in nonequilibrium open systems [73] and correlated electron systems [68], leading to unusual properties with no Hermitian counterparts. One of their salient characteristics is the emergence of exceptional points [74-76], i.e., universal non-Hermitian level degeneracies at which eigenstates coalesce with and linearly depend on each other [77]. The past decade has witnessed a plethora of rich phenomena and functionalities induced by exceptional points [73], including unidirectional invisibility [78-81], chiral transport [82-86], enhanced sensitivity [87-92], and unusual quantum criticality [93-99]. Such exceptional points also alter the nodal structures of topological semimetals in a fundamental manner [54-72]. Notably, non-Hermiticity deforms a Weyl point and spawns a ring of exceptional points [75]. This Weyl exceptional ring is characterized by two topological charges [56], a Chern number and a quantized Berry phase, and such a multiple topological structure has no analogs to Weyl and Dirac points in Hermitian systems [2-15]. Its experimental observation has also been reported in an optical waveguide array [69]. Moreover, pseudo-Hermiticity [63], PT symmetry [62, 65], and chiral symmetry [67] enable an exceptional ring (surface) in two (three) dimensions. A symmetry-protected exceptional ring has been experimentally observed in a two-dimensional photonic crystal slab ...

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confidence: 92%

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confidence: 98%

Classification of Exceptional Points and Non-Hermitian Topological Semimetals

2019

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“…[40,[168][169][170] In the NH systems, the existences of Weyl fermions across discrete points, or at exceptional rings are also presented in the literature. [69,78,80,81] Experimental evidence of Weyl exceptional point is also presented in a bipartite optical waveguide. [70] Dynamical quantum phase transition from trivial to non-trivial topological phases is demonstrated in some photonic systems [62,211,212] with sudden quench [102,213].…”

Section: Other Systemsmentioning

confidence: 99%

New topological invariants in non-Hermitian systems

Ghatak

Das

2019

J. Phys.: Condens. Matter

342

293

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Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups. Discussions are devoted to both the adaptations of topological invariants from Hermitian to non-Hermitian systems, as well as origins of new topological invariants in the latter setup. Unique properties such as exceptional points and complex energy landscapes lead to new topological invariants including winding number/vorticity defined solely in the complex energy plane, and half-integer winding/Chern numbers. New forms of Kramers degeneracy appear here rendering distinct topological invariants. Modifications of adiabatic theory, time-evolution operator, biorthogonal bulk-boundary correspondence lead to unique features such as topological displacement of particles, 'skin-effect', and edge-selective attenuated and amplified topological polarizations without chiral symmetry. Extension and realization of topological ideas in photonic systems are mentioned. We conclude with discussions on relevant future directions, and highlight potential applications of some of these unique topological features of the non-Hermitian Hamiltonians.

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“…For non-Hermitian systems with two bands in two (2D) and three (3D) spatial dimensions, generic band touchings typically lead to exceptional points and lines [35], * kristof.moors@uni.lu respectively. It was shown that an exceptional loop can be obtained from a Weyl node by adding non-Hermitian terms to the Hamiltonian [8,10,12]. This was recently identified in an optical waveguide [37].…”

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confidence: 99%

Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals

Moors

Zyuzin

et al. 2019

Phys. Rev. B

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We consider the impact of disorder on the spectrum of three-dimensional nodal-line semimetals. We show that the combination of disorder and a tilted spectrum naturally leads to a non-Hermitian self-energy contribution that can split a nodal line into a pair of exceptional lines. These exceptional lines form the boundary of an open and orientable bulk Fermi ribbon in reciprocal space on which the energy gap vanishes. We find that the orientation and shape of such a disorder-induced bulk Fermi ribbon is controlled by the tilt direction and the disorder properties, which can also be exploited to realize a twisted bulk Fermi ribbon with nontrivial winding number. Our results put forward a paradigm for the exploration of non-Hermitian topological phases of matter. arXiv:1810.03191v2 [cond-mat.mes-hall]

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Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges

Cited by 137 publications

References 76 publications

Classification of Exceptional Points and Non-Hermitian Topological Semimetals

Classification of Exceptional Points and Non-Hermitian Topological Semimetals

New topological invariants in non-Hermitian systems

Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals

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