Reciprocal skin effect and its realization in a topolectrical circuit

Hofmann, Tobias; Helbig, Tobias; Schindler, Frank; Salgo, Nora; Brzezińska, Marta; Greiter, Martin; Kießling, T.; Wolf, David; Vollhardt, A.; Kabaši, Anton; Lee, Ching Hua; Bilušić, Ante; Thomale, Ronny; Neupert, Titus

doi:10.1103/physrevresearch.2.023265

Cited by 372 publications

(226 citation statements)

References 44 publications

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“…Unlike previous works [28,29,39], we shall be primarily concerned with non-Hermitian NKMs not perturbatively connected to known Hermitian analogs. Despite their sophistication, these NKMs exhibit short-ranged tightbinding representations potentially realizable in disordered semimetals and non-reciprocal electrical or photonic circuits [40][41][42][43][44][45][46][47][48][49]. In particular, we illustrate how the topological tidal surface states can be mapped out as topolectrical resonances in non-Hermitian circuit realizations, based on recent experimental demonstrations involving analogous 1D circuit arrays [47].…”

mentioning

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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confidence: 99%

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

Lee

Li²,

Liu

et al. 2020

Preprint

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“…Such results challenge the common wisdom that bulk coherent processes in crystals are largely independent of boundaries, indicating that skin effects not only question the bulk-boundary correspondence but also coherent bulk phenomena. Owing to the recent experimental progresses in the realization of synthetic non-Hermitian lattices displaying the non-Hermitian skin effect in photonic 67 , mechanical 68 , and electrical circuit 42,69 platforms, as well as pertinent theoretical advances in cold atom engineering 70 , we expect that the disclosed distinctive physics of absorption and emission of energy in non-Hermitian crystals could be experimentally accessible in the near future.…”

Section: Discussionmentioning

confidence: 99%

Ultrafast and anharmonic Rabi oscillations between non-Bloch bands

Lee

Longhi

2020

Commun Phys

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Bloch band theory and bulk-boundary correspondence in non-Hermitian systems are attracting great attention in different areas of science. Interband transitions and Rabi flopping induced by emission or absorption of field quanta are fundamental and well-understood processes in Hermitian systems. However, they are challenged in a non-Hermitian system, where band theory is affected by system boundaries. Here we consider Rabi oscillations in non-Hermitian lattices exhibiting unbalanced non-Hermitian skin effect, and unveil an unprecedented scenario of Rabi flopping. The effective dipole moment of the transitionusually considered a bulk property-is however strongly dependent on boundary conditions. Rabi oscillations become anharmonic and transitions cease to be vertical in the energymomentum plane in systems with open boundaries. Remaining stable even in the presence of complex energies, Rabi oscillations provide a vivid illustration of how competition between non-Hermitian, non-local and Floquet effects can result in significant enhancements of physically measurable quantities.

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“…Theoretically, a wide range of non-Hermitian topological phases and phenomena have been classified and characterized according to their symmetries [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ] and dynamical signatures [ 18 , 19 , 20 , 21 , 22 , 23 ]. Experimentally, non-Hermitian topological matter have also been realized in cold atom [ 24 , 25 ], photonic [ 26 , 27 , 28 , 29 ], acoustic [ 30 , 31 , 32 ], electrical circuit [ 33 , 34 , 35 ] systems, and nitrogen-vacancy-center in diamond [ 36 ], leading to potential applications such as topological lasers [ 37 , 38 , 39 ] and high-performance sensors [ 40 , 41 , 42 , 43 ]. Additionally, non-Hermitian structures could also arise in supersymmetric quantum mechanics, where a series of supersymmetric models have been solved exactly [ 44 , 45 , 46 , 47 , 48 ].…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

Zhou

2020

Entropy

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Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants ( w 0 , w π ) ∈ 2 Z × 2 Z . Under the open boundary condition, these invariants further predict the number of zero- and π -quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.

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Reciprocal skin effect and its realization in a topolectrical circuit

Cited by 372 publications

References 44 publications

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

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

Ultrafast and anharmonic Rabi oscillations between non-Bloch bands

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

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