Experimental realization of topological corner states in long-range-coupled electrical circuits

Olekhno, Nikita A.; Rozenblit, Alina D.; Kachin, Valerii I.; Dmitriev, Alexey A.; Burmistrov, Oleg I.; Seregin, Pavel; Zhirihin, Dmitry V.; Gorlach, Maxim A.

doi:10.1103/physrevb.105.l081107

Cited by 31 publications

(20 citation statements)

References 40 publications

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“…Therefore, experimental observations of ISEs will require only a limited number of additional couplings, especially among the waveguides (on photonic lattices) or mechanical resonators (on phononic lattices), or electrical nodes (on topolectric circuits), playing the role of lattice sites, otherwise residing near the outer edges of the underlying SC fractal metamaterials. Moreover, recently longer range hopping has been engineered on topolectric circuits 81 , and SC fractal lattices have been realized on metamaterials, harboring Hermitian firstand second-order topological phases [82][83][84] . These realistic requirements and recent achievements make our proposal promising, and most vitally within the reach of the existing experimental facilities.…”

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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Section: Discussionmentioning

confidence: 99%

Inner skin effects on non-Hermitian topological fractals

Manna

Roy

2023

Commun Phys

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“…Such analysis will further increase the prospect of material realizations of PTBs at least in designer and metamaterials. Indeed, longer-range hoppings have recently been engineered on topolectric circuits 62 , which can possibly be also implemented on photonic and phononic lattices.…”

Section: Discussionmentioning

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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“…In most topological systems with true LRIs, one can consider the NNN hopping terms without missing the key physics, because higher-order terms beyond NNN can only contribute negligible effects [5,6]. Besides, the concept of LRI very recently has been adopted in systems with NNN interactions [7]. Labelling the nodes of the circuit by a = 1, 2, ... the response at frequency ω follows Kirchhoff's law: I a (ω) = b J ab (ω)V b (ω), with I a the external current flowing into node a, V b the voltage at node b, and J ab (ω) being the circuit Laplacian:…”

Section: Circuit Model and Phase Diagrammentioning

confidence: 99%

“…Physical systems with LRIs can exhibit many peculiar properties in their dynamics and statistics, such as negative specific heat and temperature jumps [1,2]. Recently, the LRIs have been shown to impose certain effects on the topological states [3][4][5][6][7][8][9]. For instance, Li et al observed a type-II corner state in the photonic breathing kagome crystal in the presence of a weak LRI [5].…”

Section: Introductionmentioning

confidence: 99%

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Observation of type-III corner states induced by long-range interactions

et al. 2022

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Long-range interactions (LRIs) are ubiquitous in nature. Higher-order topological (HOT) insulator represents a new phase of matter. A critical issue is how LRI dictates the HOT phases. In this work, we discover four topologically distinct phases, i.e., HOT phase, the bound state in the continuum, Dirac semimetal (DSM) phase, and trivial insulator phase in a breathing kagome circuit with tunable LRIs. We find an emerging type-III corner state in the HOT phase, which splits from the edge state continuum and originates from the strong couplings between nodes at different edges. We experimentally detect this novel state by impedance and voltage measurements. In the DSM phase, the Dirac cone exhibits an itinerant feature with a tunable position that depends on the LRI strength. Our findings provide a deeper understanding of the LRI effect on exotic topological states and pave the way for regulating interactions in topolectrical circuits.

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Experimental realization of topological corner states in long-range-coupled electrical circuits

Cited by 31 publications

References 40 publications

Inner skin effects on non-Hermitian topological fractals

Inner skin effects on non-Hermitian topological fractals

Projected topological branes

Observation of type-III corner states induced by long-range interactions

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