Reciprocal skin effect and its realization in a topolectrical circuit

@article{Hofmann2019ReciprocalSE,
  title={Reciprocal skin effect and its realization in a topolectrical circuit},
  author={Tobias Hofmann and Tobias Helbig and Frank Schindler and Nora Salgo and Marta Brzezińska and Martin Greiter and Tobias Kie{\ss}ling and David Wolf and Achim Vollhardt and Anton Kaba{\vs}i and Ching Hua Lee and Ante Bilu{\vs}i{\'c} and Ronny Thomale and Titus Neupert},
  journal={arXiv: Mesoscale and Nanoscale Physics},
  year={2019}
}
A system is non-Hermitian when it exchanges energy with its environment and non-reciprocal when it behaves differently upon the interchange of input and response. Within the field of metamaterial research on synthetic topological matter, the skin effect describes the conspiracy of non-Hermiticity and non-reciprocity to yield extensive anomalous localization of all eigenmodes in a (quasi) one-dimensional geometry. Here, we introduce the reciprocal skin effect, which occurs in non-Hermitian but… 

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References

SHOWING 1-10 OF 46 REFERENCES
Chiral Voltage Propagation and Calibration in a Topolectrical Chern Circuit.
TLDR
The proposed topolectrical Chern circuit features an admittance bulk gap fully tunable via the resistors used in the INICs, along with a chiral voltage boundary mode reminiscent of the Berry flux monopole present in the admittance band structure.
Electric circuits for non-Hermitian Chern insulators
We analyze the non-Hermitian Haldane model where the spin-orbit interaction is made non-Hermitian. The Dirac mass becomes complex. We propose to realize it by an $LC$ circuit with operational
Anatomy of skin modes and topology in non-Hermitian systems
A non-Hermitian system can exhibit extensive sensitivity of its complex energy spectrum to the imposed boundary conditions, which is beyond any known phenomenon from Hermitian systems. In addition to
Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
  • M. Ezawa
  • Physics, Mathematics
    Physical Review B
  • 2019
Non-Hermitian skin-edge states emerge only at one edge in one-dimensional nonreciprocal chains, where all states are localized at the edge irrespective of eigenvalues. The bulk topological number is
Topological Origin of Non-Hermitian Skin Effects.
TLDR
It is revealed that the skin effect originates from intrinsic non-Hermitian topology, which explains the universal feature of the known skin effect, and leads to new types of the skin effects-symmetry-protected skin effects.
Anomalous Edge State in a Non-Hermitian Lattice.
We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as
Topolectrical-circuit realization of topological corner modes
Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological
Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems.
TLDR
It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary conditions but exponential under open boundary conditions.
Topolectrical Circuits
Invented by Alessandro Volta and Félix Savary in the early 19th century, circuits consisting of resistor, inductor and capacitor (RLC) components are omnipresent in modern technology. The behavior of
Topological Phases of Non-Hermitian Systems
Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular
...
...