Topological properties of linear circuit lattices
arXiv:1410.1243 · doi:10.1103/PhysRevLett.114.173902
Abstract
Motivated by the topologically insulating (TI) circuit of capacitors and inductors proposed and tested in arXiv:1309.0878, we present a related circuit with less elements per site. The normal mode frequency matrix of our circuit is unitarily equivalent to the hopping matrix of a quantum spin Hall insulator (QSHI) and we identify perturbations that do not backscatter the circuit's edge modes. The idea behind these models is generalized, providing a platform to simulate tunable and locally accessible lattices with arbitrary complex spin-dependent hopping of any range. A simulation of a non-Abelian Aharonov-Bohm effect using such linear circuit designs is discussed.
5 pages, 2 figures, 1 table + supplement (2 pages); Editor's Suggestion (in press); featured in Condmat journal club at http://www.condmatjournalclub.org/?p=2528
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- Topological Photonics
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- Gain and loss induced topological insulating phase in a non Hermitian electrical circuit
- Topolectrical-circuit octupole insulator with topologically protected corner states
- Hyperbolic band topology with non-trivial second Chern numbers
- Topological Zak Phase in Strongly-Coupled LC Circuits
- Realization of a Hopf insulator in circuit systems
- Non-Abelian inverse Anderson transitions
- Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
- Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals
- Experimental realization of two-dimensional weak topological insulators
- Observation of inverse Anderson transitions in Aharonov-Bohm topolectrical circuits
- Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks
- Exploring topological phase transition andWeyl physics in five dimensions with electric circuits
- Valley Hall edge solitons in a photonic graphene
- Engineering topological phases with a three-dimensional nodal-loop semimetal
- Observation of type-III corner states induced by long-range interactions
- Topolectrical-circuit realization of quadrupolar surface semimetals
- Creation of electrical knots and observation of DNA topology
- Observation of non-Hermitian many-body skin effects in Hilbert space
- The effects of dissipation on topological mechanical systems
- Reentrant quantum spin Hall effect in the presence of an exchange field
- Generating electromagnetic modes with fine tunable orbital angular momentum by planar topological circuits
- Topological Properties and Characterizations