Chern insulators for electromagnetic waves in electrical circuit networks

Abstract

Periodic networks composed of capacitors and inductors have been demonstrated to possess topological properties with respect to incident electromagnetic waves. Here, we develop an analogy between the mathematical description of waves propagating in such networks and models of Majorana fermions hopping on a lattice. Using this analogy we propose simple electrical network architectures that realize Chern insulating phases for electromagnetic waves. Such Chern insulating networks have a bulk gap for a range of signal frequencies that is easily tunable and exhibit topologically protected chiral edge modes that traverse the gap and are robust to perturbations. The requisite time reversal symmetry breaking is achieved by including a class of weakly dissipative Hall resistor elements whose physical implementation we describe in detail.

arXiv comment10 pages, 8 figures

References in corpus (28)

• Topological Insulators
• Topological insulators and superconductors
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• New directions in the pursuit of Majorana fermions in solid state systems
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Search for Majorana fermions in superconductors
• Topological phases of non-Hermitian systems
• Topological Acoustics
• Topological Band Theory for Non-Hermitian Hamiltonians
• Topolectrical circuit realization of topological corner modes
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Topological Boundary Modes in Isostatic Lattices
• Topolectrical circuits
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Time Reversal Invariant Topologically Insulating Circuits
• Topological phonon modes and their role in dynamic instability of microtubules
• Topological Polaritons
• Topological Insulators on the Lieb and Perovskite Lattices
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Probing the Berry Curvature and Fermi Arcs of a Weyl Circuit
• Topological nodal states in circuit lattice
• Topological circuits of inductors and capacitors
• Hall Effect Gyrators and Circulators
• Simulating Quantum Spin Hall Effect in Topological Lieb Lattice of Linear Circuit
• Topological Classification Table Implemented with Classical Passive Meta-Materials
• Bandwidth and dynamic range of a widely tunable Josephson parametric amplifier

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• Non-abelian gauge fields in circuit systems
• Topological Anderson Insulator in electric circuits
• Observation of symmetry protected zero modes in topolectrical circuits
• Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$
• Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits
• Hinge solitons in three-dimensional second-order topological insulators
• Strain-induced pseudo-magnetic field in $\alpha -{\mathcal{T}}_3$ lattice
• Engineering topological states and quantum-inspired information processing using classical circuits
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