Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$

Abstract

We show that topological phases of the Dirac system in arbitral even dimensional space are simulated by $LC$ electric circuits with operational amplifiers. The lattice Hamiltonian for the hypercubic lattice in $2n$ dimensional space is characterized by the $n$-th Chern number. The boundary state is described by the Weyl theory in $2n-1$ dimensional space. They are well observed by measuring the admittance spectrum. They are different from the disentangled $n$-th Chern insulators previously reported, where the $n$-th Chern number is a product of the first Chern numbers. The results are extended to non-Hermitian systems with complex Dirac masses. The non-Hermitian $n$-th Chern number remains to be quantized for the complex Dirac mass.

6 pages, 6 figures

References in corpus (16)

• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Acoustics
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Second-Order Topological Phases in Non-Hermitian Systems
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Electric circuits for non-Hermitian Chern insulators
• Chern insulators for electromagnetic waves in electrical circuit networks

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• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
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