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arXiv · 1905.10734

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

Motohiko Ezawa
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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.

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Motohiko Ezawa. 2019-05-26. Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$. https://doi.org/10.1103/physrevb.100.075423

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