New formalism for studying topological phases of electric circuits

In recent years, topological phases have been realized not only in electronic systems but also in artificial systems such as electric circuits [1]. In order to investigate the bulk-boundary correspondence, which is one of the important properties of the topological phases, it is necessary to correctly define the norm of the eigenstates, and conservation of the norm is crucial in establishing bulk-boundary correspondence. Unlike the electronic systems, in the electric circuit systems, a proper definition of the norm has not been known, and therefore, the bulk-boundary correspondence has not been shown so far. In this presentation, we propose a new formalism in which a conserved norm is defined for certain general classes of electric circuits, and discuss its consequences in bulk-boundary correspondence. Our new formalism is expected to be useful for the comprehensive study of topological properties of electric circuits.

[1] C. H. Lee, S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, and R. Thomale, Commun. Phys. 1, 39 (2018).