Discriminant indicator with generalized rotational symmetry

TL;DR

This paper introduces discriminant indicators for systems with generalized rotational symmetry, enabling the detection of exceptional points from data at high-symmetry points, and proposes a method to realize such systems using electrical circuits.

Contribution

It develops new discriminant indicators for 2D and 3D systems with n-fold rotational symmetry, expanding the tools for analyzing symmetry-protected exceptional points.

Findings

Indicators predict exceptional points without ambiguity

Indicators can be computed from limited high-symmetry point data

Proposed electrical circuit implementation for 2D systems

Abstract

Discriminant indicators with generalized inversion symmetry are computed only from data at the high-symmetry points. They allow a systematic search for exceptional points. In this paper, we propose discriminant indicators for two- and three-dimensional systems with generalized $n$-fold rotational symmetry ($n=4$, $6$). As is the case for generalized inversion symmetry, the indicator taking a nontrivial value predicts the emergence of exceptional points and loops without ambiguity of the reference energy. A distinct difference from the case of generalized inversion symmetry is that the indicator with generalized $n$-fold rotational symmetry ($n=4$, $6$) can be computed only from data at two of four high-symmetry points in the two-dimensional Brillouin zone. Such a difference is also observed in three-dimensional systems. Furthermore, we also propose how to fabricate a two-dimensional system with generalized four-fold rotational symmetry for an electrical circuit.