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arXiv · 2202.07009

Realizing exceptional points of any order in the presence of symmetry

Sharareh Sayyad·Flore K. Kunst
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Abstract

Exceptional points~(EPs) appear as degeneracies in the spectrum of non-Hermitian matrices at which the eigenvectors coalesce. In general, an EP of order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. Our results show that these constraints can be expressed in terms of the determinant and traces of the non-Hermitian matrix. Our findings further reveal that the total number of constraints may reduce in the presence of unitary and antiunitary symmetries. Additionally, we draw generic conclusions for the low-energy dispersion of the EPs. Based on our calculations, we show that in odd dimensions the presence of sublattice or pseudo-chiral symmetry enforces $n$th order EPs to disperse with the $(n-1)$th root. For two-, three- and four-band systems, we explicitly present the constraints needed for the occurrence of EPs in terms of system parameters and classify EPs based on their low-energy dispersion relations.

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Sharareh Sayyad, Flore K. Kunst. 2022-02-14. Realizing exceptional points of any order in the presence of symmetry. https://doi.org/10.1103/physrevresearch.4.023130

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