Hopf topology of multifold exceptional points

 Non-Hermiticity induces unique topological phenomena such as exceptional points. On the exceptional point, two eigenstates coalesce as well as eigenvalues, which leads to square-root dispersion and non-trivial point-gap topology[1,2]. Recently, topological protection is extended to multifold exceptional points where more than three eigenstates coalesce[3]. For instance, the emergence of three-fold exceptional points in four-dimensional parameter space is reported for coupled acoustic cavities[3,4]. Despite these progresses, the topology of exceptional points is limited to homotopy groups of self-maps of the sphere.

 In this talk, we introduce $n$-fold exceptional points with Hopf topology dubbed Hopf exceptional points (HEP$n$) by analyzing the higher-homotopy group of spheres[5]. Saliently. HEP3 and symmetry-protected HEP5 possess Z2 topology related to the Witten anomaly. Due to the Z2 topology, an HEP3 serves as its own anti-particle, which is in sharp contrast to formerly reported multifold exceptional points.

[1] H. Shen, et al., PRL 120, 146402 (2018).

[2] K. Kawabata, et al, PRL 123, 066405 (2019).

[3] P. Delplace, et al., PRL 127, 186602 (2021); T. Yoshida et al., arXiv 2409.09153.

[4] W. Tang et al. Science 370, 1077 (2020).

[5] T. Yoshida et al., arXiv:2504.13012.