Topological Langmuir-cyclotron wave

It can be proved that the electron cyclotron wave must vanish somewhere on a 2D sphere enclosing the Weyl point of Langmuir-cyclotron resonance in the parameter space. Consequently, there must exist a topological surface excitation called Topological Langmuir-Cyclotron Wave (TLCW) in magnetized plasmas [1], which propagates unidirectionally along complex phase transition interfaces without scattering [2]. Due to this topologically protected robustness, the TLCW, whose spectrum span covers those of high harmonic ion cyclotron waves and whistler waves, could be explored for various practical applications. The topological methods recently developed for plasma waves are similar but different to those used in condensed matter physics, where periodic lattices lead to nontrivial topology in momentum space. But in plasmas and other continuous media, nontrivial topology only exists in phase space because of the contractibility of momentum space [1]. Using the algebraic topological concepts and tools developed, such as the boundary isomorphism theorem [1], and an Atiyah-Patodi-Singer type of index theorem formulated by Faure [3], we prove the existence of TLCW as a spectral flow across the band gap. We show that the TLCW can be represented by a tilted Dirac cone in phase space, the entire spectrum of which, including its spectral flow, is found analytically. [1] H. Qin & Y. Fu, Sci. Adv. 9, eadd8041(2023). [2] Y. Fu & H. Qin, Nat. Commun. 12, 3924 (2021). [3] Faure, arXiv:1901.10592 (2019).