Symmetry principles play a critical role in formulating the fundamental laws of nature, with a large number of symmetry-protected topological states identified in recent studies of quantum materials. As compelling examples, massless Dirac fermions ar
e jointly protected by the space inversion symmetry $P$ and time reversal symmetry $T$ supplemented by additional crystalline symmetry, while evolving into Weyl fermions when either $P$ or $T$ is broken. Here, based on first-principles calculations, we reveal that massless Dirac fermions are present in a layered FeSn crystal containing antiferromagnetically coupled ferromagnetic Fe kagome layers, where each of the $P$ and $T$ symmetries is individually broken but the combined $PT$ symmetry is preserved. These stable Dirac fermions protected by the combined $PT$ symmetry with additional non-symmorphic $S_{rm{2z}}$ symmetry can be transformed to either massless/massive Weyl or massive Dirac fermions by breaking the $PT$ or $S_{rm{2z}}$ symmetry. Our angle-resolved photoemission spectroscopy experiments indeed observed the Dirac states in the bulk and two-dimensional Weyl-like states at the surface. The present study substantially enriches our fundamental understanding of the intricate connections between symmetries and topologies of matter, especially with the spin degree of freedom playing a vital role.
Most of existing rendezvous algorithms generate channel-hopping sequences based on the whole channel set. They are inefficient when the set of available channels is a small subset of the whole channel set. We propose a new algorithm called ZOS which
uses three types of elementary sequences (namely, Zero-type, One-type, and S-type) to generate channel-hopping sequences based on the set of available channels. ZOS provides guaranteed rendezvous without any additional requirements. The maximum time-to-rendezvous of ZOS is upper-bounded by O(m1*m2*log2M) where M is the number of all channels and m1 and m2 are the numbers of available channels of two users.
