Multifold topological semimetals

Abstract

Abstract The discovery of topological semimetals with multifold band crossings has opened up a new and
exciting frontier in the field of topological physics. These materials exhibit large Chern numbers, leading
to long double Fermi arcs on their surfaces, which are protected by either crystal symmetries or topological
order. The impact of these multifold crossings extends beyond surface science, as they are not constrained
by the Poincar´e classification of quasiparticles and only need to respect the crystal symmetry of one of
the 1651 magnetic space groups. Consequently, we observe the emergence of free fermionic excitations
in solid-state systems that have no high-energy counterparts, protected by non-symmorphic symmetries.
In this work, we review the recent theoretical and experimental progress made in the field of multifold
topological semimetals. We begin with the theoretical prediction of the so-called multifold fermions and
discuss the subsequent discoveries of chiral and magnetic topological semimetals. Several experiments that
have realized chiral semimetals in spectroscopic measurements are described, and we discuss the future
prospects of this field. These exciting developments have the potential to deepen our understanding of the
fundamental properties of quantum matter and inspire new technological applications in the future.