Coexistence of Multifold and Multidimensional Topological Phonons in KMgBO$_{3}$

Topological interpretations of phonons facilitate a new platform for novel concepts in phonon physics. Though there are ubiquitous set of reports on topological electronic excitations, the same for phonons are extremely limited. Here, we propose a new candidate material, KMgBO 3 , which showcase the co-existence of several multifold and multidimensional topological phonon excitations, which are protected by spatial and non-spatial symmetries. This includes zero dimensional double, triple and quadratic Weyl phonon nodes, one dimensional nodal line/loop and two dimensional doubly degenerate nodal surface states. Nodal line/loop emerges from the spin- 12 phonon nodes, while the two dimensional doubly degenerate nodal surface arises from a combination of two fold screw rotational and time reversal symmetries. Application of strain breaks the C 3 rotational symmetry, which annihilates the spin-1 double Weyl nodes, but preserves other topological features. Interestingly, strain helps to create two extra single Weyl nodes, which in turn preserve the total chirality. Alloying also breaks certain symmetries, destroying most of the topological phonon features in the present case. Thus, KMgBO 3 is a promising candidate which hosts various Weyl points, large Fermi arcs with a very clean phonon spectra and tunable topological phonon excitations, and hence certainly worth for future theoretical/experimental investigation of topological phononics.