Coexistience of phononic six-fold, four-fold and three-fold excitations in ternary antimonide Zr3Ni3Sb4

Three-, four-, and six-fold excitations have significantly extended the subjects of condensed matter physics. There is an urgent need for a realistic material that can have coexisting 3-, 4-, and 6-fold excitations. However, these materials are uncommon because these excitations in electronic systems are usually broken by spin-orbit coupling (SOC) and normally far from the Fermi level. Unlike the case in electronic systems, the phonon systems with negligible SOC effect, not constrained by the Pauli exclusion principle, provide a feasible platform to realize these excitations in a wide frequency range. Hence, in this work, we demonstrate by first-principle calculations and symmetry analysis that perfect 3-, 4-, 6-fold excitations appear in the phonon dispersion rather than the band structures of Zr3Ni3Sb4, which is a well-known indirect-gap semiconductor with an Y3Au3Sb4-type structure. This material features 3-fold quadratic contact triple-point phonon, 4-fold Dirac point phonon, and 6-fold point phonon. Moreover, these nodal-point phonons are very robust to uniform strain. Two obvious phonon surface arcs of the [001] plane are extended in the whole Brillouin zone, which will facilitate their detection in future experimental studies. The current work provides an ideal model to investigate the rich excitations in a single material.

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