Degenerate line modes in the surface and bulk phonon spectra of orthorhombic NaMgF3 perovskite

Abstract

Degenerate bulk-line phonon modes have been widely reported in various crystal system types; however, degenerate surface-line phonon modes have only been reported in monoclinic crystal systems, such as SnIP with space group P2/c (No. 13). Herein, we propose that degenerate surface-line phonon modes can also emerge in solids with orthorhombic structures. Based on first-principle calculations and symmetry analysis, we propose that orthorhombic NaMgF3 fluoroperovskite with space group Pnma (No. 62) is a material candidate with degenerate line states in both the bulk phonon mode and the (010) surface phonon mode. We discovered four closed nodal loops (two type-I and two hybrid-type) on the ky = 0 plane in the bulk phonon mode, all of which coexisted with Dirac points on the Z–U and X–U paths. Moreover, we discovered symmetry-projected doubly degenerate nodal lines along the X¯–U¯ surface path in the (010) surface phonon mode. The proposed degenerate surface-line phonons in NaMgF3 is quite clean and protected by symmetries, which will aid future experimental detection.