Degenerate line modes in the surface and bulk phonon spectra of orthorhombic NaMgF3perovskite

Publication Name

Applied Physics Letters


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 P 2 / 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.

Open Access Status

This publication is not available as open access





Article Number


Funding Number


Funding Sponsor

Natural Science Foundation of Hebei Province



Link to publisher version (DOI)