Two-nodal surface phonons in solid-state materials

Abstract

This year, researchers have been on the lookout for real materials with one-nodal, two-nodal (two-NS), and three-nodal surface phonons. However, materials with two-NS phonons have been scarce until recently. This paper contributes to the understanding of the symmetry conditions of two-NS phonons. Two-NS phonons have NS states that are localized on two of three ${k}_{i}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$ $(i=x,y,z)$ planes in the three-dimensional Brillouin zone). They are dominated by twofold screw symmetry and time-reversal symmetry. This paper also contributes the prediction of a series of materials with two-NS states in their phonon dispersions. First, by screening all 230 space groups (SGs), we discovered 19 SG candidates (with Nos. 18, 55--60, 90, 94, 113, 114, 127--130, and 135--138) that have two-NS phonons. Second, based on first-principles calculations, we proposed 19 realistic material candidates hosting two-NS phonons: $P{2}_{1}{2}_{1}2$-type ${\mathrm{ZnTeMoO}}_{6}$ (with SG No. 18), $Pbma$-type ${\mathrm{Cs}}_{2}{\mathrm{Te}}_{2}$ (with SG No. 55), $Pccn$-type ${\mathrm{Sr}}_{2}{\mathrm{SnO}}_{4}$ (with SG No. 56), $Pbcm$-type CaAlPd (with SG No. 57), $Pnnm$-type ${\mathrm{PtO}}_{2}$ (with SG No. 58), $Pmmn$-type ${\mathrm{KLi}}_{2}\mathrm{As}$ (with SG No. 59), $Pbcn$-type ${\mathrm{CV}}_{2}$ (with SG No. 60), $P{42}_{1}2$-type ${\mathrm{BaVCu}}_{4}{\mathrm{P}}_{4}{\mathrm{O}}_{17}$ (with SG No. 90), $P{4}_{2}{2}_{1}2$-type ${\mathrm{Na}}_{5}{\mathrm{Fe}}_{3}{\mathrm{F}}_{14}$ (with SG No. 94), $P\overline{4}{2}_{1}m$-type ${\mathrm{BaS}}_{3}$ (with SG No. 113), $P\overline{4}{2}_{1}c$-type ${\mathrm{Na}}_{4}{\mathrm{SnS}}_{4}$ (with SG No. 114), $P4/mbm$-type ${\mathrm{ReO}}_{3}$ (with SG No. 127), $P4/mnc$-type ${\mathrm{Sr}}_{4}{\mathrm{Li}}_{2}{\mathrm{Si}}_{4}{\mathrm{N}}_{8}\mathrm{O}$ (with SG No. 128), $P4/nmm$-type ${\mathrm{BaHfN}}_{2}$ (with SG No. 129), $P4/ncc$-type ${\mathrm{Bi}}_{2}{\mathrm{CuO}}_{4}$ (with SG No. 130), $P{4}_{2}/mbc$-type ${\mathrm{YB}}_{2}\mathrm{C}$ (with SG No. 135), $P{4}_{2}/mnm$-type ${\mathrm{MgF}}_{2}$ (with SG No. 136), $P{4}_{2}/nmc$-type ${\mathrm{YB}}_{4}{\mathrm{Rh}}_{4}$ (with SG No. 137), and $P{4}_{2}/ncm$-type ${\mathrm{LiClO}}_{2}$ (with SG No. 138). Third, we discovered 622 (out of 10 037) materials with two-NS phonons by checking the phonon database at Kyoto University. Our present paper provides a better understanding of the two-NS states in phonon systems (or even other bosonic systems) and suggests a huge number of material candidates with two-NS phonons.