Two-nodal Surface Phonons in Solid-State Materials

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) = +/-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: P2(1)2(1)2-type ZnTeMoO6 (with SG No. 18), Pbma-type Cs2Te2 (with SG No. 55), Pccn-type Sr2SnO4 (with SG No. 56), Pbon-type CaAlPd (with SG No. 57), Pnnm-type PtO2 (with SG No. 58), Pmmn-type KLi2As (with SG No. 59), Pbcn-type CV2 (with SG No. 60), P42(1)2-type BaVCu4P4O17 (with SG No. 90), P4(2)2(1)2-type Na5Fe3F14 (with SG No. 94), P (4) over bar2(1)m-type BaS3 (with SG No. 113), P (4) over bar2(1)c-type Na4SnS4 (with SG No. 114), P4/mbm-type ReO3 (with SG No. 127), P4/mnc-type Sr4Li2Si4N8O (with SG No. 128), P4/nmm-type BaHfN2 (with SG No. 129), P4/ncc-type Bi2CuO4 (with SG No. 130), P4(2)/mbc-type YB2C (with SG No. 135), P4(2)/mnm-type MgF2 (with SG No. 136), P4(2)/nmc-type YB4Rh4 (with SG No. 137), and P4(2)/non-type LiClO2 (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.