Recently, Wang et al. [Phys. Rev. B 106, 195129 (2022)] challenged a widely held belief in the field of Weyl physics, demonstrating that single-pair-Weyl points (SP-WPs) can exist in nonmagnetic spinless systems, contrary to previous assumptions that they could only exist in magnetic systems. Wang et al. observed that the SP-WPs with opposite and even chiral charges (i.e., $\left|\mathcal{C}\right|$ = 2 or 4) could also exist in nonmagnetic spinless systems. In this Letter, we present a finding in which SP-WPs have a partner, namely a charged nodal surface, in nonmagnetic spinless systems. In contrast to previous observations, we show that the SP-WPs can have uneven chiral charges (i.e., $\left|\mathcal{C}\right|$ = 1). We identify six (out of 230) space groups (SGs) that contain such SP-WPs by searching the encyclopedia of emergent particles in three-dimensional crystals. Our finds were confirmed through the phonon spectra of two specific materials ${\mathrm{Zr}}_3\mathrm{O}$ (with SG 182) and ${\mathrm{NaPH}}_3{\mathrm{NO}}_3$ (with SG 173). This discovery broadens the range of materials that can host SP-WPs and applies to other nonmagnetic spinless crystals.

• Received 11 April 2023
• Revised 3 June 2023
• Accepted 26 June 2023

DOI:https://doi.org/10.1103/PhysRevB.108.L020302