D-Wave Superconducting Gap Symmetry as a Model for Nb1−xMoxB2 (x = 0.25; 1.0) and WB2 Diborides

Abstract

Recently, Pei et al. (National Science Review2023, nwad034, 10.1093/nsr/nwad034) reported that ambient pressure β-MoB2 (space group: R3¯m) exhibits a phase transition to α-MoB2 (space group: P6/mmm) at pressure P~70 GPa, which is a high-temperature superconductor exhibiting Tc=32 K at P~110 GPa. Although α-MoB2 has the same crystalline structure as ambient-pressure MgB2 and the superconducting critical temperatures of α-MoB2 and MgB2 are very close, the first-principles calculations show that in α-MoB2, the states near the Fermi level, εF, are dominated by the d-electrons of Mo atoms, while in MgB2, the p-orbitals of boron atomic sheets dominantly contribute to the states near the εF. Recently, Hire et al. (Phys. Rev. B2022, 106, 174515) reported that the P6/mmm-phase can be stabilized at ambient pressure in Nb1−xMoxB2 solid solutions, and that these ternary alloys exhibit Tc~8 K. Additionally, Pei et al. (Sci. China-Phys. Mech. Astron. 2022, 65, 287412) showed that compressed WB2 exhibited Tc~15 K at P~121 GPa. Here, we aimed to reveal primary differences/similarities in superconducting state in MgB2 and in its recently discovered diboride counterparts, Nb1−xMoxB2 and highly-compressed WB2. By analyzing experimental data reported for P6/mmm-phases of Nb1−xMoxB2 (x = 0.25; 1.0) and highly compressed WB2, we showed that these three phases exhibit d-wave superconductivity. We deduced 2Δm(0)kBTc=4.1±0.2 for α-MoB2, 2Δm(0)kBTc=5.3±0.1 for Nb0.75Mo0.25B2, and 2Δm(0)kBTc=4.9±0.2 for WB2. We also found that Nb0.75Mo0.25B2 exhibited high strength of nonadiabaticity, which was quantified by the ratio of TθTF=3.5, whereas MgB2, α-MoB2, and WB2 exhibited TθTF~0.3, which is similar to the TθTF in pnictides, A15 alloys, Heusler alloys, Laves phase compounds, cuprates, and highly compressed hydrides.