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.

Quantifying the Nonadiabaticity Strength Constant in Recently Discovered Highly Compressed Superconductors

“…In the result, we derived the nonadiabaticity strength constant, T θ T F , for these superconductors. Derived T θ T F values confirmed the previously reported empirical observation [91,101] that the superconductors with T c > 10 K obey the condition 0.025 T θ T F 0.4.…”

“…[101], and confirmed in Ref. [91], that superconductors with T c > 10 K (from a dataset of 46 superconductors from all major superconductor families) exhibit the T θ T F ratio in the range 0.025…”

“…Thus, the experiment [1,3,25] remains the final criterion. Therefore, the confirmation of the predicted T c in order to determine the other fundamental ground-state parameters, including the upper critical field, B c2 (0); the lower critical field, B c1 (0) [12,22]; the self-field critical current density, J c (s f , T) [24,[82][83][84]; the London penetration depth, λ(0) [22,23,85,86]; the superconducting energy gap amplitude, ∆(0) [87][88][89]; and gap symmetry [90,91]; is the task of the experiment and the data analysis.…”

“…In other words, Equation (1) implies that the superconductor exhibits fast electric charge carriers and slow ions. This assumption simplifies the theoretical model of electron-phonon-mediated superconductivity; however, Equation ( 1) is not satisfied for many unconventional superconductors [94][95][96][97][98][99][100][101][102] (which was first pointed out by Pietronero and co-workers [103][104][105][106]) and many highly compressed superconductors [91,101,[107][108][109].…”

Quantifying the Nonadiabaticity Strength Constant in Recently Discovered Highly-Compressed Superconductor

“…Thus, the experiment [1,3,25] remains the final criterion. Therefore, the confirmation of the predicted T c in order to determine the other fundamental ground-state parameters, including the upper critical field, B c2 (0); the lower critical field, B c1 (0) [12,22]; the self-field critical current density, J c (s f , T) [24,[82][83][84]; the London penetration depth, λ(0) [22,23,85,86]; the superconducting energy gap amplitude, ∆(0) [87][88][89]; and gap symmetry [90,91]; is the task of the experiment and the data analysis.…”