Magnesium Diboride: A New Superconductor?

By Surbhi JainReviewed by Susha Cheriyedath, M.Sc.Mar 25 2022

In an article recently published in the Journal of Applied Physics, researchers investigated the influence of strain and pressure on the superconductivity and electron-phonon coupling in magnesium diboride (MgB₂)_. They also discussed the corresponding theoretical approaches and the future of nanostructure design.

Study: The effect of strain and pressure on the electron-phonon coupling and superconductivity in MgB₂—Benchmark of theoretical methodologies and outlook for nanostructure design. Image Credit: Gorodenkoff/Shutterstock.com

Background

The discovery of MgB₂ as a high-temperature superconductor with a superconducting transition temperature (T_c) = 39 K led to a flurry of experimental and theoretical studies on the compound's various properties. Understanding superconductivity requires knowledge of both the phonon and electrical band structures. Inelastic X-ray scattering measurements of phonon band structure reveal Kohn anomalies. The depths of the Kohn anomalies can be directly linked to the superconducting transition temperature, according to theoretical investigations.

The hexagonal unit cell of MgB₂. Each unit cell consists of one magnesium atom (orange) and two boron atoms (purple). Image Credit: Johansson, E et al., Journal of Applied Physics

More research is needed, however, to compare approaches for predicting T_c based on the Kohn anomaly strength to estimate the electron-phonon coupling (EPC). The impact of positive hydrostatic pressure suppresses T_c in MgB₂. Anisotropic strain's effect on MgB₂ superconductivity has also been studied experimentally and theoretically. The Migdal–Éliashberg formalism of superconductivity is known to perform well in calculating the transition of superconductivity in MgB₂, in both anisotropic and isotropic approximations, under ambient circumstances.

About the Study

In this study, the authors investigated the effect of hydrostatic pressure, strain, and anisotropic tension on the T_c of MgB₂ by using a variety of theoretical approaches. This was accomplished by looking at Kohn anomalies in phonon dispersions alone, as well as by calculating the electron-phonon coupling explicitly. An alternative method was offered via co-deposition using ternary diborides that thermodynamically avoided mixing with MgB₂. This method encouraged columnar growth, which caused a strain in all directions.

The researchers compared alternative methods for predicting the T_c of MgB₂ under hydrostatic pressure, as well as anisotropic stress and strain. On the optical E₂g branch, the first method was based on the pressure-derived evolution of the Kohn anomaly and phonon dispersions. The discrepancies in the detected Kohn anomalies along Γ–q (q = K, M, H, L) across the procedures were quantified. Phonons obtained from both finite displacements and linear response methods were compared. The Migdal–Éliashberg formalism was used to calculate EPC as a function of pressure. T_c was calculated by using both isotropic and anisotropic approximations.

The team utilized two approaches to determine electronic and phonon characteristics in MgB₂ from first-principles computations. Two phonon-based finite displacement and linear response approaches were used to characterize the response of Kohn anomaly in the optical E₂g branch to the in-plane stretching modes of the B–B bond. The Kohn anomaly approach calculated T_c by utilizing finite displacements at ambient pressure when averaged across all directions. A 5 x 5 (a, c) grid was used to investigate the lattice parameter space around the MB₂ (M = V, Ti, Hf, Zr, Y) candidates.

Directional and pressure dependence of thermal energy T_δ that correlates with superconducting transition temperature T_c, calculated using FD and DFPT. Image Credit: Johansson, E et al., Journal of Applied Physics

Observations

T_c was suppressed by increasing pressure in all situations, whereas superconductivity was enhanced by isotropic and anisotropic strain. Under compressive load, the corresponding Kohn anomaly depth decreased, while under tensile strain, it increased. It was observed that with an increase in Tc, negative pressure increased, and with an increase in the compressing of the lattice, the Kohn anomaly was completely suppressed.

In the range, 60–80 meV (at ambient pressure), visualizing the phonon dispersion ωvq widened by the phonon linewidth γνq provided evidence of EPC in the E₂g branch along Γ–q (q = A, K, M, H, L). The anomalous phonon frequency stiffened, and the overall electron-phonon coupling decreased as pressure was increased, which effectively limited superconductivity in MgB₂.

When T_c was boosted to 38.7 K, the pressure trend closely resembled the bulk of experimental reference values. T_c was enhanced by compressive and tensile strain. Because they were projected to have clustering tendencies in comparison to MgB₂, the metal diborides MB₂ (M = V, Ti, Hf, Zr, Y) were highlighted as possible candidates for smart nanostructure design. It was observed that uniaxial out-of-plane tensile strain, biaxial in-plane tensile strain, or their combination significantly increased T_c.

Electron–phonon properties of MgB₂ derived using QE. (a) Phonon density of states F(ω). Dashed lines show contributions from Mg and solid lines from B atoms. (b) Solid lines show Éliashberg spectral function α²F(ω) at different pressures, ranging from −20 to 25 GPa in steps of 5 GPa. Dashed lines correspond to the cumulative mass enhancement parameter λ(ω) that once becoming a straight flat line as the spectral function dies out reveals the total electron–phonon coupling value λ. Image Credit: Johansson, E et al., Journal of Applied Physics

Conclusions

In conclusion, this study elucidated that both HfB₂ and ZrB₂ are potential candidates for acquiring tensile strain in smartly constructed 3D interconnected coherent columns or nanostructures that are strained in both c and a. It was observed that the highest amount of tensile strain would be possible with YB₂, but the dynamical stability of MgB₂ at those lattice parameters is yet to be determined. The authors emphasized that future research should include a thorough examination of the impacts of quaternary diboride nanostructures and their alloys.

They also believe that the findings of this study will encourage the use of this technology to examine the pressure behavior of additional materials systems with anomalous phonon branches.

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