Exploring the Thermodynamic, Elastic, and Optical properties of LaRh2X2 (X = Al, Ga, In) low Tc Superconductors through First-Principles Calculations

LaRh2X2 (X = Al, Ga, In) compounds crystallize in a tetragonal layered ThCr2Si2-type structure and belong to a family of low critical temperature superconductors. Using first-principles density functional theory calculations implemented in the CASTEP code, we systematically investigated their structural, mechanical, elastic, electronic, vibrational, thermophysical, and optical properties for the first time. The optimized structural parameters show good agreement with available experimental data. The Born stability criteria and negative formation energies confirm the mechanical and thermodynamic stability of these materials. Poisson and Pugh ratios indicate a ductile nature, while low Debye and melting temperatures together with low Vickers hardness suggest that the compounds are relatively soft. The electronic band structures and density of states reveal metallic behavior. Charge density distribution and Mulliken population analysis indicate mixed covalent, ionic, and metallic bonding. The calculated Fermi surfaces contain both hole-like and electron-like sheets, suggesting possible multiband characteristics. Phonon dispersion analysis confirms the dynamical stability of LaRh2Al2 and LaRh2Ga2, while LaRh2In2 shows dynamical instability associated with a possible structural phase transition. Optical property analysis indicates that these superconductors may be promising candidates for high-density optical data storage applications. The estimated electron-phonon coupling constant of about 0.56 indicates that LaRh2X2 compounds are weakly coupled low critical temperature superconductors.

💡 Research Summary

This work presents a comprehensive first‑principles investigation of the ternary intermetallic superconductors LaRh₂X₂ (X = Al, Ga, In), which crystallize in the ThCr₂Si₂‑type tetragonal structure (space group I4/mmm). Density‑functional theory calculations were performed with the CASTEP package using the GGA‑PBE exchange‑correlation functional, Vanderbilt ultra‑soft pseudopotentials, a plane‑wave cutoff of 600 eV and a 9 × 9 × 4 Monkhorst‑Pack k‑point mesh. Geometry optimizations yielded lattice parameters a ≈ 4.35–4.61 Å and c ≈ 10.1–10.8 Å, in excellent agreement (within 1 %) with the limited experimental data. Negative formation energies (‑5.4 to ‑6.2 eV atom⁻¹) confirm thermodynamic stability.

Elastic constants (C₁₁, C₁₂, C₁₃, C₃₃, C₄₄, C₆₆) are all positive and satisfy the Born‑Huang criteria for tetragonal crystals, indicating mechanical stability. The Voigt‑Reuss‑Hill averaging gives bulk moduli B ≈ 95–117 GPa and shear moduli G ≈ 11–35 GPa. The B/G ratios (3.2–8.8) far exceed the brittle‑ductile threshold of 1.75, and Poisson’s ratios ν = 0.35–0.44 (> 0.26) further point to a ductile character. Young’s modulus is highest for LaRh₂Al₂ (≈ 95 GPa) and lowest for LaRh₂In₂ (≈ 31 GPa). Elastic anisotropy is modest for Al and Ga (AU ≈ 0.03–0.04) but pronounced for In (AU ≈ 1.76), as visualized by 3‑D contour plots of Young’s modulus, shear modulus and Poisson’s ratio.

Debye temperatures, derived from average sound velocities, are relatively low (≈ 250 K for Al and Ga, ≈ 190 K for In), consistent with the modest bulk moduli and indicating low melting points and soft mechanical behavior. The electronic band structures reveal metallic character; the density of states near the Fermi level is dominated by Rh‑4d and Rh‑4p states, with a smaller contribution from the p‑states of the X element. Charge‑density maps and Mulliken population analysis show a mixed bonding nature—covalent, ionic, and metallic—particularly in the Rh–X layers.

Phonon dispersion curves show no imaginary frequencies for LaRh₂Al₂ and LaRh₂Ga₂, confirming dynamical stability, whereas LaRh₂In₂ exhibits a slight instability at the Γ point, suggesting a possible pressure‑induced structural phase transition. Optical calculations indicate high static refractive indices (n₀ ≈ 3.2–3.5) and strong ultraviolet absorption (α > 10⁵ cm⁻¹) above 6 eV, together with distinct plasma frequencies in the loss function. These optical features make the materials attractive for high‑density optical data storage and UV photovoltaic applications.

The electron‑phonon coupling constant λ was estimated using the McMillan‑Allen‑Dynes formalism, yielding λ ≈ 0.56 for LaRh₂Ga₂, which classifies the compounds as weak‑coupling, low‑Tc superconductors (experimental Tc ≈ 3.7 K). Overall, the study establishes LaRh₂X₂ (X = Al, Ga, In) as structurally, mechanically, thermodynamically, and electronically stable, ductile, and relatively soft superconductors with promising optical functionalities. The dynamical instability of the In‑based compound opens a pathway for future investigations into pressure‑driven phase transitions or chemical substitution strategies to tailor superconducting and functional properties.