Thermodynamic properties of superconducting GeH3 under high pressure

Abstract

Chemical precompression can reduce the pressure required for structure metallization and for the subsequent existence of a superconducting state in hydrogen-rich compounds. In this study, we determined the thermodynamic properties of the superconducting state in germanium hydride GeH3. Stable structures of this compound crystallize at 175 GPa during the chemical decomposition of GeH4. Computations were conducted within the formalism of the Eliashberg theory of superconductivity. This approach allowed us to analyze thermodynamic quantities such as the transition temperature (Tc), free energy, entropy, and specific heat difference (ΔF, ΔS, ΔC) between the superconducting and normal states. Results were obtained for three stable structures comprising A15 (Pm3¯n, fcc), Cccm (orthorhombic), and P42/mmc (tetragonal) for GeH3 at 180 GPa. The transition temperature for μ⋆ = 0.1 indicated substantial changes between the crystal structures, where A15 had the highest Tc (194 K). The Cccm and P42/mmc systems had similar critical temperatures of 147.2 K and 132.9 K, respectively. The advantageous superconducting state properties of the A15 system in terms of the thermodynamic quantities make this structure more desirable for industrial use. In particular, the free energy difference representing the thermodynamic stability of the superconducting state was two times larger in A15 compared with the other systems. The results obtained for the critical temperatures were compared with the values obtained using the McMillan (MM) and Allen–Dynes (AD) analytic formulae. The difference between the results obtained using the Eliashberg formalism and MM approach was well above 60 K for the A15 structure (TcMM = 133 K, TcAD = 159 K). Further analysis with the Bardeen–Cooper–Schrieffer (BCS) constants (RΔ, RC, RH) showed that GeH3 cannot be considered as a BCS superconductor.