Pressure induced evolution of anisotropic superconductivity and Fermi surface nesting in a ternary boride

Using Migdal-Eliashberg theory implemented in Electron Phonon Wannier (EPW) code, we have investigated anisotropic superconductivity in a ternary boride $\mathrm{Ta(MoB)_2}$. It is a single-gap, anisotropic, phonon-mediated superconductor having a critical temperature $\mathrm{T_c}\sim \, 19.3$ K. A dominant contribution to superconductivity arises from the robust coupling between electronic states, primarily created by the $\mathrm{d_{xy}}$,$\mathrm{d_{x^2 - y^2}}$ orbitals of Mo atoms and the in-plane vibrations of Mo atoms. A weak Fermi surface nesting and a small electron-phonon coupling cannot induce charge density wave-like instabilities, as evidenced by the lack of a significant peak in the real part of the total Lindhard susceptibility and the absence of phonon softening. Furthermore, we have studied its electronic and superconducting properties under hydrostatic pressure up to 76.69 GPa, owing to its low bulk modulus and metastability. The persistent reduction in the density of states at the Fermi level, Fermi surface nesting and the stiffening of phonon modes lead to a diminution of superconductivity under pressure up to 59.71 GPa. At 76.69 GPa, a modification in the topology of the Fermi surface, namely a Lifshitz transition, occurs resulting in a sudden enhancement of nesting. This enhanced nesting, in turn, induces an abrupt stabilisation of superconductivity at 76.69 GPa, resulting in a V-shaped response to pressure.