We investigate the pressure effects on the electronic structures and phonon properties of rare-earth-based cubic-Heusler compound ${\mathrm{LuPd}}_2\mathrm{In}$, on the basis of $ab$ $initio$ density functional theory. We find the occurrence of intriguing phase transition from the superconducting (SC) to charge-density wave (CDW) state under pressure ($P$), which is quite unusual in that the pressure is detrimental to the CDW state in usual systems. The SC transition temperature $T_C$ of ${\mathrm{LuPd}}_2\mathrm{In}$ increases first with increasing pressure, up to $P_C\approx 28\mathrm{GPa}$, above which a quantum phase transition into the CDW state takes place. This extraordinary transition originates from the occurrence of phonon softening instability at a special $\mathbf{q}=M$ in the Brillouin zone. We thus propose that ${\mathrm{LuPd}}_2\mathrm{In}$ is a quite unique material, in which the CDW quantum critical point is realized under the SC dome by applying the pressure.

• Received 29 July 2019
• Revised 10 March 2020
• Accepted 10 September 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.157001