Evidence of a structural quantum critical point in (Ca$_{x}$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ from a lattice dynamics study

TL;DR

This study provides microscopic evidence of a structural quantum critical point in (Ca$_{x}$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ by analyzing phonon softening, revealing its potential role in enhancing superconductivity.

Contribution

First microscopic demonstration of a structural quantum critical point in a nonmagnetic system through lattice dynamics analysis.

Findings

Phonon modes soften near the structural transition as temperature decreases.

At x=0.85, the soft mode energy squared extrapolates to zero near -5.7 K.

Enhanced low-energy phonon density-of-states may promote strong-coupling superconductivity.

Abstract

Approaching a quantum critical point (QCP) has been an effective route to stabilize superconductivity. While the role of magnetic QCPs has been extensively discussed, similar exploration of a structural QCP is scarce due to the lack of suitable systems with a continuous structural transition that can be conveniently tuned to 0~K. Using inelastic X-ray scattering, we examine the phonon spectrum of the nonmagnetic quasi-skutterudite (Ca$_{x}$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$, which represents a precious system to explore the interplay between structural instabilities and superconductivity by tuning the Ca concentration $x$. We unambiguously detect the softening of phonon modes around the M point on cooling towards the structural transition. Intriguingly, at $x=0.85$, the soft mode energy squared at the M point extrapolates to zero at $(-5.7 \pm 7.7)$~K, providing the first compelling microscopic evidence of a structural QCP in (Ca$_{x}$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$. The enhanced phonon density-of-states at low energy provides the essential ingredient for realizing strong-coupling superconductivity near the structural QCP.