Reaching Quantum Critical Point by Adding Non-magnetic Disorder in Single Crystals of Superconductor $(\text{Ca}_x\text{Sr}_{1-x})_3\text{Rh}_4\text{Sn}_{13}$

Abstract

The Remeika series superconductor, $(\text{Ca}_x\text{Sr}_{1-x})_3\text{Rh}_4\text{Sn}_{13}$, shows a rare nonmagnetic quantum critical point (QCP) associated with the continuous charge-density wave (CDW) and structural transition under the ``dome'' of superconductivity achieved by tuning composition and applying pressure. Here we use a nonmagnetic point-like disorder induced by 2.5 MeV electron irradiation to suppress the CDW and drive the system to and even beyond the QCP. This conclusion is based on a clear evolution of temperature-dependent resistivity, $ρ\left(T\right)$, from the Fermi liquid to the non-Fermi liquid regime with increasing amount of disorder. Starting on the CDW side, below the suggested QCP concentration of $x_c=0.9$, added disorder resulted in a progressively larger linear term and a reduced quadratic term in $ρ\left(T\right)$. Nearly perfect $T-$linear dependence is observed at the dose at which long-range CDW order is suppressed to $T=$0, consistent with the expectations. We refine the QCP location in this system and place it in the interval between $x=$0.75 and 0.85. Our results strongly support the concept that the disorder can tune the system to the quantum critical regime and even beyond. It follows from the argument by Imry and Ma that any ordered phase is unstable toward quenched disorder. Introduced in a controlled way, this disorder becomes a novel non-thermal tuning parameter likely applicable to a variety of different systems.

Figures (6)

• Figure 1: (Color online) Temperature-dependent resistivity, $\rho\left(T\right)$, of pristine samples of $(\text{Ca}_x\text{Sr}_{1-x})_3\text{Rh}_4\text{Sn}_{13}$. Inset shows compositional evolution of resistivity at two characteristic temperatures, $\rho\left(T=300\;\text{K}\right)$ (left axis), and just above the onset of the highest in this set of samples superconducting transition, $\rho\left(8.5\;\text{K}\right)$ (right axis).
• Figure 2: (Color online) (a) Temperature-dependent resistivity, $\rho (T)$, for the (Ca$_{0.75}$Sr$_{0.25}$)$_3$Rh$_4$Sn$_{13}$ composition, measured after repeated electron irradiations. The legend shows the accumulated irradiation dose. (b) Determination of the charge density wave onset (yellow stars) and long-range ordering (green stars). The curves were obtained by the subtraction of a linear fit of $\rho (T)$ above the transition temperature in the range indicated by the box in panel (a). (c) Power-law fits, $\Delta\rho=A+B T^n$ of the temperature-dependent resistivity used later for the analysis of the exponent $n$. Here $\Delta\rho=\rho(T)-\rho(8.5\;\text{K})$ and then offset vertically for visual clarity.
• Figure 3: (Color online) (Top panels) The dose dependence of the charge density temperatures, $T_{\text{CDW}}\left(x\right)$, in $(\text{Ca}_x\text{Sr}_{1-x})_3\text{Rh}_4\text{Sn}_{13}$ with point-like disorder introduced by electron irradiation. Yellow stars correspond to the onset of deviation from high-temperature $T-$linear behavior in panel (b) of Fig. \ref{['fig:rho(T)diffDose']}, indicating the onset of CDW correlations or short-range order. Green stars correspond to a maximum in the difference plot of Fig. \ref{['fig:rho(T)diffDose']}, signaling onset of long-range CDW ordering. Bottom panels show evolution of the exponent of the power law fit, as exemplified in the right panel of Fig. \ref{['fig:rho(T)diffDose']}.
• Figure 4: (Color online) Derivatives of the resistivity as a function of temperature, for each composition and dose of irradiation indicated in the legends. Vertical line in the right panel shows the onset of CDW transition temperature found in Hall effect measurements Fig. \ref{['fig:Hall']} below in pristine sample with $x=0.8$.
• Figure 5: (Color online) (a) evolution of the residual resistivity with irradiation dose in compositions as indicated. Note that the slope decreases drastically above $T_{CDW}$, because competing effect of CDW is removed and only disorder scattering remains. (b) evolution of the superconducting $T_c$, presented using a normalized scale, $\Delta T_c/T_c$, for each composition indicated on the legends.