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

Technical Deep Dive: Reaching Quantum Critical Point by Adding Non-magnetic Disorder in Single Crystals of Superconductor $(\text{Ca}x\text{Sr}{1-x})3\text{Rh}4\text{Sn}_{13}$

Overview

This work explores the effects of controlled non-magnetic disorder on the interplay between charge-density wave (CDW) order and superconductivity in the material $(\text{Ca}x\text{Sr}{1-x})3\text{Rh}4\text{Sn}_{13}$. The researchers demonstrate that by introducing disorder through 2.5 MeV electron irradiation, they are able to suppress the CDW order and tune the system to a quantum critical point (QCP), as evidenced by the emergence of non-Fermi liquid behavior in the temperature-dependent resistivity.

Methodology

• Single crystals of $(\text{Ca}x\text{Sr}{1-x})3\text{Rh}4\text{Sn}_{13}$ were grown from tin flux.
• Electrical resistivity was measured in a standard four-probe configuration on bar-shaped single crystals.
• Controlled non-magnetic disorder was introduced via 2.5 MeV electron irradiation at low temperatures.
• The acquired irradiation dose is measured in C/cm^2, where 1 C/cm^2 = 6.24×10^18 e^-/cm^2.

Results

1. In pristine samples, the temperature-dependent resistivity, $\rho(T)$, shows an evolution from Fermi liquid to non-Fermi liquid behavior as the composition $x$ is tuned towards the suggested quantum critical point at $x_c=0.9$.
2. For the $x=0.75$ composition, which is below the suggested QCP, successive electron irradiation leads to:
   • A progressive increase in the linear term and reduction in the quadratic term in $\rho(T)$, eventually reaching almost perfect $T$-linear dependence.
   • Suppression of the charge-density wave (CDW) order, as determined from the temperature dependence of the resistivity.
3. The analysis suggests the QCP is located in the interval between $x=0.75$ and $x=0.85$.
4. The superconducting $Tc$ shows a non-monotonic behavior with disorder, initially increasing in the stoichiometric Sr$3$Rh$4$Sn${13}$ but decreasing in the alloyed compositions.

Interpretation

• The controlled introduction of non-magnetic disorder via electron irradiation effectively suppresses the CDW order, enabling the system to be tuned through a quantum critical point.
• The emergence of nearly perfect $T$-linear resistivity at the critical dose indicates the system has reached the quantum critical regime.
• Moving beyond the QCP, the system exhibits a Fermi liquid-like $T^2$ behavior, suggesting the disorder has driven the system past the critical point.
• The non-monotonic behavior of $T_c$ with disorder is consistent with the interplay between CDW and superconductivity, where suppressing the CDW order can initially enhance superconductivity near the QCP.

Limitations & Uncertainties

• The exact location of the QCP is not definitively determined, with the analysis placing it in the interval between $x=0.75$ and $x=0.85$.
• The effect of disorder on the superconducting properties is complicated by the initial disorder present in the alloyed compositions, making it difficult to directly compare the rate of change of $T_c$ across different compositions.

What Comes Next

• The ability to tune a CDW/superconductivity system to a quantum critical point using controlled non-magnetic disorder opens new avenues for exploring quantum criticality and its connection to unconventional superconductivity.
• Future studies could investigate the emergence of Griffiths singularities, the interplay of tricritical and quantum critical points, and the role of quantum fluctuations in enhancing superconducting pairing in these types of correlated electron systems.