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Register a new userAmbient Pressure Structural Quantum Critical Point in the Phase Diagram of (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$
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The quasi-skutterudite superconductor Sr$_3$Rh$_4$Sn$_{13}$ features a pronounced anomaly in electrical resistivity at $T^*sim$138 K. We show that the anomaly is caused by a second-order structural transition, which can be tuned to 0 K by applying physical pressure and chemical pressure via the substitution of Ca for Sr. A broad superconducting dome is centred around the structural quantum critical point. Detailed analysis of the tuning parameter dependence of $T^*$ as well as insights from lattice dynamics calculations strongly support the existence of a structural quantum critical point at ambient pressure when the fraction of Ca is 0.9 (i.e., $x_c=0.9$). This establishes (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ series as an important system for exploring the physics of structural quantum criticality without the need of applying high pressures.
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We perform optical spectroscopy measurement across the charge density wave (CDW) phase transitions on single-crystal samples of Sr$_{3}$Rh$_{4}$Sn$_{13}$ and (Sr$_{0.5}$Ca$_{0.5}$)$_{3}$Rh$_{4}$Sn$_{13}$. Formation of CDW energy gap was clearly observed for both single-crystal samples when they undergo the phase transitions. The existence of a Drude component in $sigma_1(omega)$ below TCDW indicates that the Fermi surface is only partially gapped in the CDW state. The obtained value of 2$Delta$/K$_{B}$T$_{CDW}$ is roughly 13 for both Sr$_{3}$Rh$_{4}$Sn$_{13}$ and (Sr$_{0.5}$Ca$_{0.5}$)$_{3}$Rh$_{4}$Sn$_{13}$ compounds. The value is considerably larger than the mean-field value based on the weak-coupling BCS theory. The observed spectral feature in (Sr$_{x}$Ca$_{1-x}$)$_{3}$Rh$_{4}$Sn$_{13}$ resembles those seen in many other CDW systems.
The nature of the lattice instability connected to the structural transition and superconductivity of (Sr,Ca)$_3$Ir$_4$Sn$_{13}$ is not yet fully understood. In this work density functional theory (DFT) calculations of the phonon instabilities as a function of chemical and hydrostatic pressure show that the primary lattice instabilities in Sr$_3$Ir$_4$Sn$_{13}$ lie at phonon modes of wavevectors $mathbf{q}=(0.5,0,0)$ and $mathbf{q}=(0.5,0.5,0)$. Following these modes by calculating the energy of supercells incorporating the mode distortion results in an energy advantage of -14.1 meV and -9.0 meV per formula unit respectively. However, the application of chemical pressure to form Ca$_3$Ir$_4$Sn$_{13}$ reduces the energetic advantage of these instabilities, which is completely removed by the application of a hydrostatic pressure of 35 kbar to Ca$_3$Ir$_4$Sn$_{13}$. The evolution of these lattice instabilities is consistent with experimental phase diagram. The structural distortion associated with the mode at $mathbf{q}=(0.5,0.5,0)$ produces a distorted cell with the same space group symmetry as the experimentally refined low temperature structure. Furthermore, calculation of the deformation potential due to these modes quantitatively demonstrates a strong electron-phonon coupling. Therefore, these modes are likely to be implicated in the structural transition and superconductivity of this system.
We report the evolution of nematic fluctuations in FeSe$_{1-x}$S$_x$ single crystals as a function of Sulfur content $x$ across the nematic quantum critical point (QCP) $x_csim$ 0.17 via Raman scattering. The Raman spectra in the $B_{1g}$ nematic channel consist of two components, but only the low energy one displays clear fingerprints of critical behavior and is attributed to itinerant carriers. Curie-Weiss analysis of the associated nematic susceptibility indicates a substantial effect of nemato-elastic coupling which shifts the location of the nematic QCP. We argue that this lattice-induced shift likely explains the absence of any enhancement of the superconducting transition temperature at the QCP. The presence of two components in the nematic fluctuations spectrum is attributed to the dual aspect of electronic degrees of freedom in Hunds metals, with both itinerant carriers and local moments contributing to the nematic susceptibility.
The comprehensive research of the electronic structure, thermodynamic and electrical transport properties reveals the existence of inhomogeneous superconductivity due to structural disorder in Ca$_3$Rh$_4$Sn$_{13}$ doped with La (Ca$_{3-x}$La$_x$Rh$_4$Sn$_{13}$) or Ce (Ca$_{3-x}$Ce$_x$Rh$_4$Sn$_{13}$) with superconducting critical temperatures $T_c^{star}$ higher than those ($T_c$) observed in the parent compounds. The $T-x$ diagrams and the entropy $S(x)_T$ isotherms well document the relation between degree of an atomic disorder and separation of the {it high-temperature} $T_c^{star}$ and $T_c$-bulk phases. In these dirty superconductors with the mean free path much smaller than the coherence length, the Werthamer-Helfand-Hohenber theoretical model does not well fits the $H_{c2}(T)$ data. We suggest that this can result from two-band superconductivity or from the presence of strong inhomogeneity in these systems. The multiband model very well describes the $H-T$ dependencies, but the present results as well as our previous studies give arguments for the scenario based on the presence of nanoscopic inhomogeneity of the superconducting state. We also revisited the nature of structural phase transition at $T^{star}sim 130-170$ K and documented that there might be another precursor transition at higher temperatures. The impact of the magnetic Ce-Ce correlations on the increase of $T_c$ in respect to the critical temperatures of Ca$_{3-x}$La$_x$Rh$_4$Sn$_{13}$ is also discussed.
The specific heat $C$ of the cuprate superconductors La$_{2-x}$Sr$_x$CuO$_4$ and Bi$_{2+y}$Sr$_{2-x-y}$La$_x$CuO$_{6+delta}$ was measured at low temperature (down to $0.5~{rm K}$), for dopings $p$ close to $p^star$, the critical doping for the onset of the pseudogap phase. A magnetic field up to $35~{rm T}$ was applied to suppress superconductivity, giving direct access to the normal state at low temperature, and enabling a determination of $C_e$, the electronic contribution to the normal-state specific heat, at $T to 0$. In La$_{2-x}$Sr$_x$CuO$_4$ at $x=p = 0.22$, $0.24$ and $0.25$, $C_e / T = 15-16~{rm mJmol}^{-1}{rm K}^{-2}$ at $T = 2~{rm K}$, values that are twice as large as those measured at higher doping ($p > 0.3$) and lower doping ($p < 0.15$). This confirms the presence of a broad peak in the doping dependence of $C_e$ at $p^starsimeq 0.19$, as previously reported for samples in which superconductivity was destroyed by Zn impurities. Moreover, at those three dopings, we find a logarithmic growth as $T to 0$, such that $C_e / T sim {rm B}ln(T_0/T)$. The peak vs $p$ and the logarithmic dependence vs $T$ are the two typical thermodynamic signatures of quantum criticality. In the very different cuprate Bi$_{2+y}$Sr$_{2-x-y}$La$_x$CuO$_{6+delta}$, we again find that $C_e / T sim {rm B}ln(T_0/T$) at $p simeq p^star$, strong evidence that this $ln(1/T)$ dependence - first discovered in the cuprates La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ - is a universal property of the pseudogap critical point. All four materials display similar values of the $rm B$ coefficient, indicating that they all belong to the same universality class.
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