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Register a new userOptical spectroscopy study of charge density wave order in Sr$_{3}$Rh$_{4}$Sn$_{13}$ and (Sr$_{0.5}$Ca$_{0.5}$)$_{3}$Rh$_{4}$Sn$_{13}$
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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.
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Using the small angle neutron scattering (SANS) technique we investigated the vortex lattice (VL) in the mixed state of the stannide superconductor Yb$_{3}$Rh$_{4}$Sn$_{13}$. We find a single domain VL of slightly distorted hexagonal geometry for field strengths between 350 and 18500 G and temperatures between T = 0.05 and T = 6.5 K. We observe a clear in-plane rotation of the VL for different magnetic field directions relative to the crystallographic axes. We also find that the hexagonal symmetry of the VL is energetically favorable in Yb$_{3}$Rh$_{4}$Sn$_{13}$ for external fields oriented along axes of different symmetries: twofold [110], threefold [111] and fourfold [100]. The observed behavior is different from other conventional and unconventional superconductors. The superconducting state is characterized by an isotropic gapped order parameter with an amplitude of $Delta(0)$ = 1.57 $pm$ 0.05 meV. At the lowest temperatures the field dependence of the magnetic form factor in our material reveals a London penetration depth of $lambda_{L}$ = 2508 $pm$ 17 $AA$ and a Ginzburg coherence length of $xi$ = 100 $pm$ 1.3 $AA$, i.e., it is a strongly type-II superconductor, $kappa$ = $lambda_{L}/xi$ = 25.
The vortex lattice (VL) in the mixed state of the stannide superconductor Yb$_{3}$Rh$_{4}$Sn$_{13}$ has been studied using small-angle neutron scattering (SANS). The field dependencies of the normalized longitudinal and transverse correlation lengths of the VL, $xi_L/a_0$ and $xi_T /a_0$, reveal two distinct anomalies that are associated with vortex-glass phases below $mu_0H_l$~$approx$~700~G and above $mu_{0}H_h$~$sim$~1.7~T ($a_0$ is the intervortex distance). At high fields, around 1.7~T, the longitudinal correlation decreases abruptly with increasing fields indicating a weakening (but not a complete destruction) of the VL due to a phase transition into a glassy phase, below $mu_{0}H_{c_2}$(1.8 K)~$approx$~2.5~T. $xi_L/a_0$ and $xi_T /a_0$, gradually decrease for decreasing fields of strengths less than 1~T and tend towards zero. The shear elastic modulus $c_{66}$ and the tilting elastic modulus $c_{44}$ vanish at a critical field $mu_0H_l$~$approx$~700~G, providing evidence for a disorder-induced transition into a vortex-glass. A ring of scattered intensity is observed for fields lower than 700~G, $i.e.$, $mu_{0}H_{c_1}$~=~135~G~$<$~$mu_{0}H$~$<$~700~G. This low-field phenomenon is of different nature than the one observed at high fields, where $xi_L/a_0$ but not $xi_T/a_0$, decreases abruptly to an intermediate value.
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.
A structural transition in an ABO$_{3}$ perovskite thin film involving the change of the BO$_{6}$ octahedral rotation pattern can be hidden under the global lattice symmetry imposed by the substrate and often easily overlooked. We carried out high-resolution x-ray diffraction experiments to investigate the structures of epitaxial Ca$_{0.5}$Sr$_{0.5}$IrO$_{3}$ (CSIO) perovskite iridate films grown on the SrTiO$_{3}$ (STO) and GdScO$_{3}$ (GSO) substrates in detail. Although the CSIO/STO film layer displays a global tetragonal lattice symmetry evidenced by the reciprocal space mapping, synchrotron x-ray data indicates that its room temperature structure is monoclinic due to Glazers a$^{+}$a$^{-}$c$^{-}$-type rotation of the IrO$_{6}$ octahedra. In order to accommodate the lower-symmetry structure under the global tetragonal symmetry, the film breaks into four twinned domains, resulting in the splitting of the (half-integer, 0, integer) superlattice reflections. Surprisingly, the splitting of these superlattice reflections decrease with increasing temperature, eventually disappearing at T$_{S}$ = 510(5) K, which signals a structural transition to an orthorhombic phase with a$^{+}$a$^{-}$c$^{0}$ octahedral rotation. In contrast, the CSIO/GSO film displays a stable monoclinic symmetry with a$^{+}$b$^{-}$c$^{-}$ octahedral rotation, showing no structural instability caused by the substrate up to 520 K. Our study illustrates the importance of the symmetry in addition to the lattice mismatch of the substrate in determining the structure of epitaxial thin films.
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.
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