Clifford W. Hicks

Strong Increase of Tc of Sr2RuO4 Under Both Tensile and Compressive Strain

Strained Superconductor Distorting a material and observing its response can allow insight into its electronic properties. Thin films can be strained by placing them on a substrate with a different lattice constant; bulk samples present more of a challenge. Hicks et al. (p. 283) designed an apparatus to apply both tensile and compressive strain and used it to study the properties of the superconductor Sr2RuO4, which has long been hypothesized to host the unusual p-wave superconductivity. The response of the superconducting transition temperature Tc to the applied strain depended on the direction in which the strain was applied, and did not exhibit a cusp predicted to occur around zero strain. As the technique leaves a surface of the probe open to external probes, it could be adopted for a wide range of methods. An apparatus that can apply both tensile and compressive strain is used to study an unconventional superconductor. A sensitive probe of unconventional order is its response to a symmetry-breaking field. To probe the proposed px ± ipy topological superconducting state of Sr2RuO4, we have constructed an apparatus capable of applying both compressive and tensile strains of up to 0.23%. Strains applied along 〈 100 〉 crystallographic directions yield a strong, strain-symmetric increase in the superconducting transition temperature Tc. 〈 110 〉 strains give a much weaker, mostly antisymmetric response. As well as advancing the understanding of the superconductivity of Sr2RuO4, our technique has potential applicability to a wide range of problems in solid-state physics.

Evidence for a Nodal Energy Gap in the Iron-Pnictide Superconductor LaFePO from Penetration Depth Measurements by Scanning SQUID Susceptometry

Clifford W. Hicks, Thomas M. Lippman, Martin E. Huber, James G. Analytis, Jiun-Haw Chu, Ann S. Erickson, Ian R. Fisher, and Kathryn A. Moler Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California, 94305, USA and Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park CA 94025 Departments of Physics and Electrical Engineering, University of Colorado Denver, Denver, Colorado, 80217, USA (Dated: 2 April 2009)

Local Measurement of the Superfluid Density in the Pnictide Superconductor Ba ( Fe 1 − x Co x ) 2 As 2 across the Superconducting Dome

We measure the penetration depth λab(T) in Ba(Fe(1-x)Co(x))(2)As(2) using local techniques that do not average over the sample. The superfluid density ρs(T) ≡ 1/λab(T)2 has three main features. First, ρs (T = 0) falls sharply on the underdoped side of the dome. Second, λab(T) is flat at low T at optimal doping, indicating fully gapped superconductivity, but varies more strongly in underdoped and overdoped samples, consistent with either a power law or a small second gap. Third, ρs (T) varies steeply near Tc for optimal and underdoping. These observations are consistent with an interplay between magnetic and superconducting phases.

Limits on superconductivity-related magnetization in Sr2RuO4 and PrOs4Sb12 from scanning SQUID microscopy

We present scanning superconducting quantum interference device microscopy data on the superconductors Sr2RuO4 Tc=1.5 K and PrOs4Sb12 Tc=1.8 K. In both of these materials, superconductivity-related timereversal symmetry-breaking fields have been observed by muon spin rotation; our aim was to visualize the structure of these fields. However, in neither Sr2RuO4 nor PrOs4Sb12 do we observe spontaneous superconductivity-related magnetization. In Sr2RuO4, many experimental results have been interpreted on the basis of a pxipy superconducting order parameter. This order parameter is expected to give spontaneous magnetic induction at sample edges and order parameter domain walls. Supposing large domains, our data restrict domain wall and edge fields to no more than 0.1% and 0.2% of the expected magnitude, respectively. Alternatively, if the magnetization is of the expected order, the typical domain size is limited to 30 nm for random domains or 500 nm for periodic domains.

Piezoelectric-based apparatus for strain tuning

We report the design and construction of piezoelectric-based apparatus for applying continuously tuneable compressive and tensile strains to test samples. It can be used across a wide temperature range, including cryogenic temperatures. The achievable strain is large, so far up to 0.23% at cryogenic temperatures. The apparatus is compact and compatible with a wide variety of experimental probes. In addition, we present a method for mounting high-aspect-ratio samples in order to achieve high strain homogeneity.

Strong peak in Tc of Sr2RuO4 under uniaxial pressure

Squeezing out the oddness The material Sr2RuO4 has long been thought to exhibit an exotic, odd-parity kind of superconductivity, not unlike the superfluidity in 3He. How would perturbing this materials electronic structure affect its superconductivity? Steppke et al. put the material under large uniaxial pressure and found that the critical temperature more than doubled and then fell as a function of strain (see the Perspective by Shen). The maximum critical temperature roughly coincided with the point at which the materials Fermi surface underwent a topological change. One intriguing possibility is that squeezing changed the parity of the superconducting gap from odd to even. Science, this issue p. 10.1126/science.aaf9398; see also p. 133 Perturbing the electronic structure of Sr2RuO4 has profound effects on its superconductivity. INTRODUCTION A central challenge of modern condensed matter physics is to understand the range of possible collective states formed by assemblies of strongly interacting electrons. Most real materials contain high levels of disorder, which can disrupt possible ordered states and so substantially hinder the path to understanding. There is a premium, therefore, on working with extremely clean materials and identifying clean ways to tune their physical properties. Here, we show that uniaxial pressure can induce profound changes in the superconductivity of one of the model materials in the field, Sr2RuO4, and demonstrate using explicit calculations how our findings provide strong constraints on theory. RATIONALE Superconductivity remains arguably the most intriguing collective electron state. All superconductors form from the condensation of pairs of electrons into a single ground state, but in “unconventional” superconductors, a rich variety of qualitatively different ground states is possible. One of the most celebrated examples, and the one with the lowest known levels of disorder, is Sr2RuO4. Previous experimental results suggest that its superconducting condensate has odd parity, that is, its phase is reversed upon inversion of spatial coordinates. A relatively unexplored route to test this possibility is to perturb the assembly of conduction electrons through lattice distortion, which introduces no additional disorder. Electronic structure calculations suggest that if sufficient uniaxial pressure could be applied to compress the lattice along the pressure axis by about 0.8%, the largest Fermi surface of Sr2RuO4 would undergo a topological transition. One of the consequences of tuning to this transition would be to substantially lower the velocity of some of charge carriers, and because slow carriers are generally favorable for superconductivity, the superconductivity might be profoundly affected. Although this topological transition has been achieved with other experimental techniques, too much disorder was introduced for the superconductivity to survive. RESULTS Our central experimental result is summarized in the figure. We prepare the sample as a beam and use piezoelectric stacks to compress it along its length. Compressing the a axis of the Sr2RuO4 lattice drives the superconducting transition temperature (Tc) through a pronounced maximum, at a compression of ≈0.6%, that is a factor of 2.3 higher than Tc of the unstrained material. At the maximum Tc, the superconducting transition is very sharp, allowing precise determination of the superconducting upper critical magnetic fields for fields along both the a and c directions. The c-axis upper critical field is found to be enhanced by more than a factor of 20. We perform calculations using a weak-coupling theory to compare the Tc’s and upper critical fields of possible superconducting order parameters. The combination of our experimental and theoretical work suggests that the maximum Tc is likely associated with the predicted Fermi surface topological transition and that at this maximum Tc, Sr2RuO4 might have an even-parity rather than an odd-parity superconducting order parameter. The anisotropic distortion is key to these results: Hydrostatic pressure is known experimentally to decrease Tc of Sr2RuO4. CONCLUSION Our data raise the possibility of an odd-parity to even-parity transition of the superconducting state of Sr2RuO4 as a function of lattice strain and fuel an ongoing debate about the symmetry of the superconducting state even in the unstrained material. We anticipate considerable theoretical activity to address these issues, and believe that the technique developed for these experiments will also have a broader significance to future study of quantum magnets, topological systems, and electronic liquid crystals as well as superconductors. The rise and fall of Tc of Sr2RuO4. (Top left) A photograph of the uniaxial pressure apparatus. Pressure is applied to the sample by piezoelectric actuators. (Top middle) A sample, prepared as a beam and mounted in the apparatus. The susceptometer is a pair of concentric coils. (Top right) A schematic of a mounted sample. The piezoelectric actuators compress or tension the sample along its length. (Bottom) Tc of three samples of Sr2RuO4 against strain along their lengths. Negative values of εxx denote compression. Tc is taken as the midpoint of the transition, observed by ac susceptibility. Sample #1 was cracked, and so could be compressed but not tensioned. Sr2RuO4 is an unconventional superconductor that has attracted widespread study because of its high purity and the possibility that its superconducting order parameter has odd parity. We study the dependence of its superconductivity on anisotropic strain. Applying uniaxial pressures of up to ~1 gigapascals along a 〈100〉 direction (a axis) of the crystal lattice results in the transition temperature (Tc) increasing from 1.5 kelvin in the unstrained material to 3.4 kelvin at compression by ≈0.6%, and then falling steeply. Calculations give evidence that the observed maximum Tc occurs at or near a Lifshitz transition when the Fermi level passes through a Van Hove singularity, and open the possibility that the highly strained, Tc = 3.4 K Sr2RuO4 has an even-parity, rather than an odd-parity, order parameter.

Quantum Oscillations and High Carrier Mobility in the Delafossite PdCoO2

We present de Haas-van Alphen and resistivity data on single crystals of the delafossite PdCoO(2). At 295 K we measure an in-plane resistivity of 2.6  μΩ cm, making PdCoO(2) the most conductive oxide known. The low-temperature in-plane resistivity has an activated rather than the usual T(5) temperature dependence, suggesting a gapping of effective scattering that is consistent with phonon drag. Below 10 K, the transport mean free path is ∼20  μm, approximately 10(5) lattice spacings and an astoundingly high value for flux-grown crystals. We discuss the origin of these properties in light of our data.

Limits on the Superconducting Order Parameter in NdFeAsO1-xFy from Scanning SQUID Microscopy

Identifying the symmetry of the superconducting order parameter in the recently-discovered ferrooxypnictide family of superconductors, RFeAsO{sub 1-x}F{sub y}, where R is a rare earth, is a high priority. Many of the proposed order parameters have internal {pi} phase shifts, like the d-wave order found in the cuprates, which would result in direction-dependent phase shifts in tunneling. In dense polycrystalline samples, these phase shifts in turn would result in spontaneous orbital currents and magnetization in the superconducting state. We perform scanning SQUID microscopy on a dense polycrystalline sample of NdFeAsO{sub 0.94}F{sub 0.06} with T{sub c} = 48K and find no such spontaneous currents, ruling out many of the proposed order parameters.

Mott insulator phases and first-order melting in Bi 2 Sr 2 Ca Cu 2 O 8 + δ crystals with periodic surface holes

We measured the effects of periodic surface holes, created using a focused ion beam, on the phase diagram of the vortex matter in high-

Ca3Ru2O7: Density Wave Formation and Quantum Oscillations in the Hall Resistivity

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