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Abstract

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 material’}s 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 material{’}s 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. 133INTRODUCTIONA 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.RATIONALESuperconductivity 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.RESULTSOur 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.CONCLUSIONOur 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.