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Register a new userIdentifying possible pairing states in Sr$_2$RuO$_4$ by tunneling spectroscopy
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We examine the tunneling spectroscopy of three-dimensional normal-metal/Sr$_2$RuO$_4$ junctions as an experimental means to identify pairing symmetry in Sr$_2$RuO$_4$. In particular, we consider three different possible pairing states in Sr$_2$RuO$_4$: spin-singlet chiral $d$-wave, spin-triplet helical $p$-wave, and spin-nematic $f$-wave ones, all of which are consistent with recent nuclear-magnetic-resonance experiments [A. Pustogow et al., Nature 574, 72 (2019)]. The Blonder-Tinkham-Klapwijk theory is employed to calculate the tunneling conductance, and the cylindrical two-dimensional Fermi surface of Sr$_2$RuO$_4$ is properly taken into account as an anisotropic effective mass and a cutoff in the momentum integration. It is pointed out that the chiral $d$-wave pairing state is inconsistent with previous tunneling conductance experiments along the $c$-axis. We also find that the remaining candidates, the spin-triplet helical $p$-wave pairing state and the spin-nematic $f$-wave ones, can be distinguished from each other by the in-plane tunneling spectroscopy along the $a$- and $b$-axes.
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After more than 25 years of research, three even-parity superconducting states -- the $d+id$-wave, $d+ig$-wave, and $s+id$-wave states -- have emerged as leading candidates for the superconducting states of Sr$_2$RuO$_4$. In the present work, we propose a tunneling spectroscopy experiment for distinguishing among these three superconducting states. The key component of our proposal is that we examine the conductance spectra of normal-metal/Sr$_2$RuO$_4$ junctions with various angles between the junction interface and the crystal axis of the Sr$_2$RuO$_4$. The angle dependence of the conductance spectra shows a unique pattern in each superconducting state, which can function as a fingerprint for verifying the pairing symmetry of Sr$_2$RuO$_4$.
It is widely believed that the perovskite Sr$_2$RuO$_4$ is an unconventional superconductor with broken time reversal symmetry. It has been predicted that superconductors with broken time reversal symmetry should have spontaneously generated supercurrents at edges and domain walls. We have done careful imaging of the magnetic fields above Sr$_2$RuO$_4$ single crystals using scanning Hall bar and SQUID microscopies, and see no evidence for such spontaneously generated supercurrents. We use the results from our magnetic imaging to place upper limits on the spontaneously generated supercurrents at edges and domain walls as a function of domain size. For a single domain, this upper limit is below the predicted signal by two orders of magnitude. We speculate on the causes and implications of the lack of large spontaneous supercurrents in this very interesting superconducting system.
Motivated by the success of experimental manipulation of the band structure through biaxial strain in Sr$_2$RuO$_4$ thin film grown on a mismatched substrate, we investigate theoretically the effects of biaxial strain on the electronic instabilities, such as superconductivity (SC) and spin density wave (SDW), by functional renormalization group. According to the experiment, the positive strain (from lattice expansion) causes charge transfer to the $gamma$-band and consequently Lifshitz reconstruction of the Fermi surface. Our theoretical calculations show that within a limited range of positive strain a p-wave superconducting order is realized. However, as the strain is increased further the system develops into the SDW state well before the Lifshitz transition is reached. We also consider the effect of negative strains (from lattice constriction). As the strain increases, there is a transition from p-wave SC state to nodal s-wave SC state. The theoretical results are discussed in comparison to experiment and can be checked by further experiments.
Unambiguous identification of the superconducting order parameter symmetry of Sr$_2$RuO$_4$ has remained elusive for more than a quarter century. While a chiral $p$-wave ground state analogue to superfluid $^3$He-$A$ was ruled out only very recently, other proposed $p$-wave scenarios are still viable. Here, field-dependent $^{17}$O Knight shift measurements are compared to corresponding specific heat measurements, previously reported. We conclude that the shift results can be accounted for by the expected field-induced quasiparticle response only. An upper bound for the condensate magnetic response of $<10%$ of the normal state susceptibility is sufficient to exclude odd-parity candidates.
Recent experiments suggest that the superconducting order parameter of Sr$_2$RuO$_4$ has two components. A two-component order parameter has multiple degrees of freedom in the superconducting state that can result in low-energy collective modes or the formation of domain walls -- a possibility that would explain a number of experimental observations including the smallness of the time reversal symmetry breaking signal at T$_mathrm{c}$ and telegraph noise in critical current experiments. We perform ultrasound attenuation measurements across the superconducting transition of Sr$_2$RuO$_4$ using resonant ultrasound spectroscopy (RUS). We find that the attenuation for compressional sound increases by a factor of seven immediately below T$_mathrm{c}$, in sharp contrast with what is found in both conventional ($s$-wave) and high-T$_mathrm{c}$ ($d$-wave) superconductors. We find our observations to be most consistent with the presence of domain walls between different configurations of the superconducting state. The fact that we observe an increase in sound attenuation for compressional strains, and not for shear strains, suggests an inhomogeneous superconducting state formed of two distinct, accidentally-degenerate superconducting order parameters that are not related to each other by symmetry. Whatever the mechanism, a factor of seven increase in sound attenuation is a singular characteristic with which any potential theory of the superconductivity in Sr$_2$RuO$_4$ must be reconciled.
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