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Register a new userTheory of the Evolution of Superconductivity in Sr$_2$RuO$_4$ under Anisotropic Strain
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Sr$_2$RuO$_4$ is a leading candidate for chiral $p$-wave superconductivity. The detailed mechanism of superconductivity in this material is still the subject of intense investigations. Since superconductivity is sensitive to the topology of the Fermi surface (the contour of zero-energy quasi-particle excitations in the momentum space in the normal state), changing this topology can provide a strong test of theory. Recent experiments tuned the Fermi surface topology efficiently by applying planar anisotropic strain. Using functional renormalization group theory, we study the superconductivity and competing orders in Sr$_2$RuO$_4$ under strain. We find a rapid initial increase in the superconducting transition temperature $T_c$, which can be associated with the evolution of the Fermi surface toward a Lifshitz reconstruction under increasing strain. Before the Lifshitz reconstruction is reached, however, the system switches from the superconducting state to a spin density wave state. The theory agrees well with recent strain experiments showing an enhancement of $T_c$ followed by an intriguing sudden drop.
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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.
In conventional and high transition temperature copper oxide and iron pnictide superconductors, the Cooper pairs all have even parity. As a rare exception, Sr$_2$RuO$_4$ is the first prime candidate for topological chiral p-wave superconductivity, which has time-reversal breaking odd-parity Cooper pairs known to exist before only in the neutral superfluid $^3$He. However, there are several key unresolved issues hampering the microscopic description of the unconventional superconductivity. Spin fluctuations at both large and small wavevectors are present in experiments, but how they arise and drive superconductivity is not yet clear. Spontaneous edge current is expected but not observed conclusively. Specific experiments point to highly band- and/or momentum-dependent energy gaps for quasiparticle excitations in the superconducting state. Here, by comprehensive functional renormalization group calculations with all relevant bands, we disentangle the various competing possibilities. In particular we show the small wavevector spin fluctuations, driven by a single two-dimensional band, trigger p-wave superconductivity with quasi-nodal energy gaps.
Strontium ruthenate (Sr$_2$RuO$_4$) is a multiband superconductor that displays evidence of topological superconductivity, although a model of the order parameter that is consistent with all experiments remains elusive. We integrated a piezoelectric-based strain apparatus with a scanning superconducting quantum interference device (SQUID) microscope to map the diamagnetic response of single-crystal Sr$_2$RuO$_4$ as a function of temperature, uniaxial pressure, and position with micron-scale spatial resolution. We thereby obtained local measurements of the superconducting transition temperature $T_c$ vs. anisotropic strain $epsilon$ with sufficient sensitivity for comparison to theoretical models that assume a uniform $p_xpm ip_y$ order parameter. We found that $T_c$ varies with position and that the locally measured $T_c$ vs. $epsilon$ curves are quadratic ($T_cproptoepsilon^2$), as allowed by the C$_4$ symmetry of the crystal lattice. We did not observe the low-strain linear cusp ($T_cpropto left| epsilon right|$) that would be expected for a two-component order parameter such as $p_xpm ip_y$. These results provide new input for models of the order parameter of Sr$_2$RuO$_4$.
We analyze the spin anisotropy of the magnetic susceptibility of Sr$_2$RuO$4$ in presence of spin-orbit coupling and anisotropic strain using quasi-two-dimensional tight-binding parametrization fitted to the ARPES results. Similar to the previous observations we find the in-plane polarization of the low ${bf q}$ magnetic fluctuations and the out-of-plane polarization of the incommensurate magnetic fluctuation at the nesting wave vector ${bf Q}_1 = (2/3 pi ,2/3 pi)$ but also nearly isotropic fluctuations near ${bf Q}_2=(pi/6,pi/6)$. Furthermore, one finds that apart from the high-symmetry direction of the tetragonal Brillouin zone the magnetic anisotropy is maximal, i.e. $chi^{xx} eq chi^{yy} eq chi^{zz}$. This is the consequence of the orbital anisotropy of the $xz$ and $yz$ orbitals in the momentum space. We also study how the magnetic anisotropy evolves in the presence of the strain and find strong Ising-like ferromagnetic fluctuations near the Lifshitz transition for the $xy$-band.
We use functional renormalization group method to study a three-orbital model for superconducting Sr$_2$RuO$_4$. Although the pairing symmetry is found to be chiral $p$-wave, the atomic spin-orbit coupling induces near-nodes for quasiparticle excitations. Our theory explains a major experimental puzzle between $d$-wave-like feature observed in thermal experiments and the chiral $p$-wave triplet pairing revealed in nuclear-magnetic-resonance and Kerr effect.
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