Vestigial Van Hove Singularity and Higher-Temperature Superconducting Phase Induced by Perpendicular Uniaxial Pressures in Quasi-Two-Dimensional Superconductors

We examine quasi-two-dimensional superconductors near half-filling under uniaxial pressures perpendicular to conductive layers (hereafter called perpendicular pressures). It is a natural conjecture that the perpendicular pressure decreases the transition temperature T-c because it increases the interlayer electron hopping energy t(z), which weakens the logarithmic enhancement in the density of states due to the two-dimensional Van Hove singularity. It is shown that, contrary to this conjecture, the perpendicular pressure can significantly enhance T-c in systems off half-filling before it decreases T-c, and the strength of the enhancement significantly depends on the pairing symmetry. When the indices d, d', cz, and sz are defined for the basis functions gamma(d) proportional to cos k(x) - cos k(y), gamma(d)' proportional to sin k(x) sin k(y), gamma(cz) proportional to cos k(z), and gamma(sz) proportional to sin k(z), respectively, it is shown that for s-, d-, cz-, and cz-d-wave pairing, T-c steeply increases with increasing t(z) near a cusp at a certain value of t(z). On the other hand, for p-, cz-p-, sz-p-, and d'-wave pairing, T-c is almost unaffected by t(z). For sz- and sz-d-wave pairing, T-c exhibits a broad and weak peak. Here, for example, the cz-d-wave state is an interlayer spin-singlet d-wave state with an order parameter proportional to gamma(cz)gamma(d). The enhancement in T-c is the largest for this state and the second largest for the d-wave pairing and interlayer spin-singlet (cz-wave) pairing. These results may explain recent observations in Sr2RuO4 under perpendicular pressures. A comparison between the theoretical and experimental results indicates that the p-, cz-p-, and sz-p-wave states, including chiral states, and the d'-wave state are the most likely candidates for the intrinsic 1.5-K phase, and the d-, cz-d-, and cz-wave states are the most likely candidates for the 3-K phase induced by the perpendicular pressure. The cz-p- and sz-p-wave states are interlayer spin-triplet and interlayer spin-singlet p-wave states with horizontal line nodes, respectively.