The Superconductivity of Sr2RuO4 Under c-Axis Uniaxial Stress

We compress the unconventional superconductor Sr$_2$RuO$_4$ along its $c$ axis, achieving a maximum stress of 3.2~GPa, a record uniaxial stress for single-crystal Sr$_2$RuO$_4$. The energy of the Ru $4d$ $xz$ and $yz$ bands is raised relative to the $xy$ band, which causes the largest Fermi surface sheet to expand. We present evidence that 3.2~GPa is about halfway to an electron-to-hole Fermi surface topological transition of this sheet. In line with qualitative expectations for increasing density of states, the upper critical field increases. However, $T_\text{c}$ decreases. We present calculations of $T_\text{c}$ in the limit of weak interactions that indicate that decreasing $T_\text{c}$ could be obtained for order parameters that have nodes along the $\Gamma$-$X$ and $\Gamma$-$Y$ lines, but this conclusion is opposite to that reached from measurements under in-plane uniaxial stress. The data here therefore provide an important new constraint on theories of the superconductivity of Sr$_2$RuO$_4$, and the demonstration of a method to weaken the pairing interaction in Sr$_2$RuO$_4$ may provide a clue as to what the pairing interaction is.