Description
$Sr_2RuO_4$ is one of the very few candidates for $p+ip$
superconductivity. Besides the fundamental importance of
firmly establishing the existence of a spin-triplet-paired
superconductor, the interest in $Sr_2RuO_4$ also emanates
from the possibility of half-quantum vortices that host
Majorana bound states.In this talk, I will review the progress
recently made in the understanding of this material. Using a
spin-orbit-coupled weak-coupling calculation, I will analyze
the results of several recent experiments: the absence of
measurable edge currents observed by magnetometry, the
absence of cusp of $T_c$ versus uniaxial strain, and the
nodal behavior observed for example in the specific heat. I
will show that, in each case, the results do not invalidate the
presence of a $p+ip$ state. I will also discuss the evolution of
the superconducting state at a Van Hove singularity, which
was recently reached experimentally by applying uniaxial
strain.
