Competing s-wave and d-wave order in A15 superconductors

Competing pairing channels have been proposed in superfluid $^3$He, in the high temperature cuprate superconductors, and pnictide superconductors. While strong experimental support exists for this in superfluid $^3$He, the case for superconductors is weaker. Here, we show that $A15$ superconductors provide a compelling example for competing superconducting order. We present microscopic arguments that $A15$ superconductors have a competing d-wave order in addition to usual s-wave superconductivity and show that this d-wave order provides a unifying explanation for a series of diverse experimental results. These include: the emergence of a sharp mode in the superconducting state seen by Raman spectroscopy; the observed shrinking of the vortex core at anomalously low fields; and the large anisotropy measured in the upper critical field. We further show that multiple superconducting gaps can appear when these $A15$ superconductors are strained.