Optical Conductivity in Half and Quarter Metal Superconductors

Half and quarter metals are metallic states characterized by spontaneous valley and/or spin polarization, as recently observed in several two-dimensional materials, including rhombohedral graphene and monolayer transition-metal dichalcogenides. When superconductivity develops on top of such polarized metallic states, theory predicts the formation of intrinsic pair-density-wave (PDW) order—finite-momentum pairing that arises without magnetic fields or preexisting charge or spin modulations. However, direct experimental evidence identifying PDW superconductivity in these systems remains lacking.

In this talk, I will show that optical conductivity provides a powerful probe of this elusive phase. In particular, the emergence of a finite-frequency conductivity peak across the superconducting gap serves as a distinct signature of the spontaneously broken translational and valley symmetries in PDW states. I will further discuss how this feature connects to the quantum geometric properties of the underlying electronic bands. Our prediction offers a new route to detect and characterize PDW superconductivity in spin- and valley-polarized 2D materials.