Note this absrtact is for an invited talk, but I submitted this late - I apologize for this

In locally non-centrosymmetric materials, inversion symmetry relates pairs of atoms. In principle, superconducting Cooper pairs can develop a non-trivial structure associated with these two atomic degrees of freedom. Here we argue that experiments reveal such non-trivial Cooper pairs are realized in CeRh₂As₂ and UTe₂. Specifically, we show that the interplay of locally non-centrosymmetricity and observed van Hove singularities naturally lead to nearly degenerate even-parity and odd-parity superconducting states in CeRh₂As₂ [1] and that an observed pressure induced, strongly fluctuating, superconducting state [2] and a related ambient pressure field-reentrant superconducting state in UTe₂ can be understood from a pair atom-singlet/spin-triplet pairing state.

[1] Changhee Lee, Daniel F. Agterberg, and P. M. R. Brydon, Phys. Rev. Lett. 135,026003 (2025).

[2] Sahas Kamat, Jared Dans, Shanta Saha, Daniel F. Agterberg, Johnpierre Paglione, B. J. Ramshaw, arXiv:2601.09138 (2026).