Vestigial d-wave charge-4e Superconductivity from Bidirectional Pair Density Waves

E. Huecker and Y. Wang, Vestigial d-wave charge-4e Superconductivity from Bidirectional Pair Density Waves, Phys. Rev. B, 113, 045121 (2026).

• We analyze the leading vestigial instability due to the melting of a bidirectional pair-density-wave state in two dimensions.
• In a previous work by one of the authors, it was found that the interplay between pair-density-wave fluctuations with ordering momenta along the 𝑥 and 𝑦 directions can provide a strong attractive interaction for charge-4⁢𝑒 superconductivity in the 𝑑-wave channel. In this work, we go beyond the artificial large-𝑀 mean-field theory previously adopted and compute the phase diagram by incorporating phase fluctuations of the pair-density-wave order parameters.
• By investigating the relevance of various topological defects, we show that the interaction in the 𝑑-wave channel, together with the strong anisotropy of phase fluctuations around the pair-density-wave ordering momenta favors a vestigial charge-4⁢𝑒 superconducting order at intermediate temperatures.
• By contrast, a competing charge-density-wave vestigial order does not develop, due to the suppression of its stiffness.