Local condensation of charge-4e superconductivity at a nematic domain wall

Multi-component superconductivity is realized in various materials, such as doped Bi₂Se₃ and possibly twisted bilayer graphene. This type of superconductivity naturally generates bilinear composite order parameters that are either nematic, time-reversal symmetry-breaking (TRSB), or even charge-4e superconducting – the latter remains an elusive quantum state of matter. Here, to determine whether charge-4e order can emerge above the superconducting transition temperature, we consider a paradigmatic two-component superconductor in a tetragonal crystal. By solving this model with a variational approach, we find that although the s- and d-wave charge-4e pairing channels can be attractive, they are always subleading to an instability towards nematic or TRSB order. Nevertheless, using a real-space variational method, we find that charge-4e order can locally condense in the vicinity of a nematic domain wall, where the competing nematic order naturally melts. We assess the conditions under which this scenario is realized, and discuss its experimental manifestations.