A real-space perspective on modulated orders in unconventional superconductors

Spatially modulated ordered phases underlie many fascinating phenomena in strongly correlated systems and often harbor nontrivial interplay between charge, spin, and superconducting orders. This is in large part due to the inherent multicomponent nature of the corresponding order parameters, enabling intricate coupling terms in the free energy. In this talk, we first focus on the heavy-fermion superconductor UTe₂. Even though the tetragonal point group of this compound mandates that all spatially homogeneous orders are single component, modulated orders with symmetry-related wave vectors form higher-dimensional representations of the space group. Guided by experimental observations, we elucidate a potential scenario for the interplay of charge- and pair-density waves on the surface of UTe₂.

Subsequently, we highlight an example concerning spatial modulation in nonsymmorphic systems, which possess symmetry-protected band degeneracies at high-symmetry momenta at the Brillouin zone edge. Adopting a novel, real-space approach, we show that when the modulation wave vector coincides with such momenta, the resulting order parameter inherits the nonsymmorphic-symmetry-protected degeneracy. Interestingly, when the degeneracy is between inversion-even and -odd bands, the resulting multicomponent order parameter becomes parity mixed, even with inversion symmetry intact. We harness this observation in an attempt to shed light on the coexistence of magnetism and superconductivity in the nonsymmorphic heavy-fermion superconductor CeRh₂As₂.