New math rules out some ‘ghost’ orders in superconductors

Grgur Palle and Rafael M. Fernandes of the University of Illinois Urbana-Champaign have identified the root cause of ambiguity in calculations modeling secondary phases, often called “ghost” orders, in superconductors. Their work demonstrates that redundancy relations, such as Fierz identities, are responsible for the inconsistencies arising from the standard large-N approach to modeling these complex materials. The researchers propose an unbiased approach that accounts for how different vestigial channels interfere, yielding unique and reliable values for effective interactions, and revealing scenarios where vestigial orders are unexpectedly unstable. This analysis applies to materials ranging from iron pnictides to twisted bilayer graphene. Current methods for predicting partially ordered phases, known as vestigial phases, in materials like iron pnictides and twisted bilayer graphene may be flawed due to an inherent ambiguity in calculations. The standard large-N approach, used to model the Ginzburg-Landau action of primary order parameters, struggles with decoupling composite order parameters, potentially leading…