A pair of researchers have built explicit many‑body wavefunctions that describe superconductivity arising when anyons condense. Anyons are particle‑like excitations in two dimensions that have fractional exchange statistics, distinct from ordinary bosons or fermions. The work gives a concrete recipe for turning a “parent” topological state with anyons into a “daughter” superconducting state by writing down the many‑particle wavefunction for the condensed anyons.

The authors use a hierarchy‑wavefunction construction. In this approach the daughter wavefunction is written as an integral over the positions of the anyons, multiplied by a “pseudowavefunction” that encodes the correlated state the anyons form when they condense. They analyze these wavefunctions with two tools: a plasma analogy that maps the squared wavefunction to an effective classical Hamiltonian, and topological field theory formulas that read off properties like the condensate charge and the chiral central charge (a measure of edge heat flow). The paper gives explicit examples for several cases, including semions, a ν = 2/3 hierarchy state, the ν = 1/3 Laughlin state, the ν = 1 integer quantum Hall state, and the non‑Abelian Pfaffian state. Remarkably, for the semion example the many‑semion superconducting wavefunction is equivalent to Laughlin’s original semion superconductor ansatz.

At a physical level the construction signals superconductivity through off‑diagonal long‑range order (ODLRO). ODLRO means a particular two‑point reduced density matrix approaches a nonzero constant at large separation; that constant reflects a condensed charge. In the plasma picture this corresponds to the exponent matrix having a null vector: one collective mode becomes gapless and supports the superconducting order. The topological field theory associated to each wavefunction then tells whether any residual topological order remains and what electric charge the condensate carries. The authors emphasize that this superconductivity is not of the usual Bardeen–Cooper–Schrieffer (BCS) type: it comes from anyon condensation rather than electron pairing.