Deep inside a superconductor, electrons pair up into Cooper pairs and glide without resistance. But if a vortex appears in this perfect order, a tiny region where superconductivity vanishes, special excitations emerge there: Bogoliubov quasiparticles. For a long time, they were considered candidates for Majorana fermions, particles that are their own antiparticles. If that were true, braiding vortices could perform quantum computations shielded from errors by the system's very topology.

The new work dashes this hope. The authors used the eigenparticle formalism, a unitary transformation that exactly diagonalizes the Hamiltonian while preserving particle number at every step. Unlike the standard approach, where quasiparticles are introduced via an approximate mean field and particle number is broken, here each particle remains whole. It turns out that such eigenparticles always increase the particle number by exactly one and cannot be self-conjugate, that is, Majorana. Simply put, a quasiparticle is a dressed electron that cannot shed its charge.

This finding strikes at the very idea of non-Abelian braiding. If quasiparticles carry integer charge, their statistics remain Abelian: exchanging particles does not change the quantum state in the required way. The dimension of the degenerate subspace for M quasiparticles on L vortices is $C_L^M$, not $2^{L/2}$, as previously assumed. A quantum computer built on such zero modes simply will not work.

What next? Perhaps efforts will shift toward explicitly breaking particle number conservation, for instance through strong coupling to the environment or pumping charge fluctuations. Or researchers may turn to other platforms for non-Abelian anyons that do not rely on Bogoliubov zero modes. In any case, this work reminds us that fundamental symmetries cannot be ignored, even when they stand in the way of a beautiful idea.