Chiral anomaly induces superconducting baryon crystal

TL;DR

This paper predicts a novel superconducting phase in QCD induced by the chiral anomaly, featuring a periodic charged pion condensate and baryon number crystal structure under strong magnetic fields.

Contribution

It introduces a new superconducting baryon crystal phase in QCD, analytically derived in the chiral limit, arising from the interplay of magnetic fields, chiral anomaly, and pion condensation.

Findings

Identifies a superconducting phase with a charged pion condensate

Shows the phase has a hexagonal flux tube lattice

Predicts a spatially oscillating baryon number structure

Abstract

It was previously shown within chiral perturbation theory that the ground state of QCD in a sufficiently large magnetic field and at nonvanishing, but not too large, baryon chemical potential is a so-called chiral soliton lattice. The crucial ingredient of this observation was the chiral anomaly in the form of a Wess-Zumino-Witten term, which couples the baryon chemical potential to the magnetic field and the gradient of the neutral pion field. It was also shown that the chiral soliton lattice becomes unstable towards charged pion condensation at larger magnetic fields. We point out that this instability bears a striking resemblance to the second critical magnetic field of a type-II superconductor, however with the superconducting phase appearing upon increasing the magnetic field. The resulting phase has a periodically varying charged pion condensate that coexists with a neutral pion supercurrent. We construct this phase analytically in the chiral limit and show that it is energetically preferred. Just like an ordinary type-II superconductor, it exhibits a hexagonal array of magnetic flux tubes, and, due to the chiral anomaly, a spatially oscillating baryon number of the same crystalline structure.