A neutral conductor has no electric field. This is textbook electrostatics: if the total charge is zero and the conductor is isolated, the free electrons redistribute to cancel any internal field, and the external field vanishes by Gauss's law. The result holds for any shape — spheres, cylinders, irregular blobs. No charge, no field.
Kuratov, Galtsov, Dyachkov, and Igashov (arXiv:2501.04708) show that hemispherical metal nanoclusters violate this expectation. Despite being electrically neutral, they generate electrostatic fields of order 10⁸ V/m near their flat surface. The mechanism: quantum shell effects create large-scale electron density inhomogeneities that, in a hemisphere, lack the spherical symmetry needed to cancel.
In a spherical cluster, quantum shell effects exist — electron density oscillates radially as shells fill — but the oscillations are symmetric, and their fields cancel at every external point. Cut the sphere in half, and you break the symmetry but not the shell structure. The periodic orbits that create the shell filling are preserved by the hemisphere's geometry, but the resulting electron density is no longer symmetric around any center. The shells still fill the same way, but the fields they produce no longer cancel.
The structural point: the shell structure is a property of the potential (which respects the hemisphere's closed orbits), but the field cancellation is a property of the geometry (which requires full spherical symmetry). Break the geometry while preserving the potential, and you get macroscopic quantum fields from a neutral object. The charge is zero. The field is enormous. Symmetry was doing more work than anyone credited.