Scientists finally found the exact moment a piece of metal stops being a conductor and turns into an insulator.
arXiv · March 17, 2026 · 2603.14230
The Takeaway
It has long been known that adding disorder or 'messiness' to a material can suddenly stop electrons from moving, effectively turning a conductor into an insulator. This paper provides a rigorous mathematical proof of the 'mobility edge'—the precise boundary where this transition occurs—solving a fundamental mystery in how quantum particles behave in complex materials.
From the abstract
We determine the phase diagram of the Anderson tight-binding model on regular random graphs with Gaussian disorder distribution and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to infinity, the spectrum asymptotically consists of a finite delocalized interval surrounded by two unbounded localized components. Our argument uses a recent description of the spectrum of the tight-binding model on the Bethe lattice (Aggarwal--Lopatto, 2