The Mott transition — the point where a material stops conducting electricity despite having enough electrons to do so — is one of condensed matter physics' central problems. The standard explanation invokes bandwidth: when the electron-electron repulsion (Hubbard U) exceeds the kinetic energy bandwidth (W), electrons localize. Each electron sits on its atom and refuses to move because the cost of sharing a site with another electron is too high. The ratio U/W controls the transition. Increase U, decrease W, and the metal becomes an insulator.
Ding and Claassen (arXiv 2602.22548, February 2026) show that this framing is incomplete. Using exact diagonalization on the Kane-Mele-Hubbard model, they demonstrate that quantum geometric properties of the Bloch wavefunctions can drive Mott transitions independently of bandwidth.
Quantum geometry describes how wavefunctions change as you move through momentum space. The Berry curvature measures how they rotate; the quantum metric measures how much they spread. These geometric quantities are properties of the shape of the electronic state, not its energy. Two bands can have identical bandwidth — identical kinetic energy scales — but completely different quantum geometry.
Their result: tuning the quantum geometric properties while holding the bandwidth fixed can push the system across the Mott transition. The metal-insulator boundary depends on how wavefunctions curve through abstract space, not just how much kinetic energy they carry. The mechanism involves non-local Coulomb scattering: when the Wannier functions (the real-space representation of Bloch states) change their shape due to different quantum geometry, the effective electron-electron interaction changes too. The geometry modifies the interaction, and the modified interaction drives the transition.
This matters for moiré materials — twisted bilayer graphene and its relatives — where orbital character varies dramatically across the Brillouin zone. In these systems, bandwidth and geometry change together, and experimentalists have been attributing phase transitions to bandwidth when geometry may be doing the work.
The Mott transition was always about electrons refusing to move. The assumption was that the refusal was caused by the energy landscape — too expensive to hop, so they stay put. The geometric picture says the refusal can also come from the shape of the wavefunction itself. The landscape matters, but so does the shape of the thing moving through it.