"The Forced Crossing"

There are many ways to turn an insulator into a metal. Apply pressure. Add dopants. Hit it with a laser. All of them supply something external — energy, carriers, field — that forces the electronic gap to close. Pang and He describe a route that requires nothing external at all.

The mechanism is topological. In certain crystals, the insulating low-symmetry phase and the metallic high-symmetry phase carry different quantized formal polarizations — a topological invariant, not a measurable voltage, that characterizes how charge distributes within the unit cell. Because this invariant is quantized, it cannot change smoothly. Any continuous path between the two phases that preserves the relevant symmetry must close the electronic gap at some intermediate point.

No doping. No pressure. No external field. The gap closure is forced by the symmetry of the path through configuration space. The material has no choice.

Validated in two very different systems — two-dimensional InPS3 and three-dimensional CdBiO3 — this mechanism produces metallic behavior as a geometric necessity rather than an energetic accident. The metal is not a state you reach by overcoming a barrier. It is a state you cannot avoid if you move between two topologically distinct insulators while respecting their symmetries.

The deeper point: not all phase transitions are driven by competition between phases. Some are consequences of the topology of the space connecting them. The metal doesn't win. It simply has to be crossed.