Two 'incompatible' quantum phases found living together in one material

Two types of higher-order topological insulator — dipolar and quadrupolar — were thought to be mutually exclusive, like odd and even numbers. This work shows a single system can host both simultaneously, demonstrated through a design using laser-written optical waveguides confirmed by full numerical simulation. It forces a rethink of how these exotic phases are catalogued and opens new possibilities for engineering protected boundary states.