Emergence of nodal-knot transitions by disorder.

Under certain symmetries, degenerate points in three-dimensional metals form one-dimensional nodal lines. These nodal lines sometimes exhibit intricate knotted structures and have been studied in various contexts. As one of the most common physical perturbations, disorder effects often trigger novel quantum phase transitions. For nodal-knot phases, whether disorder can drive knot transitions remains an open and intriguing question. Employing renormalization-group calculations, we demonstrate that nodal-knot transitions emerge in the presence of weak disorder. Specifically, both chemical-potential-type and magnetic-type disorders can induce knot transitions, resulting in the emergence of distinct knot topologies. The transition can be quantitatively characterized by changes in topological invariants such as the knot Wilson loop integrals. Our findings open up a new avenue for manipulating the topology of nodal-knot phases through disorder effects.