Emergence of Nodal-Knot Transitions by Disorder

From vortex atom theory to modern topological quantum field theory, the mathematical concept of knots has fascinated mathematicians and physicists. Condensed matter physics offers an accessible platform for the emergence of knots: knotted topological phases. Protected by certain symmetries, these phases manifest as knotted nodal lines in three-dimensional band structures, embedded within the Brillouin zone, making them a fertile ground for non-trivial topological phenomena. On the other hand, as one of the most common physical perturbations, disorder effects often trigger novel quantum phase transitions. Considering the interplay between disorders and knotted topological

phases, it is natural to ask whether the disorder effect can provide a tuning knob to manipulate the nodal-knot configurations through triggering knot transitions? Through renormalization-group calculations, we demonstrate that weak disorder can indeed induce nodal-knot transitions. Specifically, different types of disorders drive distinct transitions thus altering the knot topology. These transitions are quantitatively captured by changes in topological invariants such as knot Wilson loop integrals, and are experimentally detectable via de Haas-van Alphen oscillations.

This work is supported by the National Natural Science Foundation of China (Grants No. 12304074, No. 12047531, and No. 12234017), and the Innovation Program for Quantum Science and Technology (No. 2021ZD0302400), Ming Gong is also supported by China National Postdoctoral Program for Innovative Talents (Grants No. BX20240004).