Disorder-induced phase transitions in higher-order nodal line semimetals

Higher-order nodal line semimetals represent a recently proposed topological semimetal class that harbors bulk nodal lines and features gapless hinge Fermi arc excitations, governed by the bulk-hinge correspondence. In this study, we investigate the disorder effect on a higher-order nodal line semimetal and the consequent phase transitions. Within the pristine higher-order nodal line semimetal model, we unveil three distinct phases: higher-order nodal line semimetal, conventional nodal line semimetal, and normal insulator. The higher-order nodal line semimetal is characterized by one-dimensional hinge Fermi arc states connecting a pair of nodal rings, contrasting with conventional nodal line semimetals that exhibit two-dimensional drumhead surface states. We demonstrate that disorder can trigger multiple phase transitions within this system. Significantly, intermediate disorder can induce higher-order topology in an initial conventional nodal line semimetal or even an initial normal insulator. Further increase in disorder drives the system through a diffusive metallic phase before ultimately reaching the Anderson insulator regime. Employing a combination of finite-size scaling analysis and an effective medium theory, we construct a comprehensive phase diagram, elucidating the intricate interplay between disorder and topology.