Nodal semimetals in a strong magnetic fields in the Hofstadter regime

Weyl and nodal line semimetals are classes of three-dimensional quantum 

materials characterized by band degeneracies protected by symmetry and topology. 

In this talk, I explore how magnetic fields induce gap openings in their spectra and 

drive phase transitions through electron tunneling between nodes. We demonstrate 

that external magnetic fields immediately gap the Weyl nodes which is exponentially 

small but finite and significant under certain conditions. For nodal line semimetals, we 

identify a critical Fermi surface area beyond which the system cannot be fully gapped 

by external fields. Additionally, we discuss the conditions under which field-induced 

gapped insulating states exhibit topological nontriviality. Lastly, we introduce straightforward 

diagrammatic rules that reliably predict the topological nature of phases resulting from 

applied magnetic fields.