3d topological insulator in Weyl semimetal in the presence of commensurate magnetic field

We study the effect of commensurate magnetic field in a time reversal broken 3d Weyl semimetal [1]. The mass term (M) which dictates the location of Weyl nodes at zero field, causes a transition from trivial insulator to Weyl-semimetal(at M = M_c1 ) to topological insulator (at M=M_c2 ) in the presence commensurate magnetic field. There are 2q number of Weyl nodes for M_c1 < M < M_c2 . For M > M_c2 , we get the signature of three-dimensional topological insulator with arc like gapless surface states with length 2π. M_c1 and M_c2 change as we change q such that (M_c1−M_c2 ) goes to zero exponentially with increasing q.

[1] Ganpathy Murthy, H. A. Fertig, and Efrat Shimshoni PRR 2, 013367 (2020)