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We revisit the Hofstadter butterfly for a subset of topologically trivialBloch bands arising from a continuum free electron Hamiltonian in a periodiclattice potential. We employ the recently developed procedure -- which waspreviously used to analyze the case of topologically non-trivial bands[\href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.106.L121111}{Phys.Rev. B \textbf{106}, L121111 (2022)}] -- to construct the finite field Hilbertspace from the zero-field hybrid Wannier basis states. Such states are Blochextended along one direction and exponentially localized along the other. Themethod is illustrated for square and triangular lattice potentials and is shownto reproduce all the main features of the Hofstadter spectrum obtained from anumerically exact Landau level expansion method.  In the regime when magnetic length is much longer than the spatial extent ofthe hybrid Wannier state in the localized direction we recover the well knownHarper equation. Because the method applies to both topologically trivial andnon-trivial bands, it provides an alternative and efficient approach to moir\'ematerials in magnetic field.

Revisiting Bloch electrons in magnetic field: Hofstadter physics via hybrid Wannier states