  We generalize Prodan's construction of radially localized generalized Wannier
bases [E. Prodan, On the generalized Wannier functions. J. Math. Phys. 56(11),
113511 (2015)] to gapped quantum systems without time-reversal symmetry,
including in particular magnetic Schr\"odinger operators, and we prove some
basic properties of such bases. We investigate whether this notion might be
relevant to topological transport by considering the explicitly solvable case
of the Landau operator.
