[Wannier] hopping parameter

[Danilo Puggioni]

Dear Wannier90 users, I am beginner in using Wannier90 code.
 I have a question about the hopping parameters that I can extract from the Hamiltonian. 
These parameters in my hamiltonian are complex. Is it correct? In PRB 56, 12847 Marzari and Vanderbilt conjecture that optimally localized Wannier functions are alway real then I suppose that the hopping parameter must be real. I don't understand. 
Thanks 
Danilo