When a gap of tunable size opens at the conic band intersections of graphene, the Berry phase does not vanish abruptly, but progressively decreases as the gap increases. The phase depends on the reciprocal-space path radius, i.e., for a doped system, the Fermi wave vector. The phase and its observable consequences can thus be tuned continuously via gap opening --by a modulating potential induced by strain, epitaxy, or nanostructuration-- and doping adjustment.
@article{arxiv.1511.01341,
title = {Tunability of the Berry phase in gapped graphene},
author = {Andrea Urru and Giulio Cocco and Vincenzo Fiorentini},
journal= {arXiv preprint arXiv:1511.01341},
year = {2015}
}