The geometric (or Berry's) phase in quantum mechanics does have experimental manifestations in macroscopic materials. For example it can be seen in the phase of Shubnikov de Haas oscillations. The graph below is based on experimental data for graphene, taken from a 2005 Nature paper. In this "fan diagram" the Landau level index is plotted versus 1/B [the magnetic field at which a peak in the resistance occurs]. The y-axis) intercept (shown in the upper right inset as a function of gate voltage) is related to the Berry phase, beta. For a linear Dirac spectrum, beta=1/2 and for a quadratic spectrum, beta=0.
Similar experiments and analysis of data for topological insulators produces ambiguous results, which I will discuss in a forthcoming post about this recent PRB.
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