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Zak phase

In physics, the Zak phase is the Berry phase of a Bloch wavefunction evaluated on a noncontractible loop in the Brillouin zone. In other words, it's the geometric phase acquired by an electron in a crystal as its wave vector, , slowly (more precisely, adiabatically) loops over the Brillouin zone.[1] Because the (abelian) Berry phase is only defined for an adiabatic evolution, the Zak phase is only defined for systems where for a given there are no degeneracies, which corresponds to an insulator. Furthermore, certain symmetries, such as chiral symmetry, may cause the Zak phase to be quantized,[1] in which case the Zak phase will be an adiabatic invariant. In the presence of such symmetries, the Zak phase may be used to give a topological index to a given phase. Insulating Hamiltonians with a nontrivial quantized Zak phase are topological insulators.

References

  1. ^ a b Zak, J. (1989-06-05). "Berry's phase for energy bands in solids". Physical Review Letters. 62 (23): 2747–2750. doi:10.1103/PhysRevLett.62.2747.
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