Berry's phase of bloch oscillation

[wdlang]

we know in bloch oscillation, the wavefunction of an electron returns to its initial state after a period, but up to a phase.

my question is, can this phase be nontrivial?

 

[gptejms]

we know in bloch oscillation, the wavefunction of an electron returns to its initial state after a period, but up to a phase.

my question is, can this phase be nontrivial?

I don't think a periodic potential by itself leads to berry phase--berry phase arises when the Hamiltonian depends on parameters which are taken around a closed path in the parameter space.