Do Bloch waves interfere with one another ?

Here we show that two Bloch states, which are energy eigenstates of a quantum periodic potential problem, with different wavevectors can not be linearly superposed to display interference any kind captures the relative phase between them. This is due existence superselection rule in these systems, whose origin lies discrete translation symmetry. A topological reason leading such found. temporal analogue this periodically driven systems also uncovered, forbids coherent superposition quasi-periodic Floquet states quasienergies.