The Berry phase in condensed matter systems. Left, intraband Berry phase, accumulated as the wavepacket, continuously evolves in the k -space within the band. When the trajectory forms a closed loop through the entire Brillouin zone, a gauge-invariant phase is accumulated (known as the Zak phase). Right, interband Berry phase, the wavepacket evolution includes discrete transitions between the two bands, closing a loop in the energymomentum space.
