Bose-Einstein condensation in an one-dimensional imperfect crystal

We report the emergence of a Bose-Einstein condensation in a Bose gas within an infinite one-dimensional crystal, promoted by its imperfections. The imperfect crystal is modeled with a Dirac comb potential, where one or several deltas are different. The energy-momentum dispersion relation is calculated numerically with the transfer matrix method. For one imperfection in the crystal, we are able to give analytical expressions from where we obtain the energy spectrum which shows an energy gap between the grown state and the first excited state. The energy gap originates the emergence of a Bose-Einstein condensation at finite temperature that otherwise would not exist. Furthermore, the specific heat of the bose gas shows a jump at the critical temperature proportional to energy gap size. We report the results for several values of the network parameters such as the strenghts and separations of the delta potentials.