It has been well established that delta-like transport distribution of electron gives the best thermoelectric performance. On another front, it has been experimentally verified that graphene nano-ribbon with nano-break in the channel region exhibits tunnelling. Here, we utilize the tunnelling phenomena observed in graphene break junctions to achieve delta like transport distribution. Indeed our device exhibit record ZT ranging from 10 to 100. This high ZT can be attributed to complete blockage of phonon transport due to the break. The electrical conductance also goes very low, however, near the tunnelling energy it becomes significant, giving rise to an enhanced ZT value. In this report we investigate the effect edge orientation and the width of the ribbon on thermoelectric property. Moreover, we investigate the effect of temperature on tunnelling and how it affect thermoelectric performance. We find that there is an optimal temperature at which the device performs best. In the simulations, we assumed ballistic transport and used first principle approach to obtain the electrical properties. The phononic system was characterized by a Tersoff empirical potential model. The proposed device structure has potential applications as a two-dimensional nanoscale local cooler and as a thermoelectric power generator when connected in arrays.