  We derive the efficiency at maximal power of a scale-invariant (critical)
quantum junction in exact form. Both Fermi and Bose statistics are considered.
We show that time-reversal invariance is spontaneously broken. For fermions we
implement a new mechanism for efficiency enhancement above the Curzon-Ahlborn
bound, based on a shift of the particle energy in each heat reservoir,
proportional to its temperature. In this setting fermionic junctions can even
reach at maximal power the Carnot efficiency. The bosonic junctions at maximal
power turn out to be less efficient then the fermionic ones.
