We review the properties of a new mechanism for spontaneous supersymmetry breaking which is built from complex linear superfields. Using superspace higher derivative terms which deform the auxiliary field potential we find that, in addition to the standard supersymmetric vacuum, there is a new vacuum where supersymmetry is spontaneously broken and nonlinearly realized. From the Noether method we identify the chiral superfield X which enters the Ferrara-Zumino supercurrent equation and show that it becomes nilpotent in the broken vacuum.