Not yet reviewed by Pith; the record is open.

Josephson junction field-effect transistors (JJFETs) have recently re-emerged as promising candidates for superconducting computing. For JJFETs to perform Boolean logic operations, the so-called gain factor $\alpha_{R}$ must be larger than 1. In a conventional JJFET made with a classical channel material, due to a gradual dependence of superconducting critical current on the gate bias, $\alpha_{R}$ is much smaller than 1. In this Letter, we propose a new device structure of quantum enhanced JJFETs in a zero-energy-gap InAs/GaSb heterostructure. We demonstrate that, due to an excitonic insulator quantum phase transition in this zero-gap heterostructure, the superconducting critical current displays a sharp transition as a function of gate bias, and the deduced gain factor $\alpha_{R}$ ~ 0.06 is more than 50 times that (~ 0.001) reported in a classical JJFET. Further optimization may allow achieving a gain factor larger than 1 for logic applications.