The use of thermoelectricity in a cryogenic environment opens pathways for ultrasensitive passive detection and for control and cooling of quantum technology applications.

We introduce the Superconductor-Insulator-2DEG junction (Lucchesi & Paolucci, arXiv:2604.02123) as a novel nonlinear thermoelectric element. We assess its potential via a fully nonlinear model where we consider the temperatures of both sides, T_S and T_Sm, and the conduction band edge of the 2DEG, E_c. Its band structure allows the formation of nonlinear thermoelectricity even for relatively small temperature gradients, enhancing the thermoelectric figures of merit.

For T_S>T_Sm, we obtain a maximum Seebeck potential larger than the superconductor gap Δ₀ V_S~6.75 Δ₀ in the E_c=0.03 Δ₀ regime, and a maximum efficiency of η=0.96 η_c when used as a heat engine. For the relevant case Δ₀=200 μeV and tunnel resistance R_t=1 kΩ, we obtain a maximum Seebeck coefficient of ~1 mV/K, a maximum Peltier current of I₀ ~ 20 nA, and a maximum output power of 4 pW for T_S-T_sm ~ 0.9T_c, with T_c=1.3 K.

We discuss the causes and the implications for these large figures of merit, in particular, the impact of energy filtering on efficiency.

In different regimes, the system also shows a large dV_S /dT_S and a bistability pattern, which respectively show potential for detection and control applications. It also shows bidirectional cooling, being the first system to cool a superconductor via a tunnel junction without another superconductor.