We study theoretically a process of cooling electrons using a superconducting tunnel junction with a $\pi$ phase difference and a usual insulator or a ferroelectric in between, and an array of such junctions with ferroelectric layers in between. These setups have a complex structure of entropy due to nodal lines, where the density of states can be divergent or larger than for a free electron gas at a chemical potential level. We consider a small current running from the bath of electrons through the setup, where electrons have to have higher entropy, and thus remove heat from the bath.

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• Density of states
• Ferroelectricity
• Heat transfer
• Mesoscopics
• Spin-orbit coupling
• Superconductivity
• Ferroelectrics
• Superconducting devices
• Tunnel junctions
• BCS theory
• Green's function methods
• Mean field theory
• Symmetries in condensed matter