  We propose altermagnet-superconductor junctions as a way to achieve a
thermoelectric response in metals free of external or stray magnetic fields. We
combine qualitative analysis in a simplified model with a more rigorous
approach based on the inverse proximity effect in the functional-integral
formulation. We show that coupling an altermagnet to a superconductor in a
bilayer induces a momentum-dependent spin-splitting in the superconductor. When
tunneling occurs between this bilayer and a different altermagnet, a
spin-dependent particle-hole symmetry breakdown arises in the transport, which
leads to a thermoelectric response. Our results show that the
altermagnet-superconductor junctions may achieve comparable thermoelectric
performance to ferromagnet-superconductor junctions, featuring a nonmonotonic
dependence of the figure of merit on the strength of the altermagnetic
splitting. We also point out an often overlooked fact regarding the inverse
proximity effect in superconductors, namely that even in a normal
metal-superconductor junction there is a minigap in the superconductor, which
gives rise to a four-peak structure in the DOS reminiscent of spin-split
superconductors. Our results show that altermagnetic metals, unlike
conventional antiferromagnets, can be used for efficient cryogenic
thermoelectricity.
