Biexciton-like quartet condensates in an electron-hole liquid

We theoretically study the ground-state properties and the condensations of exciton-like Cooper pairs and biexciton-like Cooper quartets in an electron-hole system. Applying the quartet Bardeen-Cooper-Schrieffer (BCS) theory to the four-component fermionic system consisting of spin-21 electrons and spin-21 holes, we show how Cooper pairs and quartet correlations appear in the equation of state at the thermodynamic limit. The biexciton-like four-body correlations survive even at the high-density regime as a many-body BCS-like state of Cooper quartets. Our results are useful for further understanding of exotic matter in the interdisciplinary context of quantum many-body physics with multiple degrees of freedom.