Superconductivity in cuprate superconductors is associated to a doped Mott insulator scenario and this antiferromagnetic insulating state is considered to be universal. The phase diagram of cuprate superconductors aims at the fundamental comparison of hole- and electron doping into CuO₂ planes. While these CuO₂ planes are, indeed, common among all cuprate superconductors, variations of the coordination of the Cu²⁺ ions are entirely ignored. It is well established that superconductivity is induced by hole doping to the CuO₂ planes with 5- or 6-fold coordinated copper. The induction of superconductivity in cuprates with 4-fold coordinated copper is – against common understanding – not associated to doping but to elimination of defects. Cuprates with 4-fold coordinated copper are metals per se and this fact has not been recognized [1]. It would therefore be revealing if one could alter the copper coordination by keeping chemical elements as well as their stoichiometry constant while solely varying the coordination of copper. That is what we did using La₂CuO₄. Molecular beam epitaxy allows to explore thermodynamic synthesis conditions entirely inaccessible by other synthesis methods. In particular, low synthesis temperatures are key. We synthesized La₂CuO₄ with three different copper coordination: 6-fold coordination (T-phase), 5-fold coordination (T*-phase), and 4-fold coordination (T’-phase). All three phases were grown coherently onto SrLaAlO₄, DyScO₃, and PrScO₃ substrates, respectively. Among the three isomers of La₂CuO₄ the T-phase (6-fold coordinated copper) is the thermodynamically stable polymorph and its electronic response is well known. So, it is not surprising that T-La₂CuO₄ is insulating [Fig. 1(a)]. The T*-phase of La₂CuO₄ is, however, a new material as it is not a thermodynamic stable polymorph. So far we shed some light on its electronic response (it is insulating) and magnetic ordering phenomena are currently investigated by low-energy muon spin resonance spectroscopy. The T’-phase of La₂CuO₄ is also only accessible by low-temperature synthesis methods and its electronic response strongly deviates from its isomers. T’-La₂CuO₄ is a superconductor [2, 3].