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It has been more than 40 years since superconductivity was discovered inorganic conductors, and the way scientists view organic superconductors haschanged over time. At first, the fact that organic conductors exhibitsuperconductivity was a novelty in itself, and subsequently it was shown thatbehind the superconductivity is the physics of electron correlation, which hasbeen a focus in condensed matter physics at large. Amid the remarkabledevelopment of correlation physics, the unique characteristics of organicconductors, e.g., a variety of lattice geometries and the highly compressiblefeature, led to the elucidation of fundamental principles and the finding ofnew phenomena, such as bandwidth-controlled Mott transitions and possiblequantum spin liquids. However, most organic superconductors have commensurateband fillings, such as a half or a quarter, whereas inorganic superconductors,such as high-$T_{\rm c}$ cuprates and iron-based superconductors, have oftenbeen investigated under the variation of their band fillings. Thus, thephysical linkage between organic and inorganic superconductors has remainedunresolved. In this review article, we focus on the layered nonstoichiometricsuperconductor, $\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$, which is exceptionalamong organic conductors in that the nonstoichiometry serves as doping to ahalf-filled band. Moreover, the strong correlation of electrons and ageometrically frustrated triangular lattice make this system exhibit the uniquephenomena involved in Mottness, spin liquidity, and superconductivity, whichare key concepts of correlated electron physics. This review will summarizewhat we learned from the pressure study of$\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$ and how they relate to the extensivelystudied issues in inorganic materials.

Mottness and spin liquidity in a doped organic superconductor $\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$