  It has been more than 40 years since superconductivity was discovered in
organic conductors, and the way scientists view organic superconductors has
changed over time. At first, the fact that organic conductors exhibit
superconductivity was a novelty in itself, and subsequently it was shown that
behind the superconductivity is the physics of electron correlation, which has
been a focus in condensed matter physics at large. Amid the remarkable
development of correlation physics, the unique characteristics of organic
conductors, e.g., a variety of lattice geometries and the highly compressible
feature, led to the elucidation of fundamental principles and the finding of
new phenomena, such as bandwidth-controlled Mott transitions and possible
quantum spin liquids. However, most organic superconductors have commensurate
band fillings, such as a half or a quarter, whereas inorganic superconductors,
such as high-$T_{\rm c}$ cuprates and iron-based superconductors, have often
been investigated under the variation of their band fillings. Thus, the
physical linkage between organic and inorganic superconductors has remained
unresolved. In this review article, we focus on the layered nonstoichiometric
superconductor, $\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$, which is exceptional
among organic conductors in that the nonstoichiometry serves as doping to a
half-filled band. Moreover, the strong correlation of electrons and a
geometrically frustrated triangular lattice make this system exhibit the unique
phenomena involved in Mottness, spin liquidity, and superconductivity, which
are key concepts of correlated electron physics. This review will summarize
what we learned from the pressure study of
$\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$ and how they relate to the extensively
studied issues in inorganic materials.
