Abstract
Mott insulators with a half-filled band of electrons on the triangular lattice have been recently studied in a variety of organic compounds. All of these compounds undergo transitions to metallic and/or superconducting states under moderate hydrostatic pressure. We describe the Mott insulator using its hypothetical proximity to a ${Z}_{2}$ spin liquid of bosonic spinons. This spin liquid has quantum phase transitions to descendant confining states with N\'eel or valence bond solid order, and the insulator can be on either side of one of these transitions. We present a theory of fermionic charged excitations in these states and describe the route to metallic states with Fermi surfaces. We argue that an excitonic condensate can form near this insulator-metal transition due to the formation of charge neutral pairs of charge $+e$ and charge $\ensuremath{-}e$ fermions. This condensate breaks the lattice space group symmetry, and we propose its onset as an explanation of a low temperature anomaly in $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{C}\mathrm{N})}_{3}$. We also describe the separate BCS instability of the metallic states to the pairing of like-charge fermions and the onset of superconductivity.
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