  We study a model of correlated electrons coupled by tunnelling to a layer of
itinerant metallic electrons, which allows to interpolate from a frustrated
limit favorable to spin liquid states to a Kondo-lattice limit favorable to
interlayer coherent heavy metallic states. We study the competition of the
spinon fermi surface state and the interlayer coherent heavy Kondo metal that
appears with increasing tunnelling. Employing a slave rotor mean-field
approach, we obtain a phase diagram and describe two regimes where the spin
liquid state is destroyed by weak interlayer tunnelling, (i) the Kondo limit in
which the correlated electrons can be viewed as localized spin moments and (ii)
near the Mott metal-insulator-transition where the spinon Fermi surface
transitions continuously into a Fermi liquid. We study the shape of LDOS
spectra of the putative spin liquid layer in the heavy Fermi liquid phase and
describe the temperature dependence of its width arising from quasiparticle
interactions and disorder effects throughout this phase diagram, in an effort
to understand recent STM experiments of the candidate spin liquid 1T-TaSe$_2$
residing on metallic 1H-TaSe$_2$. Comparison of the shape and temperature
dependence of the theoretical and experimental LDOS suggest that this system is
either close to the localized Kondo limit, or in an intermediate coupling
regime where the Kondo coupling and the Heisenberg exchange interaction are
comparable.
