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The frustrated magnetism on the Kondo lattice system motivates intriguingKondo-breakdown beyond the traditional Doniach scenario. Among them, thefractionalized Fermi liquid (FL*) has drawn a particular interest by virtue ofits fractionalized nature. Here, we study the phase diagram of $J_{1}$-$J_{2}$Kondo-Heisenberg model on a honeycomb lattice at a quarter filling. Employingthe slave-fermion mean-field theory with $d \pm id$ spin liquid ansatz andexact diagonalization, we discuss the emergence of partial Kondo screening inthe frustrated regime with comparable $J_{1}$ and $J_{2}$, and thefractionalized superconductor (SC*) which is superconductor analogy of the FL*.Due to the larger number of local spin moments than itinerant electrons, themagnetic fluctuation is still significant even in the strong-coupling limit,which influences the thermodynamic and transport properties qualitatively. Inparticular, we estimate the thermal conductance to probe the low-energyexcitation and show the anomalous behaviour in the SC* phase contrast to theconventional superconductors.

Partial Kondo Screening and Anomalous Thermal Conductance