  Quantum spin-orbital liquids are elusive strongly correlated states of matter
that emerge from quantum frustration between spin and orbital degrees of
freedom. A promising route towards the observation of those states is the
creation of artificial Mott insulators where antiferromagnetic correlations
between spins and orbitals can be designed. We show that Coulomb impurity
lattices on the surface of gapped honeycomb substrates, such as graphene on
SiC, can be used to simulate SU(4) symmetric spin-orbital lattice models. We
exploit the property that massive Dirac fermions form mid-gap bound states with
spin and valley degeneracies in the vicinity of a Coulomb impurity. Due to
electronic repulsion, the antiferromagnetic correlations of the impurity
lattice are driven by a super-exchange interaction with SU(4) symmetry, which
emerges from the bound states degeneracy at quarter filling. We propose that
quantum spin-orbital liquids can be engineered in artificially designed
solid-state systems at vastly higher temperatures than achievable in optical
lattices with cold atoms. We discuss the experimental setup and possible
scenarios for candidate quantum spin-liquids in Coulomb impurity lattices of
various geometries.
