Designing Quantum Spin-Orbital Liquids in Coulomb Impurity Lattices on Gapped Honeycomb Substrates

Quantum spin-orbital liquids are elusive states of matter in which quantum fluctuations of orbitals and spins conspire to create strongly correlated states which do not break any symmetries. A promising development in the observation of those states is the creation of artificial Mott insulators where antiferromagnetic correlations between spin and orbital degrees of freedom can be designed. Here we exploit the fact that massive Dirac fermions form bound states with spin and valley degrees of freedom in the vicinity of a Coulomb impurity. In the presence of electron-electron interactions, the interaction of the spin and valley polarized electrons bound to different Coulomb impurities naturally maps into a superexchange interaction with SU(4) symmetry. We propose that quantum spin-orbital liquids can be engineered in artificial Coulomb impurity lattices on the surface of gapped honeycomb substrates, such as graphene on SiC.