Designing Quantum Spin Liquids
Triangular lattice of Coulomb impurities sitting on top of a honeycomb substrate with unequal sublattices.
Ratio between on-site Coulomb repulsion and hopping energy between impurities (top) as a function of the separation between impurities. Left: triangular and (right) square impurity lattices. Bottom: superexchange interaction.
Mott insulators are materials that would be naively expected to conduct electricity, but nevertheless behave as insulators due to the presence of very strong electronic interactions. In a recent work published in Scientific Reports, graduate student Xu Dou and Prof. Bruno Uchoa have shown that Coulomb impurity lattices on the surface of gapped honeycomb substrates, such as graphene on SiC, can be used to simulate a special class of Mott insulators described by SU(4) symmetric spin lattice models. Those systems are believed to host quantum spin-orbital liquids, exotic and elusive strongly correlated states that have topological non-local excitations emerging from quantum frustration between orbitals and spins.
Frustration is a property that appears in spin lattices when all competing exchange interactions cannot be satisfied at the same time. In quantum systems, fluctuations can produce or enhance frustration. When strong enough, they forbid antiferromagnetic spin lattices to order in a Neel state. The resulting frustrated state is called a spin liquid, and has the unique property that albeit being strongly correlated, it does not break any symmetries of the lattice even at zero temperature.
Spin-orbital liquids are an even more elusive class of spin liquids, where the frustration derives from quantum entanglement between spins and orbital degrees of freedom. Dou and Uchoa have used the property that massive Dirac fermions, the electronic excitations in gapped honeycomb lattices, form bound states with four-fold degeneracy in the vicinity of a Coulomb impurity. The degeneracy is due to spin and valley quantum numbers.
In the presence of interactions and at quarter filling, each Coulomb impurity bound state fluctuates between four different “color" states, with each color being formed by a different combination between the two valleys and spins. In this situation, they showed that a superlattice of Coulomb impurities behaves as an antiferromagnetic spin lattice driven by SU(4) symmetric super-exchange interactions.
Most of the current efforts to simulate quantum spin liquids are concentrated in cold atom systems, where the Mott physics is present only at ultra low temperatures. This proposal may lead to significant advances in the experimental design and observation of quantum spin-orbital liquids in solid-state settings.