Mott physics in multi-band Hubbard model with strong spin-orbit interaction

H. L. Nourse

The single-orbital Hubbard model is often a good description of the low energy dynamics of strongly correlated electron systems. Importantly, the single-orbital Hubbard model at half-filling is able to capture the Mott metal-insulator transition that occurs in many materials. However, there are insulating phases (as well as other exotic phases) that occur due to strong electronic correlations in materials that are away from half-filling. In many cases, these additional phases occur because the constituent electrons of the material come from multi-orbital atomic environments that require more complicated descriptions such as the multi-orbital Hubbard model. In other cases, as we show in this thesis, the rich phase diagram arises from the underlying lattice because of special geometric features.For example, decorated lattices, which often occur in organometallics (e.g., metal-organic frameworks (MOFs)), have geometrical complexity due to the molecular structures that decorate the lattice. We argue that the effective description for many of these materials is the single-orbital Hubbard model. Yet, these materials still have rich phase diagrams because the molecular structures of the material cause effective multi-orbital interactions generated from the local Coulomb interaction.We investigate the single-orbital Hubbard model on the decorated honeycomb lattice at zero temperature using rotationally invariant slave-boson (RISB) theory in the mean-field approximation, at a range of fillings. Numerous metal-insulator transitions occur - the insulating phases include a real-space Mott insulator, a dimer Mott insulator, a trimer Mott insulator, flat-band ferromagnets, and a spin-1 Mott insulator, dominated by spin-triplet fluctuations. This menagerie of phases is caused by effective multi-orbital interactions arising from the interplay of electronic correlations, lattice structure, and band filling effects. For example, with only on-site Coulomb interactions, the spin-1 Mott insulator is driven by an effective Hund's coupling on a three-site ring that favors the formation of triplets when the three-site ring has four electrons. We argue that this exotic phase may be realized in layers of the organometallic molecular crystal Mo3S7(dmit)3.

T. A. Kaplan

Nils Blümer, C. Knecht, Krunoslav Požgajčić +1 more

J P Hague

I investigate band and Mott insulating states in a two-band Hubbard model, with the aim of understanding the differences between the idealised one-orbital model and the more realistic multi-band case. Using a projection ansatz I show that additional orbitals suppress the metal-insulator transition, leading to a critical coupling of approximately eight times the bare band-width. I also demonstrate the effects of orbital ordering, which hinder Mott-Hubbard states and open a band gap. Since multi-band correlations are common in real materials, this work suggests that the existence of very strongly correlated band insulators may be more common than Mott-Hubbard insulators.

昌久 古賀, Akihisa Koga

Hague, J. P.

I investigate band and Mott insulating states in a two-band Hubbard model, with the aim of understanding the differences between the idealised one-orbital model and the more realistic multi-band case. Using a projection ansatz I show that additional orbitals suppress the metal-insulator transition, leading to a critical coupling of approximately eight times the bare band-width. I also demonstrate the effects of orbital ordering, which hinder Mott-Hubbard states and open a band gap. Since multi-band correlations are common in real materials, this work suggests that the existence of very strongly correlated band insulators may be more common than Mott-Hubbard insulators.