The Lieb lattice possesses three bands and with intrinsic spin orbit coupling $lambda$, supports topologically non-trivial band insulating phases. At half filling the lower band is fully filled, while the upper band is empty. The chemical potential l
ies in the flat band (FB) located at the middle of the spectrum, thereby stabilizing a flat band insulator. At this filling, we introduce on-site Hubbard interaction $U$ on all sites. Within a slave rotor mean field theory we show that, in spite of the singular effect of interaction on the FB, the three bands remain stable up to a fairly large critical correlation strength ($U_{crit}$), creating a correlated flat band insulator. Beyond $U_{crit}$, there is a sudden transition to a Mott insulating state, where the FB is destroyed due to complete transfer of spectral weight from the FB to the upper and lower bands. We show that all the correlation driven insulating phases host edge modes with linearly dispersing bands along with a FB passing through the Dirac point, exhibiting that the topological nature of the bulk band structure remains intact in presence of strong correlation. Furthermore, in the limiting case of $U$ introduced only on one sublattice where $lambda=0$, we show that the Lieb lattice can support mixed edge modes containing contributions from both spinons and electrons, in contrast to purely spinon edge modes arising in the topological Mott insulator.
We propose the concept of hybridization-switching induced Mott transition which is relevant to a broad class of ABO$_3$ perovskite materials including BiNiO$_3$ and PbCrO$_3$ which feature extended $6s$ orbitals on the A-site cation (Bi or Pb), and A
-O covalency induced ligand holes. Using {it ab initio} electronic structure and slave rotor theory calculations, we show that such systems exhibit a breathing phonon driven A-site to oxygen hybridization-wave instability which conspires with strong correlations on the B-site transition metal ion (Ni or Cr) to induce a Mott insulator. These Mott insulators with active A-site orbitals are shown to undergo a pressure induced insulator to metal transition accompanied by a colossal volume collapse due to ligand hybridization switching.
We study a model for the metal-insulator (MI) transition in the rare-earth nickelates RNiO$_3$, based upon a negative charge transfer energy and coupling to a rock-salt like lattice distortion of the NiO$_6$ octahedra. Using exact diagonalization and
the Hartree-Fock approximation we demonstrate that electrons couple strongly to these distortions. For small distortions the system is metallic, with ground state of predominantly $d^8ligand$ character, where $ligand$ denotes a ligand hole. For sufficiently large distortions ($delta d_{rm Ni-O} sim 0.05 - 0.10AA$), however, a gap opens at the Fermi energy as the system enters a periodically distorted state alternating along the three crystallographic axes, with $(d^8ligand^2)_{S=0}(d^8)_{S=1}$ character, where $S$ is the total spin. Thus the MI transition may be viewed as being driven by an internal volume collapse where the NiO$_6$ octahedra with two ligand holes shrink around their central Ni, while the remaining octahedra expand accordingly, resulting in the ($1/2,1/2,1/2$) superstructure observed in x-ray diffraction in the insulating phase. This insulating state is an example of a new type of charge ordering achieved without any actual movement of the charge.
We present a comprehensive theory of the temperature- and disorder-dependence of half-metallic ferrimagnetism in the double perovskite Sr$_2$FeMoO$_6$ (SFMO) with $T_c$ above room temperature. We show that the magnetization $M(T)$ and conduction elec
tron polarization $P(T)$ are both proportional to the magnetization $M_S(T)$ of localized Fe spins. We derive and validate an effective spin Hamiltonian, amenable to large-scale three-dimensional simulations. We show how $M(T)$ and $T_c$ are affected by disorder, ubiquitous in these materials. We suggest a way to enhance $T_c$ in SFMO without sacrificing polarization.
