We study the spinless and spinful extended Hubbard models with repulsive interactions on kagome decorated honeycomb (star) lattice. Using Hartree-Fock mean-field theory, we show that interaction-driven insulating phases nontrivial topological invariants (Chern number or ${Z}_{2}$ invariant) exist for an experimentally reasonable range of parameters. These occur at filling fractions which involve either Dirac points quadratic band crossing in noninteracting limit. present comprehensive phase...

Topological band insulators which are dynamically generated by electron-electron interactions have been theoretically proposed in two- and three-dimensional lattice models. We present evidence that the two-dimensional version can be stabilized digital (111) heterostructures of transition-metal oxides as a result purely local interactions. The topological phases accompanied spontaneous ordering complex orbitals we discuss their stability with respect to Hund's rule coupling, Jahn-Teller...

We provide a self-consistent mean-field framework to study the effect of strong interactions in quantum spin Hall insulator on honeycomb lattice. identify an exotic phase for large spin-orbit coupling and intermediate Hubbard interaction. This is gapped does not break any symmetry. Instead, we find fourfold topological degeneracy ground state torus fractionalized excitations with semionic mutual braiding statistics. Moreover, argue that it has gapless edge modes protected by time-reversal...

The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\ifmmode\times\else\texttimes\fi{}2$ Dirac Hamiltonians are discussed. In one dimension, the function measures charge-polarization between Wannier states at different positions, while two dimensions it itinerant-circulation states. is nonzero both topologically trivial and nontrivial states, allows us extract a length that diverges transitions. curvature defines invariants...

We review a representation of Hubbard-like models that is based on auxiliary pseudospin variables. These pseudospins refer to the local charge modulo two in original model and display ${\mathsf{Z}}_{2}$ gauge freedom. discuss associated mean-field theory variety different contexts which are related problem interaction-driven metal-insulator transition at half-filling including Fermi surface deformation spectral features beyond approximation. Notably, level, Hubbard bands derived from...

The electronic structure of a LaNiO${}_{3}$ bilayer grown along the [111] direction and confined between insulating layers LaAlO${}_{3}$ is theoretically investigated using combination first-principles calculations effective multiorbital lattice models. local density approximation (LDA) band well reproduced by tight-binding model for Ni ${e}_{g}$ orbitals defined on buckled honeycomb lattice. We highlight peculiar properties this model, which include almost flat bands as linear quadratic...

We study a two-dimensional system of spin-polarized fermions on the kagome lattice at filling fraction $f=1/3$ interacting through nearest-neighbor interaction $V$. Above critical strength ${V}_{c}$ charge-density wave with broken ${Z}_{3}$ symmetry is stabilized. Using unrestricted mean-field approximation, we present several arguments showing that elementary topological point defects in order parameter bind fractional charge. Our analysis makes use two appealing properties model: (i) For...

We investigate the electronic structure induced by wedge-disclinations (conical singularities) in a honeycomb lattice model realizing Chern numbers $\gamma=\pm 1$. establish correspondence between bound state of (i) an isolated $\Phi_0/2$-flux, (ii) pentagon $(n=1)$ or heptagon $(n=-1)$ defect with external flux magnitude $n\gamma \Phi_0/4$ through center and (iii) square octagon without flux, where $\Phi_0=h/e$ is quantum. Due to above correspondence, existence states disclinations robust...

We construct a lattice model for cubic Kondo insulator consisting of one spin-degenerate $d$ and $f$ orbital at each site. The odd-parity hybridization between the two orbitals permits us to obtain various trivial topological insulating phases, which we classify in presence symmetry. In particular, depending on choice our parameters, find strong phase with band inversion $X$ point, modeling situation potentially realized ${\mathrm{SmB}}_{6}$, crystalline ${\mathbb{Z}}_{2}$ indices but...

We show that the decorated honeycomb lattice supports a number of topological insulating phases with non-trivial Z_2 invariant and time-reversal symmetry protected gapless edge modes. investigate stability these respect to various breaking perturbations demonstrate connection recently discovered exactly solvable S=1/2 chiral spin liquid model [Phys. Rev. Lett. 99, 247203 (2007)] non-Abelian Abelian excitations on same lattice. Our work highlights relationship between band insulators...

We theoretically study a multi-band Hubbard model of pyrochlore oxides the form A$_2$B$_2$O$_7$, where B is heavy transition metal ion with strong spin-orbit coupling, in thin film geometry orientated along [111] direction. Along this direction, lattice consists alternating kagome and triangular planes ions. consider single layer, bilayer, two different trilayers. As function strength direct indirect $d$-orbital hopping, band filling, we identify number scenarios non-interacting...

We theoretically investigate the influence of lattice distortion effects on possible topological phases in (LaNiO${}_{3}$)${}_{2}$/(LaAlO${}_{3}$)${}_{N}$ heterostructures grown along [111] direction. At Hartree-Fock level, originate from an interaction-generated effective spin-orbit coupling that opens a gap band structure. For unstrained system, there is quadratic touching at $\ensuremath{\Gamma}$ point Fermi energy for spin-unpolarized electrons and Dirac points K, K${}^{\ensuremath{'}}$...

The recent discovery of topological Kondo insulators has triggered renewed interest in the well-known insulator samarium hexaboride, which is hypothesized to belong this family. In Letter, we study spin texture topologically protected surface states such a insulator. particular, derive close relationships between (i) form hybridization matrix at certain high-symmetry points, (ii) mirror Chern numbers system, and (iii) observable states. way, robust classification their surface-state...

The experimental investigation of quantum phases in optical lattice systems provides major challenges. Recently, dynamical generation double occupancy via modulation the hopping amplitude $t$ has been used to characterize strongly correlated phase fermionic atoms. Here, we want validate this technique with a theoretical study driven Hubbard model using analytic methods. We find that conclusive evidence for Mott can be inferred from such measurement, provided sufficiently low temperatures...

We study the effect of electron-electron interactions in a spinful Chern insulator. For weak on-site repulsive at half-filling, system is weakly correlated insulator adiabatically connected to noninteracting ground state, while limit infinitely strong repulsion described by an effective spin model recently predicted exhibit chiral liquid state. In regime large but finite repulsion, we find exotic gapped phase with characteristics partaking both and liquid. This has integer quantized Hall...

Most of the previously suggested scenarios for realization Weyl semimetal on a pyrochlore lattice require breaking time-reversal symmetry. In this study authors show that spontaneous deformations crystal break inversion symmetry can stabilize phase as well. They demonstrate in temperature-elasticity diagram shows reentrant behavior.

We study the superfluid and insulating phases of interacting bosons on triangular lattice with an inverted dispersion, corresponding to frustrated hopping between sites. The resulting single-particle dispersion has multiple minima at nonzero wave vectors in momentum space, contrast unique zero-wave-vector minimum unfrustrated problem. As a consequence, phase is unstable against developing additional chiral order that breaks time-reversal ($\mathcal{T}$) parity ($\mathcal{P}$) symmetries by...

The unusual electronic properties of the quantum spin Hall or Chern insulator become manifest in form robust edge states when samples with boundaries are studied. In this work, we ask if and how topologically nontrivial structure these two-dimensional systems can be passed on to their zero-dimensional relatives, namely, fullerenes other closed-cage molecules. To address question, study Haldane's honeycomb lattice model polyhedral nanosurfaces. We find that for sufficiently large surfaces,...

Lattices with a basis can host crystallographic defects which share the same topological charge (e.g.~the Burgers vector $\vec b$ of dislocation) but differ in their microscopic structure core. We demonstrate that insulators particle-hole symmetry and an odd number orbitals per site, details drastically affect electronic structure: modifications create or annihilate non-trivial bound states associated fractional charge. show this observation is related to behavior end modes dimerized chain...

We present aspects of strong electron correlation in a model BI/M/BI heterostructure where BI is band insulator and M can be tuned from metal to Mott by varying the on-site repulsion. An effective one-dimensional Schroedinger equation for low-energy part derived framework Kotliar-Ruckenstein slave-boson mean-field theory solved self-consistently wide range interaction strength width sandwiched material M. In strongly interacting limit coherent quasiparticles responsible metallic behavior are...