Slave rotor approach to exciton condensation in a two-band system.

We have studied exciton formation and condensation in an extended Falicov-Kimball model, going beyond the weak coupling approach, employing a semi-analytical technique: the slave-rotor mean-field theory (SRMF). In this essentially strong coupling theory, charge and spin (or orbital/pseudospin) degrees are treated as independent degrees of freedom, coupled by a local constraint. Using a two-site-extension of SRMF, we capture the effective many body scale beyond conventional mean-field theory. While the formation of excitons is favoured by the interband hybridization [Formula: see text], it is strongly influenced by the on-site Coulomb interaction [Formula: see text]. Beyond a critical hybridization, there is condensation of excitons, leading to a transition from a metal to an excitonic insulator phase. Moreover, the behaviour of excitonic averages differs from the usual Hartree-Fock mean-field theory. Low-[Formula: see text] results show that excitonic order parameter (Δ) is continuous across the transition both for single as well as two-site approximation, changing to weakly first order one at intermediate [Formula: see text] for the later. The large-[Formula: see text] limit shows a continuous transition for two-site analysis but remains first order in the single-site approximation. The slave rotor theory gives a mixed state of excitons and metal in both the analyses. We have also checked the effect of intersite correlation and localized band hopping on the exciton condensation.

Hofstadter butterfly in the Falicov-Kimball model on some finite 2D lattices.

Spinless, interacting electrons on a finite size triangular lattice moving in an extremely strong perpendicular magnetic field are studied in comparison to a square lattice. Using a Falicov-Kimball model, the effects of Coulomb correlation, magnetic field and finite system size on their energy spectrum are observed. Exact diagonalization and Monte Carlo simulation methods (based on a modified Metropolis algorithm) have been employed to examine the recursive structure of the Hofstadter spectrum in the presence of several electronic correlation strengths for different system sizes. It is possible to introduce a gap in the density of states even in the absence of electron correlation, which is anticipated as a metal to insulator transition driven by an orbital magnetic field. With further inclusion of the interaction, the gap in the spectrum is modified and in some cases the correlation is found to suppress extra states manifested by the finite size effects. At a certain flux, the opened gap due to magnetic field is reduced by the Coulomb interaction. An orbital current is calculated for both the square and the triangular lattice with and without electron correlation. In the non-interacting limit, the bulk current shows several patterns, while the edge current shows oscillations with magnetic flux. The oscillations persist in the interacting limit for the square lattice, but not for the triangular lattice.