An addition spectral analysis on a finite cluster from the double-layered lattice model, which has been introduced to describe quantum dot arrays under an external electric field perpendicular to the array, is presented. When the density of electrons is near to quarter-filled, we found a new type of Mott transition, in which the metal-insulator transition goes through a heavy-electron phase. In this new Mott transition, the Mott insulating state becomes unstable because Gibbs states having more pairs of electrons are favored as well as the Mott insulating state, resulting in an enhancement of electron-density fluctuation.
The Mott metal-insulator transition induced by an external electric field is discussed based on an analysis of a double-layered two-dimensional lattice model. A sharp transition between a metallic phase with the antiferromagnetic order and a Mott insulating phase is found to be driven by the voltage difference between the two layers. A sharp metal-insulator transition is transformed to a smooth metal-insulator transition by a change in the coupling between sites This model is applicable to a Mott transition in a two-dimensional array of very small quantum dots whose shape is asymmetric in the direction perpendicular to the substrate. \textcopyright{} 1996 The American Physical Society.
The ground-state properties of a paramagnetic Mott insulator at half-filling are investigated in the presence of an external electric field using the inhomogeneous Gutzwiller approximation for a single-band Hubbard model in a slab geometry. We find that the metal-insulator transition is shifted toward higher Hubbard repulsions by applying an electric field perpendicular to the slab. The main reason is the accumulation of charges near the surface. The spatial distribution of site-dependent quasiparticle weight shows that it is maximal in a few layers beneath the surface, while the central sites where the field is screened have a very low quasiparticle weight. Our results show that above a critical-field value, states near the surface will be metallic, while the bulk quasiparticle weight is extremely suppressed but never vanishing, even for large Hubbard repulsions above the bulk zero-field critical value. Below the critical-field value, our results hint toward an insulating state in which the electric field is totally screened and the slab is again at half-filling.
We investigate the metal-to-insulator phase transition driven by the density-density electronic interaction in the quarter-filled model on a cubic lattice with two orbitals split by a crystal field. We show that a systematic consideration of the non-local collective electronic fluctuations strongly affects the picture of the phase transition provided by the dynamical mean field theory. Our calculations reveal the appearance of metallic and Mott insulating states characterised by the same density but different values of the chemical potential, which is missing in the local approximation to electronic correlations. We find that the region of concomitant metastability of these two solutions is remarkably broad in terms of the interaction strength. It starts at a critical value of the interaction slightly larger than the bandwidth and extends to more than twice the bandwidth, where the two solutions merge into a Mott insulating phase. Our results illustrate that non-local correlations can have crucial consequences on the electronic properties in the strongly correlated regime of the simplest multi-orbital systems.
Strong correlations effects, which are often associated to the approach to a Mott insulating state, in some cases may be observed even far from half filling. This typically happens whenever the intersite Coulomb repulsion induces a tendency toward charge ordering, an effect that confines the electrons, and in turn favors local moment formation, i.e., Mott localization. A distinct intermediate regime then emerges as a precursor of such a Wigner-Mott transition, which is characterized by both charge and spin correlations, displaying large mass enhancements and strong renormalizations of other Fermi-liquid parameters. Here we present a careful study of a quarter-filled extended Hubbard model---a simple example where such physics can be studied in detail, and discuss its relevance for the understanding of the phenomenology of low-density two-dimensional electron gases.
Coulomb repulsion between electrons moving on a frustrated lattice can give rise, at simple commensurate electronic densities, to exotic insulating phases of matter. Such a phenomenon is illustrated using an extended $t\text{\ensuremath{-}}J$ model on a planar pyrochlore lattice for which the work on the quarter-filled case [D. Poilblanc et al., Phys. Rev. B 75, 220503 (2007)] is complemented and extended to
1∕8 and
3∕8 fillings. The location of the metal-insulator transition as a function of the Coulomb repulsion is shown to depend strongly on the sign of the hopping. Quite generally, the metal-insulator transition is characterized by lattice symmetry breaking but the nature of the insulating Mott state is more complex than a simple charge density wave. Indeed, in the limit of large Coulomb repulsion, the physics can be described in the framework of (extended) quantum fully packed loop or dimer models carrying extra spin degrees of freedom. Various diagonal and off-diagonal plaquette correlation functions are computed and the low-energy spectra are analyzed in detail in order to characterize the nature of the insulating phases. We provide evidence that, as for an electronic density of
n=1∕2 (quarter filling), the system at
n=1∕4 or
n=3∕4 exhibits also plaquette order by forming a (lattice rotationally invariant) resonant singlet pair crystal, although with a quadrupling of the lattice unit cell (instead of a doubling for
n=1∕2) and a fourfold degenerate ground state. Interestingly, qualitative differences with the bosonic analog (e.g., known to exhibit columnar order at
n=1∕4) emphasize the important role of the spin degrees of freedom in, e.g., stabilizing plaquette phases with respect to rotational symmetry-breaking phases.