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Register a new userMott transition in two-band fermion model with on-site Coulomb repulsion
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Authors
Igor N.Karnaukhov
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We provide analytical and numerical solution of the two band fermion model with on-site Coulomb at half filling. In limiting cases for generate bands and one flat band, the model reduces to the Hubbard and Falicov-Kimball models, respectively. We have shown that the insulator state emerges at half filling due to hybridization of fermions of different bands with momenta k and k$+pi$. Such hybridization breaks the conservation of the number of particles in each band, the Mott transition is a consequence of spontaneous symmetry breaking. A gap in the spectrum is calculated depending on the magnitude of on-site Coulomb repulsion and the width of the band for the chain, as well as for square and cubic lattices. The proposed approach allows us to describe the formation of the gap in the fermion spectra in the Hubbard and Falicov-Kimball models within the framework of the same mechanism for an arbitrary dimension of the system.
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In the framework of mean field approach, we study topological Mott transition in a two band model of spinless fermions on a square lattice at half filling. We consider the combined effects of the on-site Coulomb repulsion and the spin-orbit Rashba coupling. The spin-orbit Rashba coupling leads to a distinct phase of matter, the topological semimetal. We are talking about a new type of phase transition between the non-topological insulator state and topological semimetal state. New phase state is characterized by the zero energy Majorana states, which there are in defined region of the wave vectors and are localized at the boundaries of the sample. The zero energy Majorana states are dispersionless (they can be considered as flat bands), the Chern number and Hall conductance are equal to zero (note in two dimensional model).(note in two dimensional model).
While defects such as oxygen vacancies in correlated materials can modify their electronic properties dramatically, understanding the microscopic origin of electronic correlations in materials with defects has been elusive. Lanthanum nickelate with oxygen vacancies, LaNiO$_{3-x}$, exhibits the metal-to-insulator transition as the oxygen vacancy level $x$ increases from the stoichiometric LaNiO$_3$. In particular, LaNiO$_{2.5}$ exhibits a paramagnetic insulating phase, also stabilizing an antiferromagnetic state below $T_Nsimeq152$K. Here, we study the electronic structure and energetics of LaNiO$_{3-x}$ using first-principles. We find that LaNiO$_{2.5}$ stabilizes a vacancy-ordered structure with an insulating ground state and the nature of the insulating phase is a site-selective paramagnetic Mott state as obtained using density functional theory plus dynamical mean field theory (DFT+DMFT). The Ni octahedron site develops a Mott insulating state with strong correlations as the Ni $e_g$ orbital is half-filled while the Ni square-planar site with apical oxygen vacancies becomes a band insulator. Our oxygen vacancy results can not be explained by the pure change of the Ni oxidation state alone within the rigid band shift approximation. Our DFT+DMFT density of states explains that the peak splitting of unoccupied states in LaNiO$_{3-x}$ measured by the experimental X-ray absorption spectra originates from two nonequivalent Ni ions in the vacancy-ordered structure.
Strong correlation effects, such as a dramatic increase in the effective mass of the carriers of electricity, recently observed in the low density electron gas have provided spectacular support for the existence of a sharp metal-insulator transitions in dilute two dimensional electron gases. Here we show that strong correlations, normally expected only for narrow integer filled bands, can be effectively enhanced even far away from integer filling, due to incipient charge ordering driven by non-local Coulomb interactions. This general mechanism is illustrated by solving an extended Hubbard model using dynamical mean-field theory. Our findings account for the key aspects of the experimental phase diagram, and reconcile the early view points of Wigner and Mott. The interplay of short range charge order and local correlations should result in a three peak structure in the spectral function of the electrons which should be observable in tunneling and optical spectroscopy.
We focus our quantitative analysis on the stability of the insulator state in the Hubbard model at a half-filling. Taking into account large-scale fluctuations (with a long relaxation time) of the on-site Coulomb repulsion, we consider the possibility of realizing a stabile state which is characterized by pairing for electrons. The pairing mechanism is as follows: due to fluctuations of on-site repulsion of electrons, holes, as excited states, are formed electron pairs. The bare values of on-site Coulomb repulsion and its fluctuations, for which the states with electron pairing are stable, are calculated. The proposed pairing mechanism is to some extent similar to the formation of a localized moment in the Wolf model. The calculations were performed for the chain, as well as square and cubic lattices.
Two-dimensional materials can be strongly influenced by their surroundings. A dielectric environment screens and reduces the Coulomb interaction between electrons in the two-dimensional material. Since the Coulomb interaction is responsible for the insulating state of Mott materials, dielectric screening provides direct access to the Mottness. Our many-body calculations reveal the spectroscopic fingerprints of Coulomb engineering. We demonstrate eV-scale changes to the position of the Hubbard bands and show a Coulomb engineered insulator-to-metal transition. Based on this theoretical analysis, we discuss prerequisites for an effective experimental realization of Coulomb engineering.
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