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Physics of the Solid State

Excitonic metal–insulator phase transition of the Mott type in compressed calcium

T. O. Voronkova, A. M. Sarry, M. F. Sarry, S. G. Skidan

Published May 1, 2017• 0 citations

Abstract

It has been experimentally found that, under the static compression of a calcium crystal at room temperature, it undergoes a series of structural phase transitions: face-centered cubic lattice → body-centered cubic lattice → simple cubic lattice. It has been decided to investigate precisely the simple cubic lattice (because it is an alternative lattice) with the aim of elucidating the possibility of the existence of other (nonstructural) phase transitions in it by using for this purpose the Hubbard model for electrons with half-filled ns-bands and preliminarily transforming the initial electronic system into an electron–hole system by means of the known Shiba operators (applicable only to alternative lattices). This transformation leads to the fact that, in the new system of fermions, instead of the former repulsion, there is an attraction between electrons and holes. Elementary excitations of this new system are bound boson pairs—excitons. This system of fermions has been quantitatively analyzed by jointly using the equation-of-motion method and the direct algebraic method. The numerical integration of the analytically exact transcendental equations derived from the first principles for alternative (one-, two-, and three-dimensional) lattices has demonstrated that, in systems of two-species (electrons + hole) fermions, temperature-induced metal–insulator phase transitions of the Mott type are actually possible. Moreover, all these crystals are in fact excitonic insulators. This conclusion is in complete agreement with the analytically exact calculations of the ground state of a one-dimensional crystal (with half-filled bands), which were performed by Lieb and Wu with the aim to find out the Mott insulator–metal transition of another type.

DOI: 10.1134/s1063783417050316

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We study the metal-insulator transition and magnetic ordering in the Hubbard model using the particle-hole mapping. This representation facilitates the exact solution of the half-filled band in the limit of high spin. We find that the two-dimensional Hubbard model has a charge-excitation gap at half filling for any finite U in the high-spin region on both the bipartite square lattice and the nonbipartite triangular lattice. We show, using the Kohn insulator criteria, that this bound-state phase is indeed insulating. Using the information from the single-pair solution, we construct a generalized BCS type of many-body wave function and derive the gap equation for lower-spin states. We find that in some cases, the system goes through a phase transition to become a metal as the total spin

{\mathit{S}}_{\mathit{z}}

is lowered.

We study the optical properties of an electron–hole two-band Hubbard model with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction U '. In the case of two types of correlated insulators at half filling, viz. , the Mott–Hubbard type and the biexciton type, interband linear absorption/gain spectra including excitonic effects are calculated analytically using two-site dynamical mean-field theory and ladder approximation. We show that an exciton-like peak structure emerges because of an “exciton” in the sea of correlated fermions when U ' is larger than a certain critical value. The binding energy of the photoinduced excitonic bound state and the spectral intensity are evaluated as a function of U '. The emergence and absence of the exciton-like peak suggests that there are two different insulating mechanisms in the Mott–Hubbard insulating state of the electron–hole system: one is attributable to only U and the other is attributable to both U and U '; the latter is called the excitonic Mott–Hubbard insulating state. The intrinsic difference of the mechanisms cannot be captured from only single-particle properties such as the density of states, but it appears clearly in optical properties reflecting two-particle correlations.

A detailed study of electronic phase transitions in the ionic Hubbard model at half filling is presented. Within the dynamical mean field approximation a series of transitions from the band insulator via a metallic state to a Mott--Hubbard insulating phase is found at intermediate values of the one-body potential $\ensuremath{\Delta}$ with increasing the Coulomb interaction

U

. We obtain a critical region in which the metallic phase disappears and a coexistence phase between the band and the Mott insulating state sets in. Our results are consistent with those obtained at low dimensions, thus they provide a concrete description for the charge degrees of freedom of the ionic Hubbard model.

We consider a one-dimensional two-band model of electrons on a lattice with equal nearest-neighbour hopping, an interband splitting Delta and a Hubbard-like repulsion U. The model is defined via the SU(4) generalization of Lieb and Wu's Bethe ansatz solution of the one-dimensional Hubbard model. At T=0 the model has a Mott metal-insulator transition at a critical value U c ( Delta ) for a band filling of exactly one electron per site. U c decreases with Delta , being zero if the excited-electron band is empty, and U c =2.981 when the bands are degenerate. We discuss the ground-state properties, the spectrum of elemental excitations, the specific heat and the magnetic susceptibility, in both the metallic and insulating phases, as a function of the crystal-field splitting for exactly one electron per site. There are four branches of elemental excitations: (i) charge excitations, (ii) crystalline-field excitations and (iii) two branches of spin waves. The Fermi velocity is finite in the metallic phase, diverges as the metal-insulator transition is approached from the metallic side and vanishes for the insulator. Each band contributes to the susceptibility with a term that is inversely proportional to the spin-wave velocity for that band. The low-temperature specific heat is proportional to T and to the sum of the inverses of the velocities of the four branches.