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Register a new userTwo Aspects of the Mott-Hubbard Transition in Cr-doped V_2O_3
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The combination of bandstructure theory in the local density approximation with dynamical mean field theory was recently successfully applied to V$_2$O$_3$ -- a material which undergoes the f amous Mott-Hubbard metal-insulator transition upon Cr doping. The aim of this sh ort paper is to emphasize two aspects of our recent results: (i) the filling of the Mott-Hubbard gap with increasing temperature, and (ii) the peculiarities of the Mott-Hubbard transition in this system which is not characterized by a diver gence of the effective mass for the $a_{1g}$-orbital.
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We have studied the impact of non-local electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -- irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.
Calculations employing the local density approximation combined with static and dynamical mean-field theories (LDA+U and LDA+DMFT) indicate that the metal-insulator transition observed at 32 GPa in paramagnetic LaMnO3 at room temperature is not a Mott-Hubbard transition, but is caused by orbital splitting of the majority-spin eg bands. For LaMnO3 to be insulating at pressures below 32 GPa, both on-site Coulomb repulsion and Jahn-Teller distortion are needed.
$V_2O_3$ has long been studied as a prototypical strongly correlated material. The difficulty in obtaining clean, well ordered surfaces, however, hindered the use of surface sensitive techniques to study its electronic structure. Here we show by mean of X-ray diffraction and electrical transport that thin films prepared by pulsed laser deposition can reproduce the functionality of bulk $V_2O_3$. The same films, when transferred in-situ, show an excellent surface quality as indicated by scanning tunnelling microscopy and low energy electron diffraction, representing a viable approach to study the metal-insulator transition (MIT) in $V_2O_3$ by means of angle-resolved photoemission spectroscopy. Combined, these two aspects pave the way for the use of $V_2O_3$ thin films in device-oriented heterostructures.
We consider the one-band Hubbard model on the square lattice by using variational and Greens function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction $U$, we can identify a hidden critical point $U_{rm Mott}$, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of $U$), where magnetism induces a potential energy gain, and a Mott insulator (at large values of $U$), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of $U_{rm Mott}$ has crucial consequences when doping the system: We observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above $U_{rm Mott}$, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above $U_{rm Mott}$ shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.
At the Mott transition, electron-electron interaction changes a metal, in which electrons are itinerant, to an insulator, in which electrons are localized. This phenomenon is central to quantum materials. Here we contribute to its understanding by studying the two-dimensional Hubbard model at finite temperature with plaquette cellular dynamical mean-field theory. We provide an exhaustive thermodynamic description of the correlation-driven Mott transition of the half-filled model by calculating pressure, charge compressibility, entropy, kinetic energy, potential energy and free energy across the first-order Mott transition and its high-temperature crossover (Widom line). The entropy is extracted from the Gibbs-Duhem relation and shows complex behavior near the transition, marked by discontinuous jumps at the first-order boundary, singular behavior at the Mott endpoint and inflections marking sharp variations in the supercritical region. The free energy allows us to identify the thermodynamic phase boundary, to discuss phases stability and metastability, and to touch upon nucleation and spinodal decomposition mechanisms for the transition. We complement this thermodynamic description of the Mott transition by an information-theoretic description. We achieve this by calculating the local entropy, which is a measure of entanglement, and the single-site total mutual information, which quantifies quantum and classical correlations. These information-theoretic measures exhibit characteristic behaviors that allow us to identify the first-order coexistence regions, the Mott critical endpoint and the crossovers along the Widom line in the supercritical region.
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