Diagrammatic perturbation theory based investigation of the mott transition physics

Abstract

The interaction driven metal-to-insulator transition, widely known as Mott transition, is still an open problem in electronic correlation physics. In this thesis, we use quantum many-body approaches within the framework of dynamical mean-field theory (DMFT) to understand issues related to the Mott transition. Specifically, diagrammatic perturbation theory based approximations have been made for the self-energy associated with the impurity problem in this context. We apply our approaches to the single band Hubbard model, which is a standard and simplest model to study Mott transition physics. One of our approximation for the self-energy is the iterated perturbation theory (IPT), where a second order diagram constructed using Hartree propagators is used as an ansatz for the self-energy in the particle-hole symmetric case. Though IPT has been extensively used earlier for the Hubbard model, here we develop an improved implementation that can capture the sharp features of the spectral function near the Mott transition. We use analytical approaches as well to predict the residue of the pole that arises in the selfenergy at the chemical potential in the Mott insulating and the coexistence regimes. We make successful comparison with pressure dependent resistivity iii experiments on Se-doped NiS2 and resistivity hysteresis found in V2O3 . We discuss the optical conductivity in great detail and point out an anomaly that arises in the specific heat calculation. The second approach, which underlies a major part of this thesis, is another diagrammatic approximation, known as the local moment approach (LMA) for the impurity solver within DMFT. The LMA considers a spinsymmetry broken mean field as its starting point in contrast to the Hartree limit used in IPT. The self-energy ansatz here incorporates spin-flip dynamics to all orders through random phase approximation (RPA). In order to restore the spin-independent Fermi liquid metallic phase, we impose the condition of adiabatic continuity to the non-interacting limit. With this approach, we study properties for the particle-hole symmetric and asymmetric cases both at zero and finite temperature. In the zero temperature symmetric case, we find Mott transition and coexistence regime, similar to what we have already seen in IPT (though values are different). In the metallic regime, apart from the Fermi liquid at very low frequencies, we find a strong correlation induced universal scaling regime which is very different from the renormalized noninteracting limit and extends all the way to infinity as we approach the Mott insulator. We find similar strong-coupling universality in the asymmetric and the finite temperature cases as well. We report the doping dependence of the spectra and compare that to our IPT results. Very interestingly, we find a large T-linear regime in the temperature dependence of resistivity along with presence of negligibly small T2-regime, specially in the vicinity of a doped Mott insulator. We show that this happens due to the marginal Fermi liquid nature of the self-energy that emerges from our theory. Thus we infer that, presence of local transverse spin-flip scattering can bring a possible scenario where one can indeed observe linear temperature dependence of resistivity extending over a decade or more (in temperature). This could be relevant for understanding the “normal” state of high temperature cuprate superconductors. The last chapter in this thesis deviates from the other chapters in terms of the techniques, but does conform to the theme of this thesis namely Mott transition physics. In this, we examine the out-of-equilibrium physics associated with the Mott transition, namely hysteresis and avalanches in the resistivity as observed in experiments on transition metal oxides. Since hysteresis is a non-equilibrium phenomenon involving inhomogeneities, the DMFT becomes inappropriate as it is a single-site equilibrium approach. Motivated by recent resistance experiments on VO2 thin films by Sharoni et al (2008), we formulate an approach that may produce the correct statistical behavior associated with the avalanche sizes in the resistance hysteresis experiments (e.g. device size effect, power law behavior). In our approach we use a mapping from the random-field Ising model to a resistor network model. By this scheme we find reasonable agreement with experiments. We also discuss possibilities to get more quantitative agreement and predict results (e.g. dependence of power law exponent on the contrast ratio) that can be verified in future experiments.