Spectral And Transport Properties Of FalicovKimball Related Models And Their Application To Manganites
Abstract
From the time of the unexpected discovery of the insulating nature of NiO by Verwey half a century ago, Oxide materials have continued to occupy the centre stage of condensed matter physics. The recent discovery of high temperature superconductivity in doped cuprates has given a new impetus to the study of the strongly correlated electron systems. Besides, the occurrence of Colossal MagnetoResistance (CMR) in doped rare earth manganite has also created renewed interest in these rather old systems. Understanding of the rich and complex phase diagram of these materials and their sensitivity to small perturbations e.g. external magnetic field of a few Tesla, temperature, change in isotope etc. are of great theoretical interest and also these materials have many potential technological applications. A common feature of all these oxide materials is that the transition metal ions have partially filled dshells. Unlike s and pelectrons which gives rise to hybridized Bloch states, the delectrons retain their atomic nature in a solid. This gives rise to strong Coulomb interaction among delectrons which may be comparable or more than its kinetic energy. The strong correlation effects are evident from the experimental fact that the undoped parent compounds are insulators rather than metals as suggested by band theory, which favours a metallic state for systems with one electron per unit cell since this gives rise to partially filled bands (and hence a metallic state). These insulators termed Mott insulators, arise solely due to strong electronelectron correlations as compared to the band insulators which arise due to complete filling of one electron bands thereby giving rise to a gap (band gap)in the excitation spectra. The delicate competition between the kinetic energy and the Coulomb energy for delectrons is broadly responsible for the wide variety of phenomena like Mott metalinsulator transition (MIT), magnetic transitions, charge ordering, orbital ordering, ferro/antiferroelectricity, and most interestingly the observation of high Tc superconductivity in doped cuprates. In this thesis we will restrict our interest to one such class of oxide materials, namely the doped rare earth manganites.
In Chapter 1 we give a brief overview of the structure and basic interactions present in the doped manganites. Also, in the same Chapter we give a brief introduction to the phenomenology of manganites, particularly its phase diagram in the doping and temperature plane and various experimental features, e.g. the wide variety of phase transitions and phenomena particularly the observation of CMR, charge ordering and incipient mesoscale phase separations etc.. Then we briefly introduce a recently proposed microscopic model which is believed to be a minimal model which, for the first time, includes the three most important interactions present in the manganites namely the following 1)coupling of the orbitally degenerate eg electrons to local lattice distortions of JahnTeller type which gives rise to two species of electrons. The one denoted by by ℓ is associated with JahnTeller effects and hence is localized whereas the other denoted by b is an extended state and propagates through the lattice. 2) The strong Hund’s couplingof ℓ and b electrons to the t2g core spin and 3) the strong Coulomb correlation between the two species of electrons. Additionally, the model includes a new doping dependent ferromagnetic exchange between the t2g core spins which can arise from “virtual double exchange” mechanism which will be discussed in great detail in Chapter 1 . Finally, we give a brief account on Dynamical Mean Field Theory (DMFT) and Numerical Renormalization Group (NRG) as an impurity solver for the single impurity problem arising under single site DMFT approximation.
In Chapter 2 we study the effect of intersite ℓ  b hybridization on the ‘ℓ  b’ model. The single impurity problem arising under DMFT approximation has close connection with the VigmanFinkelshtein (VF)model. Then we briefly introduce the VF model and bring out its close connection with the impurity problem. We consider both the particlehole symmetric as well as the U → ∞ particlehole asymmetric cases. We derive various spectral functions at T = 0K and discuss the nature of fixed points under various circumstances.
We explicitly show that for the particlehole symmetric case the Hamiltonian flows from Xray edge singularity fixed point to Free Electron fixed point under Renormalization Group transformation. This is evident from the spectral properties of the model. We write down the effective Hamiltonian at the free electron fixed point. For the particlehole asymmetric case the model flows from Xray edge singularity fixed point to Free Electron/Strong Coupling fixed point with additional potential scattering terms. We write down the effective Hamiltonian at this fixed point and derive various leading order deviations. We found all of them to be irrelevant in nature also most interestingly the quasiparticles describing the under lying Fermi liquid state are found to be asymptotically noninteracting. We also calculate the Fermi liquid parameter, z, by analyzing the energy level structure of a noninteracting Hamiltonian with effective renormalized parameter.
Also, we consider the case of ‘self consistent bath hybridization’ without ℓ  b hybridization for Bethe lattice with infinite coordination. Low energy qualitative features are found to be same but some of the high energy features get qualitatively modified.
In Chapter 3 we discuss the transport properties of doped manganites in the insulating phases and also the Hall effect in the metallic phase. In the ﬁrst part of this chapter we calculate the resistivity based on the ‘ℓ  b’model and try to fit it to the semiconducting form: ρ(T )= ρ0(T /T0)−nexp[Δ(T )/kBT ] and extract the “transport gap”, Δ(T ). This gap can be characterized in terms of the “spectral gap” which can be defined for the ℓ  b model. It is found that the transport gap in the paramagnetic phase can be characterized in terms of the near constant “spectral gap” in this phase whereas the same in the ferromagnetic phase can be characterized in terms of the zero temperature spectral gap. In the last part of this chapter we calculate the Hall resistivity (ρxy) of these materials in the metallic phase. Ρxy is found to be negative and linear in applied field quite consistent with the experimental findings but this fails to explain the positive linear Hall resistivity at low temperatures and its crossover as a function of field and temperature. We then present a reasonable explanation for this discrepancy and support it by calculating the Hall density of states for a two band “toy model” involving inter species hybridization.
In Chapter 4 we calculate the optical conductivity, σ(ω), in ℓ  b model. σ(ω) arises from two independent processes. One of the processes involves ‘b’ electrons only and termed as ‘b  b channel’ and this gives rise to a Drude peak in the low frequency region. another process termed as the ‘ℓ  b channel’ involves hopping of an ℓelectron to a neighbouring empty site and transforms into a ‘b’like state. This process gives rise to a broad midinfrared peak. The total conductivity is the sum of contributions from these two incoherent channels. Calculated σ(ω) for metallic systems shows lot of similarities with experimental observations particularly the temperature evolution of the midinfrared peak and the spectral weight transfer between the two peaks. But for the insulating systems the calculated optical conductivity showed trends similar to more recent experimental observations on some insulating systems (x =0.125) but contradicts with earlier experimental observations on some other insulating system (x =0.1).
Finally, in the concluding chapter, we summarize results from all the chapters and also sketch some possible future directions of investigations.
Collections
 Physics (PHY) [453]
Related items
Showing items related by title, author, creator and subject.

Phase Transitions And Magnetic Order In Multiferroic And Ferromagnetic Rare Earth Manganites
Harikrishnan, S (20110329)Recent findings of multiferroicity and magnetoelectric effects in rare earth manganites have fuelled research in this class of materials. These multiferroics can be structurally divided into two classes – orthorhombic and ... 
Spatially Resolved Studies Of Electronic Phase Separation And Microstructure Effects In Hole Dopped Manganites
Kar, Sohini (20100817)The main focus of this thesis is in understanding the role of phase separation and microstructure in determining the physical properties of manganites. We also aim to be able to tune certain material properties using ... 
Magnetization, Magnetotransport And Electron Magnetic Resonance Studies Of Doped Praseodymium And Bismuth Based Charge Ordered Manganites
Anuradha, K N (20100906)Studies on perovskite rare earth manganites of general formula R1xAxMnO3 (where R is a trivalent rare earth ion such as La3+, Pr3+ etc. and A is a divalent alkaline earth ion such as Ca2+, Sr2+, Ba2+, have been a very ...