Spectral and transport properties of low-dimensional mott-hubbard insulators and electronic conductors

Abstract

"Sem resumo feito pelo autor" The main goal of this thesis is the study of the many-electron problem in low-dimensional quantum liquids. In three-dimensional systems (3D) the electron-electron interaction can be treated with success by mean-field approximations, band theory or the Fermi-Liquid Theory [1, 2, 3, 4, 5]. The one-particle spectral function of a Fermi Liquid (FL) contains a coherent peak (the quasi-particle peak), which is well-defined for energies close to the Fermi level, followed by an incoherent structure at higher energies. Thus, the low-energy properties are essentially determined by the quasi-particle coherent part of the spectral function. In low-dimensinal systems, the effects of the electronic correlations axe qualitatively different and change completely the nature of the quantum problem relatively to the corresponding non-interacting problem. There exists a class of one-dimensional (1D) systems which are exactly solvable by the Bethe ansatz (BA) technique [6]. These systems show a completely incoherent one-particle spectral function and belong an universality class of 1D quantum liquids which was named Luttinger Liquid (LL) [7]. There are many open questions in what the problem of strongly correlated electronic systems is concerned. On the analytical side, this follows from the lack of exact solutions and of controlled approximations and from the difficulty in extracting physical information from the BA solution. On the numerical side, the problem arises both from the smallness of the systems that can be treated exactly and from the fermionic "sign" problem. The motivation of this thesis is a better understanding of the physical properties of low-dimensional materials where the effects of electronic correlations are expected to be particularly important. We will consider the Hubbard model [8, 9, 10], which is the simplest and standard model for the study of the effect of electronic correlations in a discrete lattice. The model contains two parameters the hopping kinetic integral t, which gives the probability amplitude for one electron to hop to a nearest neighbour site and the on-site Coulomb electronic repulsion integral U. We denote electronic density of the model by n. It is such that 0 < n < 2. In the strong coupling limit, i.e. when U >> t, the model can be mapped into the t — J model [11], where J is the antiferromagnetic (AF) exchange coupling between adjacent sites and is given, in second order perturbation theory, by J = 4t2/U. In Chapters 2-5 of this work we, will consider mainly the 1D Hubbard model. We will study its one-particle spectral properties, which distinguish the LL and FL like behaviours. The main motivation for this study is the recent and renewed experimental interest on the one-electron spectral properties of quasi 1D conductors and insulators [12, 13, 14, 15]. The symmetries of the model are easier to be identified within the pseudoparticle operational representation [16]. This basis is also often the most suitable for the extraction of the physical information contained in these symmetries. In this thesis we use symmetries of the 1D Hubbard model to extract important information on the energy dependence of the one-particle spectral function and associated density of states. These studies include energies in the range of the upper-Hubbard-band (UHB) [17] For instance, we find that the energy dependence of the one-particle density of states just above the UHB bottom edge is, for densities below half-filling, of power-law LL type. Since the experimental observation of the UHB requires inverse photoemission measurements, we suggest new experiments to be compared with our theoretical predictions. Luttinger Liquids show unusual properties relatively to FL's [18], such as (i) supression of the FL characteristic step at the Fermi level energy in the one-particle density of states, which in a LL is replaced by a power-law singularity with positive exponent and (ii) spin-charge separation, the original degrees of freedom of the electrons are decoupled into charge and spin elementary excitations called holons and spinons, respectively [19]. On the other hand, in Chapters 6-7, we will study charge transport properties associated with the metal-insulator transition, which is one of the most interesting and intricate phenomenon in the many-body theory. Materials can be grosso modo divided in conductors (metals) and insulators. An electronic system can, in principle, exhibit a transition from a conducting phase to an insulating phase by tuning some characteristic parameter. The metal-insulator transition [20, 21, 22, 23, 24] is still not completely understood, despite the progresses that has been dope during the last decades. Namely the development of new techniques for treating 1D many-fermion models, the application of renormalization group, scaling theory and the advances in the limit of largo dimensions. It should be mentioned, that a sharp qualitative distinction between a conductor and an insulator can only be made at temperature T = OK. Thus, the metal-insulator transtion is actually a quantum phase transition, i.e. a fundamental change in the ground state of the system [25], for which less is known if we compare with the achieved understanding of classical phase transitions. Even the search for an order parameter for the metal-insulator transition has not revealed fruitful and its consideration in terms of a Landau theory has only been recently been suggested [26]. The main reason of this slow progress is that several mechanisms such as electronic correlations (Mott transition [27]), disorder effects (Anderson transition [28]), Fermi surface magnetic instabilities (Slater transition [29]), phononic effects (Peierls transition [30]), band structure effects, structural transitions, pressure, temperature or doping can induce a metal-insulator transition and be present at the same time. The question whether the metal-insulator transition is a discontinuous first-order or a continuous second-order depends crucially on the mechanism which drives the transition. The Anderson metal-insulator transition occurs at a critical value of disorder that localizes electrons through quantum interference giving rise to a continuous second-order transtion at T = OK (amorphous alloys and doped semiconductors are experimental examples). The Mott metal-insulator transition usually gives rise to a discontinuous first-order transition at non-zero temperature. This is mainly due to the fact that strongly correlated systems have structural transitions coincident with the Mott transition driving the transition to be of first-order. This is the case of the typical strongly correlated compound V203 [31, 32]. An interesting compound is the also strongly electronic correlated chalcogenide doped. compound NiS2-.,Se,,, where a continuous transition at very low temperatures is observed by tuning the applied pressure, without the presence of a structural transition [33]. The main reason for the slow progress in the understanding of the Mott transition is of course the diffilculty of mastering the problem of strong correlations. In addition, the pure Mott transition is often masked by an antiferromagnetic instability of the metallic phase. The metal-insulator transition produced by electron correlations, when treated within the framework of the Hubbard modal, is known as the Mott-Hubbard transition. In this thesis, we will study the Mott-Hubbard transition at T = OK and at half filling n = 1 by means of variational wavefunctions. The metal-insulator transition is a key issue of general interest. In particular, the understanding of a doped Mott insulator is of great importance in the theory of high-temperature superconductors [34, 35] and more recently in the understanding of the properties of novel two-dimensional electronic systems in the presence of both interaction and disorder [36].