In this thesis we describe a new theoretical approach to the problem of non-Fermi liquid behavior in heavy fermion systems. For almost forty years our comprehension of the metallic behavior in many materials has been founded on the Landau physical intuition about interacting Fermi systems [6, 69]. The idea of Landau, that interacting fermions could be regarded as free particles with renormalized parameters, is at the basis of the standard picture of the solids in terms of single independent electrons delocalized throughout the systems. The extraordinary success of this scenario is demonstrated by the impressive number of predictions and results, on which has root a large part of the actual technology. The Fermi-liquid concept has been also extended to systems showing a strong electronelectron interaction, i.e. strongly correlated electrons systems. Under suitable conditions the low temperature metallic properties of these systems can be interpreted in terms of renormalized quasiparticles. Nevertheless, recent experiments on some strongly correlated materials have shown remarkable deviations from the Fermi liquid predictions concerning different physical observables, such as specific heat C, resistivity ρ or susceptibility χ [94]. The theoretical understanding of the breakdown of the Fermi liquid paradigm observed heavy fermion systems or in high Tc superconductors is one of the open challenges in the correlated electrons physics. In this thesiswe shall showthat a new approach to the heavy fermions physics can be based on the DMFT solution of one of the canonical model of this area, namely the periodic Anderson model. In particular we demonstrate that, contrary to conventional expectations, a non-Fermi liquid state is readily obtained from this model within the DMFT framework. In agreement with the quantum criticality scenario, this novel NFL state is located in the neighborhood of a quantum phase transition, but unlike the standard quantum criticality scenario sketched before, the relevant quantum transition here is a Mott transition. Thus, the present study sheds a different light onto the NFL problem, showing that the coupling to long wavelength magnetic fluctuations (absent in DMFT) is not a prerequisite for the realization of a NFL scenario. Local temporalmagnetic fluctuations alone can provide sufficient scattering to produce an incoherent metallic state. The presence of such large local magnetic fluctuations in ourmodel has origin in the competition between magnetic interactions, namely the super-exchange antiferromagnetic interaction between the correlated electrons and the ferromagnetic interaction indirectly driven by the delocalization of the doped charges. Thus, we are able to obtain a DMFT description of the non-Fermi liquid phase in heavy fermion systems which is based on the proximity to a Mott point, i.e. Mottness scenario. Our study shows that the PAM, solved within DMFT, may be considered as a “bare bones” or minimal approach able to capture the physical scenario for the formation of a NFL state and that is in qualitative agreement with some observed phenomenology in heavy fermion systems. The entire thesis is structured as follows. • In the first chapter we review briefly the Landau theory of Fermi liquid and we give an overview on the heavy fermion phenomenology under both the theoretical and the experimental point of view. In particular, we present briefly some experimental evidences for the non-Fermi liquid phase in heavy fermions materials. Finally we discuss the main theoretical ideas proposed to explain the breakdown of the Fermi liquid paradigm. • In the second chapterwe introduce the theoretical tool used throughout this thesis, namely the DMFT. We derive the basic equations of the theory, step by step comparing with the well known classical mean-field theory (reviewed in the first part of the same chapter). An overview of the main techniques used to solve the DMFT equations is presented at the end of the chapter. • In the third chapter we introduce the periodic Anderson model. After having studied the solvable limits of the model we proceed by deriving the related DMFT equations and briefly discuss the algorithm used to obtain their solution. Next, we illustrate the derivation of the internal energy expression for the PAMin the framework of DMFT. This will be used later on to obtain the thermodynamical properties of the model. Finally, we extend the DMFT equations to deal with long range magnetically ordered phases. • In the fourth chapter we discuss the various parameter regimes of the model respect to the so-called ZSA diagram. We will demonstrate numerically the existence of a Mott insulating state for large values of the correlation, in two physically relevant regimes. Then we will study the Mott metal-insulator transitions driven by doping. In particular we show the existence of two different transition scenarios, each of which will be discussed. One of the two transitions will constitute the framework for the derivation of the Mottness scenario, that is the subject of the next chapter. • In the fifth chapter we shall demonstrate the existence of a non-Fermi liquid state in the neighborhood of a Mott point. Then,we showthe existence of a crossover regime towards a Fermi liquid phase for temperatures exponentially small in the doping. This coherence temperature scale is estimated and discussed in terms of the exhaustion problem [68, 67]. Next, we study the magnetic properties of the non-Fermi liquid regime. The main finding being the stability of this phase respect to the magnetic order. We present a study of the thermodynamical properties of the system, such as entropy of specific heat, finding for this latter remarkable evidences of logarithmic divergences, in agreement with experimental observations [94]. Finally we shall summarize the results in two phase diagrams that are in qualitatively accord with the observed phenomenology of heavy fermions systems.

Amaricci, A. (2009). Mottness scenario for the non-Fermi liquid phase in heavy fermions.

Mottness scenario for the non-Fermi liquid phase in heavy fermions

AMARICCI, ADRIANO
2009-04-30

Abstract

In this thesis we describe a new theoretical approach to the problem of non-Fermi liquid behavior in heavy fermion systems. For almost forty years our comprehension of the metallic behavior in many materials has been founded on the Landau physical intuition about interacting Fermi systems [6, 69]. The idea of Landau, that interacting fermions could be regarded as free particles with renormalized parameters, is at the basis of the standard picture of the solids in terms of single independent electrons delocalized throughout the systems. The extraordinary success of this scenario is demonstrated by the impressive number of predictions and results, on which has root a large part of the actual technology. The Fermi-liquid concept has been also extended to systems showing a strong electronelectron interaction, i.e. strongly correlated electrons systems. Under suitable conditions the low temperature metallic properties of these systems can be interpreted in terms of renormalized quasiparticles. Nevertheless, recent experiments on some strongly correlated materials have shown remarkable deviations from the Fermi liquid predictions concerning different physical observables, such as specific heat C, resistivity ρ or susceptibility χ [94]. The theoretical understanding of the breakdown of the Fermi liquid paradigm observed heavy fermion systems or in high Tc superconductors is one of the open challenges in the correlated electrons physics. In this thesiswe shall showthat a new approach to the heavy fermions physics can be based on the DMFT solution of one of the canonical model of this area, namely the periodic Anderson model. In particular we demonstrate that, contrary to conventional expectations, a non-Fermi liquid state is readily obtained from this model within the DMFT framework. In agreement with the quantum criticality scenario, this novel NFL state is located in the neighborhood of a quantum phase transition, but unlike the standard quantum criticality scenario sketched before, the relevant quantum transition here is a Mott transition. Thus, the present study sheds a different light onto the NFL problem, showing that the coupling to long wavelength magnetic fluctuations (absent in DMFT) is not a prerequisite for the realization of a NFL scenario. Local temporalmagnetic fluctuations alone can provide sufficient scattering to produce an incoherent metallic state. The presence of such large local magnetic fluctuations in ourmodel has origin in the competition between magnetic interactions, namely the super-exchange antiferromagnetic interaction between the correlated electrons and the ferromagnetic interaction indirectly driven by the delocalization of the doped charges. Thus, we are able to obtain a DMFT description of the non-Fermi liquid phase in heavy fermion systems which is based on the proximity to a Mott point, i.e. Mottness scenario. Our study shows that the PAM, solved within DMFT, may be considered as a “bare bones” or minimal approach able to capture the physical scenario for the formation of a NFL state and that is in qualitative agreement with some observed phenomenology in heavy fermion systems. The entire thesis is structured as follows. • In the first chapter we review briefly the Landau theory of Fermi liquid and we give an overview on the heavy fermion phenomenology under both the theoretical and the experimental point of view. In particular, we present briefly some experimental evidences for the non-Fermi liquid phase in heavy fermions materials. Finally we discuss the main theoretical ideas proposed to explain the breakdown of the Fermi liquid paradigm. • In the second chapterwe introduce the theoretical tool used throughout this thesis, namely the DMFT. We derive the basic equations of the theory, step by step comparing with the well known classical mean-field theory (reviewed in the first part of the same chapter). An overview of the main techniques used to solve the DMFT equations is presented at the end of the chapter. • In the third chapter we introduce the periodic Anderson model. After having studied the solvable limits of the model we proceed by deriving the related DMFT equations and briefly discuss the algorithm used to obtain their solution. Next, we illustrate the derivation of the internal energy expression for the PAMin the framework of DMFT. This will be used later on to obtain the thermodynamical properties of the model. Finally, we extend the DMFT equations to deal with long range magnetically ordered phases. • In the fourth chapter we discuss the various parameter regimes of the model respect to the so-called ZSA diagram. We will demonstrate numerically the existence of a Mott insulating state for large values of the correlation, in two physically relevant regimes. Then we will study the Mott metal-insulator transitions driven by doping. In particular we show the existence of two different transition scenarios, each of which will be discussed. One of the two transitions will constitute the framework for the derivation of the Mottness scenario, that is the subject of the next chapter. • In the fifth chapter we shall demonstrate the existence of a non-Fermi liquid state in the neighborhood of a Mott point. Then,we showthe existence of a crossover regime towards a Fermi liquid phase for temperatures exponentially small in the doping. This coherence temperature scale is estimated and discussed in terms of the exhaustion problem [68, 67]. Next, we study the magnetic properties of the non-Fermi liquid regime. The main finding being the stability of this phase respect to the magnetic order. We present a study of the thermodynamical properties of the system, such as entropy of specific heat, finding for this latter remarkable evidences of logarithmic divergences, in agreement with experimental observations [94]. Finally we shall summarize the results in two phase diagrams that are in qualitatively accord with the observed phenomenology of heavy fermions systems.
A.A. 2008/2009
Fisica
20.
Settore FIS/03 - Fisica della Materia
English
Tesi di dottorato
Amaricci, A. (2009). Mottness scenario for the non-Fermi liquid phase in heavy fermions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/879
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