Academic literature on the topic 'Anderson-Mott transition'

The Mott and the Anderson routes to localization have long been recognized as the two basic processes that can drive the metal–insulator transition (MIT). Theories separately describing each of these mechanisms were discussed long ago, but an accepted approach that can include both has remained elusive. The lack of any obvious static symmetry distinguishing the metal from the insulator poses another fundamental problem, since an appropriate static order parameter cannot be easily found. More recent work, however, has revisited the original arguments of Anderson and Mott, which stressed that the key diference between the metal end the insulator lies in the dynamics of the electron. This physical picture has suggested that the "typical" (geometrically averaged) escape rate [Formula: see text] from a given lattice site should be regarded as the proper dynamical order parameter for the MIT, one that can naturally describe both the Anderson and the Mott mechanism for localization. This article provides an overview of the recent results obtained from the corresponding Typical-Medium Theory, which provided new insight into the the two-fluid character of the Mott–Anderson transition.

A solvable model of d = 1 spinless fermions at half-filling which exhibits a Mott transition is studied in detail. Many response functions are computed: at zero and nonzero temperatures, in the insulating and metallic sites, at the transition, and at q ≃ 0, 2k F . Some quantities are computed exactly, others only upto a scale factor. Some results are old, but mentioned here for completeness. Some are rederived using new tools such as conformal invariance. The rest are new. Next, the effect of randomness on the Mott state is explored. It is found, on the basis of Imry-Ma type arguments that no matter how large the gap is, the Mott insulator turns into an Anderson insulator immediately.

We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder 1 c ss U= 2. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.

J’ai étudié la transition méta-isolant avec la théorie du champ moyen dynamique appliquée à deux Hamiltoniens largement employés pour décrire les systèmes d’électrons fortement corrélés : le modèle de Hubbard et le modèle d’Anderson périodique. Le scénario pour la transition dans le modèle de Hubbard a été passé en revue et l’analyse du spectre de photoémission près de la transition a été présentée en détail. La transition de Mott induite par le dopage dans le modèle d’Anderson périodique a été discutée par rapport à celle réalisée dans le modèle de Hubbard. Le résultat principal nous conduit à établir un scénario qualitativement différent pour les transitions induites par dopage avec des électrons ou avec des trous. Dans le premier cas, la transition est, comme attendue, similaire à la transition du premier ordre du modèle de Hubbard. Toutefois, dans le dernier cas, une transition du deuxième ordre a été trouvée. J’ai donc démontré que le scénario pour la transition de Mott du modèle de Hubbard n’est pas générique pour le modèle d’Anderson périodique
I study the Mott metal-insulator transition within the dynamical mean-field theory in two schematic Hamiltonians widely used to describe the strongly correlated electron systems : the Hubbard model and the periodic Anderson model. The scenario for the transition in the Hubbard model is reviewed and the analysis of the photoemission spectra near the transition is presented in detail. The doping driven Mott transition in the periodic Anderson model is discussed with respect to the one realized in the Hubbard model. The main finding is a qualitatively different scenario for electron or hole driven transitions. In the former case the transition is expectedly similar to the first order transition of the Hubbard model. However, in the latter case, a second order transition is found. Thus I demonstrate that the transition scenario of the Hubbard model is not generic for the periodic Anderson model

In this thesis we consider a variational wave function approach as a possible route to describe the competition between disorder and strong electron-electron interaction in two dimensions. In particular we aim to obtain a transparent and physically intuitive understanding of the competition between these two localizing forces within the simplest model where they both are active, namely the disordered Hubbard model at half filling and in a square lattice. Our approach is based on an approximate form of the ground-state wave function, which we believe contains the physically relevant ingredients for a correct description of both the Mott and the Anderson insulators, where electrons are localized by the Coulomb repulsion and by disorder, respectively. For strongly interacting fermionic systems, a standard variational wave function is constructed by a correlation term acting on a Slater determinant, the latter being an uncorrelated metallic state. Previous variational calculations showed that a long-range density-density correlation factor, so called Jastrow factor, is needed to correctly describe the Mott insulator [9]. This term, which is collective by definition, correlates spatially charge uctuations, thus preventing their free motion that would otherwise imply metallic conductance. For this reason, our variational wave function does include such a term. Anderson localization is instead mostly a matter of single-particle wave functions, hence it pertains to the uncorrelated Slater determinant which the Jastrow factor acts onto. We consider both the case in which we enforce paramagnetism in the wave function and the case in which we allow for magnetic ordering. Summarizing briefly our results, we find that, when the variational wave function is forced to be paramagnetic, the Anderson insulator to Mott insulator transition is continuous. This transition can be captured by studying several quantities. In particular, a novel one that we have identified and that is easily accessible variationally is the disconnected density-density fluctuation at long wavelength, defined by lim where ^nq is the Fourier transform of the charge density at momentum q, (...) denotes quantum average at fixed disorder and the overbar represents the average over disorder configurations. We find that Ndisc q!0 is everywhere finite in the Anderson insulator and vanishes critically at the Mott transition, staying zero in the Mott insulator. When magnetism is allowed and the hopping only connects nearest neighbor sites, upon increasing interaction the paramagnetic Anderson insulator first turns antiferromagnetic and finally the magnetic and compressible Anderson insulator gives way to an incompressible antiferromagnetic Mott insulator. The optimized uncorrelated Slater determinant is always found to be the eigenstate of a disordered non-interacting effective Hamiltonian, which suggests that the model is never metallic. Finally, when magnetism is frustrated by a next to nearest neighbor hopping, the overall sequence of phases does not change. However, the paramagnetic to magnetic transition within the Anderson insulator basin of stability turns first order. Indeed, within the magnetically ordered phase, we find many almost degenerate paramagnetic states with well defined local moments. This is suggestive of an emerging glassy behavior when the competition between disorder and strong correlation is maximum.

Cette thèse vise à étudier la stabilité des phases métalliques et isolantes en compétition dans les systèmes 2D 1T-VS2 et composés dérivés, Cu⅔V⅓V2S4 et Sr3V5S11. Pour atteindre cet objectif, nous avons développé et optimisé des voies ad hoc de synthèse à hautes pressions pour stabiliser les nouvelles phases sous forme de monocristal de haute qualité, qui nous permettrait d’étudier les propriétés électroniques et de transport. Un important résultat de notre étude est le contrôle de la concentration, x, des atomes interstitiels V situés entre les plans adjacents VS2 dans le système V1+xS2, qui est obtenu en variant la pression de synthèse. Cela nous a permis d’explorer le diagramme de phase T-x du système. Le résultat principal de cette étude est que la phase CDW observée dans la phase stoichiométrique (x = 0) disparait rapidement avec x, alors que les propriétés métalliques sont augmentées. Dans Cu⅔V⅓V2S4, la substitution partielle du V par Cu dans le site interstitiel change complètement le système en un fermion semi-lourd aux caractéristiques prononcées du liquide de Fermi jusqu’à ~ 20 K, où la transition de Kondo apparait. Ce phénomène inattendu dans les sulfures suggère que la force des corrélations électroniques dans ces composés peut être pilotée en variant simplement la nature chimique et la concentration de l’atome intercalé. La force modérée des corrélations dans Cu⅔V⅓V2S4 ouvre le chemin vers une description théorique fiable de la disparition du régime de liquide de Fermi. Les corrélations électroniques apparaissent importantes aussi pour piloter une phase isolante dans Sr3V5S11, qui devrait être un métal d’après la théorie conventionnelle de bande. Dans ce cas, les corrélations peuvent être augmentées par la dimensionnalité réduite créée par un large écartement des couches VS2 et par une modulation structurale 1D des couches. Des études supplémentaires pourront clarifier s’il s’agit d’un mécanisme d’Anderson de faible localisation qui contribue à la stabilisation d’un état isolant dans les plans pristine métalliques VS2
This thesis work aims at studying the stability of the metallic and insulating phases that compete in the two-dimensional 1T-VS2 system and related compounds, Cu⅔V⅓V2S4, and Sr3V5S11. We have developed and optimized ad hoc high-pressure synthesis routes in order to stabilize the above novel phases in the form of high-quality single crystals, which enabled us to reliably investigate their electronic and transport properties. An important achievement of our study is the control of the concentration, x, of interstitial V atoms located between adjacent VS2 planes in the V1+xS2 system, which is obtained by varying synthesis pressure. This has enabled us to explore the T-x phase diagram of the system. The main result of this study is that the CDW phase observed in the stoichiometric (x=0) phase quickly disappears with x, whilst the metallic properties are enhanced. In Cu⅔V⅓V2S4, the partial substitution of V for Cu in the interstitial site is found to completely change the system into a semi-heavy fermion with pronounced Fermi-liquid characteristics down to ~20 K, where a Kondo transition occurs. These unexpected phenomena in sulfides suggest that the strength of the electronic correlations in these compounds can be tuned by simply varying the chemical nature and concentration of the intercalant atom. The moderate strength of the correlations in Cu⅔V⅓V2S4 opens the way towards a reliable theoretical description of the breakdown of the Fermi liquid regime. Electronic correlations appear to be important also to drive an insulating phase in Sr3V5S11, which should be a metal within a conventional band picture. In this case, the correlations may be enhanced by the reduced dimensionality caused by a large spacing between VS2 layers and by a 1D structural modulation of the layers. Further studies may clarify whether the Anderson’s mechanism of weak localization contributes to the stabilization of an insulating state in the pristine metallic VS2 planes