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We study electronic inhomogeneities in manganites using simulations on a microscopic model with Coulomb interactions amongst two electronic fluids-one localized (polaronic), the other extended-and dopant ions. The long range Coulomb interactions frustrate phase separation induced by the large on site repulsion between the fluids. A single phase ensues which is inhomogeneous at a nanoscale, but homogeneous on mesoscales, with many features that agree with experiments. This, we argue, is the origin of nanoscale inhomogeneities in manganites, rather than phase competition or disorder effects.

PACS 71.10.-w -Electronic structure: theories and models of condensed matter PACS 71.30.+h -Insulator-metal transitions PACS 75.10.Kt -Magnetic ordering: quantum spin liquids Abstract -Dynamics of magnetic moments near the Mott metal-insulator transition is investigated by a combined slave-rotor and Dynamical Mean-Field Theory solution of the Hubbard model with additional fully-frustrated random Heisenberg couplings. In the paramagnetic Mott state, the spinon decomposition allows to generate a Sachdev-Ye spin liquid in place of the collection of independent local moments that typically occurs in the absence of magnetic correlations. Cooling down into the spin-liquid phase, the onset of deviations from pure Curie behavior in the spin susceptibility is found to be correlated to the temperature scale at which the Mott transition lines experience a marked bending. We also demonstrate a weakening of the effective exchange energy upon approaching the Mott boundary from the Heisenberg limit, due to quantum fluctuations associated to zero and doubly occupied sites. serge.florens@grenoble.cnrs.frIntroduction. -The Mott metal-insulator transition, wherein electronic waves are localized by short-range electron-electron interactions (see [1] for a review), is one of the most complex phenomenon observed in strongly correlated electronic systems. Even though the appearance of a Mott gap is purely driven by the charge degrees of freedom, it is expected that magnetic fluctuations play a very crucial role in determining the true nature of this phase transition. In the paramagnetic Mott insulator, local moments are indeed well defined objects after their creation at high temperature (at a scale set by the local Coulomb interaction) and before their ultimate antiferromagnetic ordering at the Néel temperature, offering a window in which complex behavior of the spin excitations is yet to be clearly understood. Experimentally, the simplest situation in this respect occurs when the low-temperature magnetic ordering is first order, as in the case of Cr-doped V 2 O 3 . Since the magnetic correlations are expected to be weak in this case, many predictions can be made from a single-site approach like the Dynamical Mean Field Theory (DMFT) [2], where local moments are described as freely fluctu-

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid ᐉ-b model proposed recently for manganites ͓Phys. Rev. Lett. 92, 157203 ͑2004͔͒ leads to an excellent description of such inhomogeneities. In the ᐉ-b model two very different kinds of electronic states, one localized and polaronic ͑ᐉ͒ and the other extended or broad band ͑b͒ coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory ͑DMFT͒ framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance ͑CMR͒, qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V 0 , our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V 0 ; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer ͑meso͒ scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

We study the dimensional dependence of the interplay between correlation and disorder in two dimension at half filling using 2D t−t ′ disordered Hubbard model with deterministic disorder both at zero and finite temperatures. Inclusion of t ′ without disorder leads to a metallic phase at half filling below a certain critical value of U . Above this critical value Uc correlation favours antiferromagnetic phase. Since disorder leads to double occupancy over the lower energy site, the competition between Hubbard U and disorder leads to the emergence of a metallic phase, which can be quantified by the calculation of Kubo conductivity, gap at half-filling , density of states, spin order parameter, Inverse participation ratio (IPR) and bandwidth. We have studied the effect of disorder on the system in a very novel way through a deterministic disorder which follows a Fibonacci sequence. Behaviour of different parameters show interesting features on going from a two to quasi one dimensional system.

We consider a BCS-like model of interacting electrons on a square lattice. Within mean field theory, our model has an instability towards the formation of a d-wave superconducting state. We calculate the longitudinal ultrasonic attenuation rate in the superconducting phase in the clean limit for parameters appropriate to the cuprates. We find that the temperature dependence of the attenuation rate is similar to that observed in conventional superconductors for phonon wavevectors along the direction of the anti-nodes of the gap. However, the attenuation rate for phonon wavevectors along the nodal direction is found to be strikingly different in its temperature and doping dependence. The attenuation rate α S (T) increases in magnitude and shows a sign change in its curvature (when plotted as a function of temperature) with increasing value of dopant concentration.

The Mott metal to insulator transition is a remarkable phenomenon observed in strongly correlated materials, where the localization of electronic waves is driven by on-site electron-electron repulsion (see [7] for a review). Although the appearance of a Mott gap is clearly a charge-related effect, magnetism is expected to play a key role in elucidating the true nature of this phase transition. Indeed, since the Mott insulating state is purely paramagnetic, local moments are well-defined objects between their formation at high temperature (about the local Coulomb interaction ) and their ultimate ordering at the Neel temperature. This offers a window for the Mott transition to occur, in which the behavior of these local spin excitations is yet to be clearly understood. The simplest situation lies in case where the low-temperature magnetic ordering is first order, as in Cr-doped V 2 O 3 . Accordingly magnetic fluctuations should be expected to be weak, so that many predictions can be made from a single-site approach such as the Dynamical Mean Field Theory (DMFT) [4]. In particular, the fact that a low-temperature metallic state leads upon heating to an insulating phase can be understood as a Pomeranchuk effect, where the entropy gain benefits the state with magnetic degeneracy. On the contrary, there are other classes of materials, such as the κ-organics, where the magnetic transition happens to be continuous, so that localized spins will experience strong collective fluctuations. The

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