Dimensional and temperature dependence of metal insulator transition in correlated and disordered systems

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 $U_c$ 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.Comment: 6 Pages, 16 figure

Coulomb Interactions and Nanoscale Electronic Inhomogeneities in Manganites

We address the issue of endemic electronic inhomogeneities in manganites using extensive simulations on a new model with Coulomb interactions amongst two electronic fluids, one localized (polaronic), the other extended (band-like), and dopant ions. The long range Coulomb interactions frustrate phase separation induced by the strong on site repulsion between the fluids. A single quantum phase ensues which is intrinsically and strongly inhomogeneous at a nano-scale, but homogeneous on meso-scales, with many characteristics (including colossal responses)that agree with experiments. This, we argue, is the origin of nanoscale inhomogeneities in manganites, rather than phase competition and disorder related effects as often proposed.Comment: 4 pages, 3 figure

Ultrasonic Attenuation in Clean d-Wave Superconductors

We calculate the low temperature longitudinal ultrasonic attenuation rate $\alpha_S$ in clean d-wave superconductors. We consider the contribution of previously ignored processes involving the excitation of a pair of quasi-holes or quasi-particles. These processes, which are forbidden by energy conservation in conventional s-wave superconductors, have a finite phase space in d-wave superconductors due to the presence of nodes in the gap which give rise to soft low-energy electronic excitations. We find the contribution to $\alpha_S$ from these processes to be proportional to $T$ in the regime $k_B T\ll Qv_{\Delta} \ll \Delta_0$,(ultra-low temperature regime) and to be proportional to 1/T in the region $Qv_F \ll k_BT \ll \Delta_0$, (low temperature regime) where ${\bf Q}$ is the ultrasound wave-vector and $\Delta_0$ is the maximum gap amplitude. We explicitly evaluate these terms, for parameters appropriate to the cuprates, for ${\bf Q}$ along the nodal and the antinodal directions and compare it with the contribution from processes considered earlier(I.Vekhter et al {\it Phys. Rev.}{\bf B59}, 7123(1999)). In the ultra-low temperature regime, the processes considered by us make a contribution which is smaller by about a factor of 10 for ${\bf Q}$ along the nodal direction, while along the antinodal direction it is larger by a factor of 100 or so. In the low temperature regime on the other hand the contribution made by these terms is small. However taken together with the original terms we describe a possible way to evaluate the parameter $v_F/v_\Delta$.Comment: 9 pages, RevTex, accepted for publication in Physica

Ultrasonic Attenuation in the Vortex State of d-wave Superconductors

We calculate the low temperature quasi-particle contribution to the ultrasonic attenuation rate in the mixed state of d-wave superconductors. Our calculation is performed within the semi-classical approximation using quasi-particle energies that are Doppler shifted, with respect to their values in the Meissner phase, by the supercurrent associated with the vortices. We find that the attenuation at low temperatures and at fields $H_{c1} \leq H \ll H_{c2}$ has a temperature independent contribution which is proportional to $\surd H$ where $H$ is the applied magnetic field. We indicate how our result in combination with the zero-field result for ultrasonic attenuation can be used to calculate one of the parameters $v_F$, $H_{c2}$ or $\xi$ given the values for any two of them.Comment: 10 pages, RevTeX, submitted to Physica

Long Range Coulomb Interactions and Nanoscale Electronic Inhomogeneities in Correlated Oxides

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. We show here that an extension, to include long range Coulomb interactions, of a quantum two-fluid $\ell-b$ model proposed recently for manganites [Phys. Rev. Lett., {\bf 92}, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the $\ell-b$ model two very different kinds of electronic states, one localized and polaronic ($\ell$), and the other extended or broad band ($b$) co-exist. For model parameters appropriate to manganites, and even within a simple dynamical mean-filed theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), 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 {\em macroscopic} phase separation gets suppressed, and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a new kind of quantum Coulomb glass. Our work points to an interplay of strong correlations, long range Coulomb interaction and dopant ion disorder as the origin of nanoscale inhomogeneities, rather than disorder frustrated phase competition as is generally believed. Based on this, we argue that the observed micrometer(meso)-scale inhomogeneities owe their existence to extrinsic causes, eg. strain due to cracks and defects. We suggest possible experiments to validate our speculation.Comment: 24 Pages, 19 Figure

H₂/CH₄ Gas Separation by Variation in Pore Geometry of Nanoporous Graphene

We studied the behavior of H₂ and CH₄ flowing through various pore geometries of nanoporous graphene using molecular dynamics method. Ten different geometries of pore-18, with different eccentricities, were prepared. It was found that the gas permeance and adsorption layer were heavily influenced by the eccentricity of the pores. On further investigation, it was also found that the jaggedness of the pore geometry played a role as well. It was also noted that at specific eccentricities, pore-18 exhibited hydrogen selective behavior, which was found to extend to pore-12, -14, -16, -20, -24, and -30 as well. Furthermore, it was shown that the H₂ permeance of these pores can reach 9 times the value of that of pore-10 (which was previously found to be the only selective pore). Hence, these pores show H₂ selectivity with high H₂ yields. Thus, this study demonstrates the exciting possibility of creating highly efficient H₂ separators by pore geometry variation. Recent experimental studies, which involve an atom-by-atom removal technique to create nanopores, point to the possibility of obtaining these geometries in the lab

Context-Aware Influential Nodes Tracking in Online Social Networks

Influence Maximization (IM) is a problem of detecting a small set of highly influential users in a social network. Application areas of IM include the spread of news, viral marketing, and the outbreak of diseases. In most of the existing IM approaches, the nodes\u27 structural information has been considered for computing their influence spread ability. The users\u27 interest, their interaction behavior, popularity, and location sharing information are being neglected. Although many existing works have considered a few of these measures; however, they do not consider them collectively and face challenges in time efficiency and suitable seed node accuracy. To overcome these challenges, this paper proposes Context-Aware Influential Nodes Tracking (CINT) algorithm, which uses users\u27 interest, popularity, location information to compute the topic-based diffusion ability of the network, find the topic-wise influential seeds and finally, evaluate the spread of influence for a given message/product. We propose a Contextaware Independent Cascade (CIC) model and a Topic-aware Influence sub-Graph (TIG) model to make our framework efficient and effective. Experimental results on six real-world networks show that the proposed model performs better in terms of effective influence spread as compared to the considered existing state-of-the-art influence maximization algorithms

Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

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 l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), 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 (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation