We theoretically study scattering process and superconducting triplet correlations in a graphene junction comprised of ferromagnet-RSO-superconductor in which RSO stands for a region with Rashba spin orbit interaction. Our results reveal spin-polarized subgap transport through the system due to an anomalous equal-spin Andreev reflection in addition to conventional back scatterings. We calculate equal-and opposite-spin pair correlations near the F-RSO interface and demonstrate direct link of the anomalous Andreev reflection and equal-spin pairings arised due to the proximity effect in the presence of RSO interaction. Moreover, we show that the amplitude of anomalous Andreev reflection, and thus the triplet pairings, are experimentally controllable when incorporating the influences of both tunable strain and Fermi level in the nonsuperconducting region. Our findings can be confirmed by a conductance spectroscopy experiment and provide better insights into the proximity-induced RSO coupling in graphene layers reported in recent experiments 30,31,33,34.

Employing a Keldysh-Eilenberger technique, we theoretically study the generation of a spontaneous supercurrent and the appearance of the ϕ0 phase shift parallel to uniformly in-plane magnetized superconducting interfaces made of the surface states of a three-dimensional topological insulator. We consider two weakly coupled uniformly magnetized superconducting surfaces where a macroscopic phase difference between the s-wave superconductors can be controlled externally. We find that, depending on the magnetization strength and orientation on each side, a spontaneous supercurrent due to the ϕ0-states flows parallel to the interface at the junction location. Our calculations demonstrate that nonsinusoidal phase relations of current components with opposite directions result in maximal spontaneous supercurrent at phase differences close to π. We also study the Andreev subgap channels at the interface and show that the spin-momentum locking phenomenon in the surface states can be uncovered through density of states studies. We finally discuss realistic experimental implications of our findings.

Using a wavefunction Dirac Bogoliubov-de Gennes method, we demonstrate that the tunable Fermi level of a graphene layer in the presence of Rashba spin orbit coupling (RSOC) allows for producing an anomalous nonlocal Andreev reflection and equal spin superconducting triplet pairing. We consider a graphene junction of a ferromagnet-RSOC-superconductor-ferromagnet configuration and study scattering processes, the appearance of spin triplet correlations, and charge conductance in this structure. We show that the anomalous crossed Andreev reflection is linked to the equal spin triplet pairing. Moreover, by calculating current cross-correlations, our results reveal that this phenomenon causes negative charge conductance at weak voltages and can be revealed in a spectroscopy experiment, and may provide a tool for detecting the entanglement of the equal spin superconducting pair correlations in hybrid structures. PACS numbers: 72.80.Vp, 74.45.+c, 74.50.+r, 81.05.ue Introduction-Superconductivity and its hybrid structures with other phases can host a wide variety of intriguing fundamental phenomena and functional applications such as Higgs mechanism [1], Majorana fermions [2], topological quantum computation [3], spintronics [4], and quantum entanglement [5][6][7][8]. The quantum entanglement describes quantum states of correlated objects with nonzero distances [6,8] that are expected to be employed in novel ultra-fast technologies such as secure quantum computing [3,6].

Using extensive Monte Carlo simulations, we study the effective permeability, porosity, and percolation properties of two-dimensional fracture networks in which the fractures are represented by rectangles of finite widths. The parameters of the study are the width of the fractures and their number density. For low and intermediate densities, the average porosity of the network follows a power-law relation with the density. The exponent of the power law itself depends on the fractures' width through a power law. For an intermediate range of the densities, the effective permeability scales with the fractures' width as a power law, with an exponent that depends on the density. For high densities the effective permeability also depends on the porosity through a power law, with an exponent that depends on the fractures' width. In agreement with the results, experimental data also indicate the existence of a power-law relationship between the effective permeability and porosity in consolidated sandstones and sedimentary rocks with a nonuniversal exponent. The percolation threshold or critical number density of the fractures depends on their width and is maximum if they are represented by squares, rather than rectangles.

We propose an efficient method of generating long-range correlations in large systems. The development of this method was motivated by the problem of constructing an optimal model for a large-scale porous medium. There are typically long-range correlations in the properties of such porous media, such as their permeability and porosity, for which there are usually only limited data. The optimal model must not only honor (preserve) the available data and their correlation function, but also accurately predict the future behavior of fluid flow in the media. We formulate the problem of generating the long-range correlations as one of optimization, and utilize simulated annealing to generate a d-dimensional array which contains the correlations and honors the existing data. The optimization process is based on the data's correlation function. The method is, therefore, free of the many numerical difficulties and/or limitations that most previous techniques suffer from. It is completely general and may be used for generating long-range correlations with any type of correlation function, in both isotropic and anisotropic media. Representative examples are presented, and the method's efficiency and accuracy are discussed.