Real space Dynamical Super Cell Approximation for interacting disordered systems

Effective medium super-cell approximation method which is introduced for disordered systems is extended to a general case of interacting disordered systems. We found that the dynamical cluster approximation (DCA) and also the non local coherent potential approximation (NLCPA) are two simple case of this technique. Whole equations of this formalism derived by using the effective medium theory in real space.Comment: 6 page

New Real space method for calculation of physical properties of a disordered system

We introduce a new real space super cell approximation method for treating the electronic states of disordered systems. This method is general and allows both randomness in the on-site energies and in the hopping integrals. In the special case of randomness in the on-site energies only, this method is equivalent to the Non Local Coherent Potential Approximation (NLCPA) derived previously

Validity of Anderson's theorem for s-wave superconductors

We investigate validity of Anderson's theorem (AT) for disordered s-wave superconductors in a negative U Hubbard model with random on-site energies, $\epsilon_{i}$. The superconducting critical temperature, $T_{c}$, is calculated in the coherent potential approximation (CPA) as a function of impurity concentration, $c$, the random potentials for different band filling. In contradiction to Anderson's theorem, we found that $T_{c}$ is dramatically sensitive with respect to $c$ and $\epsilon_{i}$. Our results shows that for low impurity concentrations and weak on-site energies, $\epsilon_{i}$, the AT is valid, while in the strong scattering limit even for low impurity concentration, $T_{c}$ is very small with respect to the clean system and by increasing $c$ it is completely suppressed, hence AT is violated in this regime.Comment: 5 pages and 5 figure

Beyond real space super cell approximation, corrections to the real space cluster approximation

Motion of a single electron in a disordered alloy and or interacting electrons systems such as magnetic materials, strongly correlated systems and superconductors is replaced by motion of that in an effective medium which is denoted by self-energy. The study of disordered alloy and interacting electrons systems based on single electron motion is an old challenge and an important problem in condensed matter physics. In this paper we introduce a real space approximation beyond super cell approximation for the study of these systems to capture multi-site effects. Average disordered alloy or interacting system is replaced by a self-energy, $\Sigma(i,j,E)$. We divided self-energy in q-space $\Sigma({\bf q}; E)=\frac{1}{N}\sum_{ij}e^{i{\bf q}.{\bf r}_{ij}}\Sigma(i,j; E)$ into two parts \Sigma({\bf q}; E)=\frac{1}{N_{c}}\sum_{IJ\in\; \mbox{\tiny same cluster}}e^{i{\bf q}.{\bf r}_{IJ}}\Sigma(I,J; E)+\frac{1}{N}\sum_{ij\notin \:\mbox{\tiny same cluster}}e^{i{\bf q}.{\bf r}_{IJ}}\Sigma(I,J,E) where $\{Lc_{1}, Lc_{2},Lc_{3}\}$ are dimensions of the super cell. We show that neglecting the second term of q-space self-energy leads to super cell approximation $e^{iq_{j} Lc_{j}}=1$, hence $q_{j}$ determined by $q_{j} Lc_{j}=2\pi n_{j}$. Then we kept this correction in the second step to add self energies of sites in different super cells which leads to fully q-dependent self energy in the first Brillouin zone (FBZ). Our self-energy in FBZ is casual, fully q-dependent, and continuous with respect to ${\bf q}$. It recovers coherent potential approximation in the single site approximation and is exact when the number of sites in the super cell approaches to the total number of lattice sites. We illustrate that this approximation undertakes electrons localization for one and two dimensional alloy systems which isn't observed by previous multi site approximations.Comment: 6 pages, 5 figure

Local moment formation in bilayer graphene

The local properties of bilayer graphene (BLG) due to the spatial inhomogeneity of its sublattices are of interest. We apply Anderson impurity model to consider the local moment formation on a magnetic impurity which could be adsorbed on different sublattices of BLG. We find different features for the impurity magnetization when it is adsorbed A and B sublattices. The impurity adsorbed on A sublattice can magnetize even when the impurity level is above the Fermi level and the on-site coulomb energy is very small. But when the impurity is adsorbed on B sublattice the magnetization is possible for limited values of the impurity level and the on-site coulomb energy. This is due to different local density of the low energy states at A and B sublattices which originates from their spatial inhomogeneity. Also we show that electrical controlling the magnetization of adatoms besides it's inhomogeneity in BLG allow for possibility of using BLG in spintronic devices with higher potential than graphene.Comment: 16 pages, 4 figures, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Strongly Correlated Electrons (cond-mat.str-el

RKKY interaction in bilayer graphene

We study the RKKY interaction between two magnetic impurities located on same layer (intralayer case) or on different layers (interlayer case) in undoped bilayer graphene in the four-bands model, by directly calculating the Green functions in the eigenvalues and eigenvectors representation. Our results show that both intra- and interlayer RKKY interactions between two magnetic impurities located on same (opposite) sublattice are always ferromagnetic (antiferromagnetic). Furthermore we find unusual long-distance decay of the RKKY interaction in BLG. The intralyer RKKY interactions between two magnetic impurities located on same sublattice, $J^{A_{n}A_{n}}(\mathbf{R})$ and $J^{B_{n}B_{n}}(\mathbf{R)}$, decay closely as $1/R^{6}$ and $1/R^{2}$ at large impurity distances respectively, but when they are located on opposite sublattices the RKKY interactions exhibit $1/R^{4}$ decays approximately. In the interlayer case, the RKKY interactions between two magnetic impurities located on same sublattice show a decay close to $1/R^{4}$ at large impurity distances, but if two magnetic impurities be on opposite sublattices the RKKY interactions, $J^{A_{1}B_{2}}(\mathbf{R})$ and $J^{B_{1}A_{2}}(\mathbf{R)}$, decay closely as $1/R^{6}$ and $1/R^{2}$ respectively. Both intra- and interlayer RKKY interactions have anisotropic oscillatory factors which for intralayer case is equal to that for single layer graphene. Our results at weak and strong interlayer coupling limits reduce to the RKKY interaction of SLG and that of BLG in the two-bands approximation respectively.Comment: 28 pages, 7 figure

On the Contributions to the UY(1)\bf U_Y(1) Chern-Simons Term and the Evolution of Fermionic Asymmetries and Hypermagnetic Fields

We study simultaneous evolution of electron, neutrino and quark asymmetries, and large scale hypermagnetic fields in the symmetric phase of the electroweak plasma in the temperature range $100$GeV$\leq T\leq 10$TeV, taking into account the chirality flip processes via inverse Higgs decays and fermion number violation due to Abelian anomalies. We present a derivation of the coefficient of the Chern-Simons term for the hypercharge gauge field, showing that the left-handed and right-handed components of each fermion species contribute with opposite sign. This is in contrast to the results presented in some of the previous works. The $\textrm{U}_{\textrm{Y}}(1)$ Chern-Simons term affects the resulting anomalous magnetohydrodynamic (AMHD) equations. We solve the resulting coupled evolution equations for the lepton and baryon asymmetries, as well as the hypermagnetic field to obtain their time evolution along with their values at the electroweak phase transition ($T_{EW} \sim 100$GeV) for a variety of critical ranges for their initial values at $T=10$TeV. We first investigate the results of this sign change, by directly comparing our results with those obtained in one of the previous works and find that matter asymmetry generation increases considerably in the presence of a strong hypermagnetic field. Furthermore, we find that a strong hypermagnetic field can generate matter asymmetry starting from absolutely zero asymmetry, while matter asymmetry can generate a hypermagnetic field provided the initial value of the latter is nonzero.Comment: 29 pages, 4 figure

A Minimal System Including Weak Sphalerons for Investigating the Evolution of Matter Asymmetries and Hypermagnetic Fields

We study simultaneous evolution of large scale hypermagnetic fields and the asymmetries of quarks, leptons and Higgs boson in the temperature range from 10TeV to 100GeV. Above 10TeV, we identify all of the major fast interactions and use the associated conservation laws as constraints on the initial conditions at 10TeV. Below 10TeV, we identify the major processes which fall out of equilibrium or emerge as non-negligible processes and derive the relevant evolution equations. These include the Abelian anomalies which violate fermion numbers, direct and inverse Higgs decays that change the chiralities of fermions, and weak sphalerons which violate the left-handed fermion numbers. We also consider the contributions of all fermionic chemical potentials to the UY(1) Chern-Simons term which affects the evolution through the AMHD equations. Thus, we present a minimal set of self-consistent initial conditions and evolution equations which respect all constraints coming from conservation laws, fast processes and charge neutrality of the plasma. We solve the coupled evolution equations and find that initial large hypermagnetic field can produce matter asymmetries starting from zero initial value, and vice versa provided an initial seed of hypermagnetic field is present and the rate of the electron Yukawa processes is lower. We find that our model yields acceptable values for baryon asymmetry and magnetic field. However, the scale of the magnetic field obtained is much smaller than the observational data, even when the turbulence driven inverse cascade mechanism in the broken phase is taken into account.Comment: 40 pages, 5 figures, 7 table

Effects of doping and bias voltage on the screening in AAA-stacked trilayer graphene

We calculate the static polarization of AAA-stacked trilayer graphene (TLG) and study its screening properties within the random phase approximation (RPA) in all undoped, doped and biased regimes. We find that the static polarization of undoped AAA-stacked TLG is a combination of the doped and undoped single layer graphene static polarization. This leads to an enhancement of the dielectric background constant along a Thomas-Fermi screening with the Thomas-Fermi wave vector which is independent of carrier concentrations and a 1/r^3 power law decay for the long-distance behavior of the screened coulomb potential. We show that effects of a bias voltage can be taken into account by a renormalization of the interlayer hopping energy to a new bias-voltage-dependent value, indicating screening properties of biased AAA-stacked TLG can be tuned electrically. We also find that screening properties of doped AAA-stacked TLG, when $\mu$ exceeds $\sqrt{2}\gamma$, are similar to that of doped SLG only depending on doping. While for $\mu<\sqrt{2}\gamma$, its screening properties are a combination of SLG and AA-stacked screening properties and they are determined by doping and the interlayer hopping energy.Comment: 19 pages, 1 figur

The effects of the UY_\textrm{Y}(1) Chern-Simons term and its baryonic contribution on matter asymmetries and hypermagnetic fields

In this paper, we study the significance of the U$_\textrm{Y}$(1) Chern-Simons term in general, and its baryonic contribution in particular, for the evolution of the matter asymmetries and the hypermagnetic field in the temperature range $100$GeV$\leq T \leq 10$TeV. We show that an initial helical hypermagnetic field, denoted by $B_Y^{(0)}$, can grow matter asymmetries from zero initial value. However, the growth which is initially quadratic with respect to $B_Y^{(0)}$, saturates for values larger than a critical value. The inclusion of the baryonic contribution reduces this critical value, leading to smaller final matter asymmetries. Meanwhile, $B_Y(T_{EW})$ becomes slightly larger than $B_Y^{(0)}$. In the absence of the U$_\textrm{Y}$(1) Chern-Simons term, the final values of matter asymmetries grow without saturation. Conversely, we show that an initial matter asymmetry can grow an initial seed of hypermagnetic field, provided the Chern-Simons term is taken into account. The growth process saturates when the matter asymmetry drops abruptly. When the baryonic contribution is included, the saturation occurs at an earlier time, and $B_Y (T_{EW})$ becomes larger. We also show the results can be within the acceptable range of present day data, provided the inverse cascade process is also taken into account.Comment: 34 pages, 4 figure