First-principles materials design of CuInSe2-based high-efficiency photovoltaic solar cells

Based on ab initio   electronic structure calculations by self-interaction-corrected local-density-approximation (SIC-LDA) with the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA), we propose a materials design for high efficiency photovoltaic solar cells (PVSCs). It is shown that (i) the concentration dependence of the mixing energy of CuIn_1−xGa_xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Ga}}_x{\mathrm{Se}}_2$ shows upward convexity, thus this system favors phase separation. Due to the type II band alignment between CuInSe₂${\mathrm{CuInSe}}_2$ and CuGaSe₂${\mathrm{CuGaSe}}_2$, efficient electron–hole separation is realized in decomposed phase of this system. (ii) CuIn_1−xZn_0.5xSn_0.5xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Zn}}_{0.5x}{\mathrm{Sn}}_{0.5x}{\mathrm{Se}}_2$ has a direct band gap and no impurity state appears in the gap. Therefore, cost reduction is possible by using Zn and Sn instead of In. (iii) n-type CuAl_1−xSn_xS₂${\mathrm{CuAl}}_{1-x}{\mathrm{Sn}}_x{\mathrm{S}}_2$ and p-type Cu_1−xV_CuxAlS₂${\mathrm{Cu}}_{1-x}{\mathrm{V}}_{\mathrm{Cu}x}{\mathrm{AlS}}_2$ have negative activation energy for doped impurities and are expected to be low-resistive transparent conducting sulfides, which should be useful for CuInSe₂${\mathrm{CuInSe}}_2$-based PVSCs.     

Fluxmetric and magnetometric demagnetizing factors for cylinders

Fluxmetric and magnetometric demagnetizing factors, _Nf$N_{\mathrm{f}}$ and _Nm$N_{\mathrm{m}}$, for cylinders along the axial direction are numerically calculated as functions of material susceptibility χ$\chi$ and the ratio γ$\gamma$ of length to diameter. The results have an accuracy better than 0.1% with respect to min(_Nf,m,1-_Nf,m)$\min (N_{\mathrm{f},\mathrm{m}},1-N_{\mathrm{f},\mathrm{m}})$ and are tabulated in the range of 0.01?γ?500$0.01?\gamma ?500$ and -1?χ<∞$-1?\chi <\infty$. _Nm$N_{\mathrm{m}}$ along the radial direction is evaluated with a lower accuracy from _Nm$N_{\mathrm{m}}$ along the axis and tabulated in the range of 0.01?γ?1$0.01?\gamma ?1$ and -1?χ<∞$-1?\chi <\infty$. Some previous results are discussed and several applications are explained based on the new results.     

The Haldane–Shastry spin chain and the topological basis realization

In this paper, based on the topological basis states, we investigate the Hamiltonian family {H₂,H₃,H₄}$\{H_2,H_3,H_4\}$ of a closed four-qubit Haldane–Shastry spin chain. Not only the two-qubit interaction form, but also the three-qubit interaction form and the four-qubit interaction form are presented in terms of spin operators. Meanwhile, we explore some particular properties of the topological basis states in these systems. With Yangian algebra, the symmetry of the systems and the transitions between the eigenstates have been investigated. We find a really useful effect of Y(sl(2))$Y\left(sl\left(2\right)\right)$ operators {J_±,J₃}$\{J_{\pm },J_3\}$, which is that they can describe the transitions between the spin single state and the spin triple states. Furthermore, we construct a new Hamiltonian, whose energy degeneracies can be changed by adjusting the strengths of the two-qubit interactions, three-qubit interactions, four-qubit interactions, and the external magnetic field.     

A hidden analytic structure of the Rabi model

The Rabi model describes the simplest interaction between a cavity mode with a frequency ω_c${\omega }_c$ and a two-level system with a resonance frequency ω₀${\omega }_0$. It is shown here that the spectrum of the Rabi model coincides with the support of the discrete Stieltjes integral measure in the orthogonality relations of recently introduced orthogonal polynomials. The exactly solvable limit of the Rabi model corresponding to Δ=ω₀/(2ω_c)=0$\Delta ={\omega }_0/\left(2{\omega }_c\right)=0$, which describes a displaced harmonic oscillator, is characterized by the discrete Charlier polynomials in normalized energy ?$?$, which are orthogonal on an equidistant lattice. A non-zero value of Δ$\Delta$ leads to non-classical discrete orthogonal polynomials ?_k(?)${?}_k\left(?\right)$ and induces a deformation of the underlying equidistant lattice. The results provide a basis for a novel analytic method of solving the Rabi model. The number of ca. 1350 calculable energy levels per parity subspace obtained in double precision (cca 16 digits) by an elementary stepping algorithm is up to two orders of magnitude higher than is possible to obtain by Braak’s solution. Any first n$n$ eigenvalues of the Rabi model arranged in increasing order can be determined as zeros of ?_N(?)${?}_N\left(?\right)$ of at least the degree N=n+n_t$N=n+n_t$. The value of n_t>0$n_t>0$, which is slowly increasing with n$n$, depends on the required precision. For instance, n_t?26$n_t?26$ for n=1000$n=1000$ and dimensionless interaction constant κ=0.2$\kappa =0.2$, if double precision is required. Given that the sequence of the l$l$th zeros x_nl$x_{nl}$’s of ?_n(?)${?}_n\left(?\right)$’s defines a monotonically decreasing discrete flow with increasing n$n$, the Rabi model is indistinguishable from an algebraically solvable model in any finite precision. Although we can rigorously prove our results only for dimensionless interaction constant κ<1$\kappa <1$, numerics and exactly solvable example suggest that the main conclusions remain to be valid also for κ≥1$\kappa \ge 1$.     

High order resolution of the Maxwell–Fokker–Planck–Landau model intended for ICF applications

A high order, deterministic direct numerical method is proposed for the non-relativistic 2D_x×3D_v$2D_{\mathbf{x}}\times 3D_{\mathbf{v}}$ Vlasov–Maxwell system, coupled with Fokker–Planck–Landau collision operators. The magnetic field is perpendicular to the 2D_x$2D_{\mathbf{x}}$ plane surface of computation, whereas the electric fields occur in this plane. Such a system is devoted to modelling of electron transport and energy deposition in the general frame of Inertial Confinement Fusion applications. It is able to describe the kinetics of the plasma electrons in the nonlocal equilibrium regime, and permits to consider a large anisotropy degree of the distribution function. We develop specific methods and approaches for validation, that might be used in other fields where couplings between equations, multiscale physics, and high dimensionality are involved. Fast algorithms are employed, which makes this direct approach computationally affordable for simulations of hundreds of collisional times.     

Three PT-symmetric Hamiltonians with completely different spectra

We discuss three Hamiltonians, each with a central-field part H₀$H_0$ and a PT-symmetric perturbation igz$igz$. When H₀$H_0$ is the isotropic Harmonic oscillator the spectrum is real for all g$g$ because H$H$ is isospectral to H₀+g²/2$H_0+g^2/2$. When H₀$H_0$ is the Hydrogen atom then infinitely many eigenvalues are complex for all g$g$. If the potential in H₀$H_0$ is linear in the radial variable r$r$ then the spectrum of H$H$ exhibits real eigenvalues for 0<g<g_c$0<g<g_c$ and a PT phase transition at g_c$g_c$.     

Deformed quantum double realization of the toric code and beyond

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Z_n${\mathbb{Z}}_n$ and S₃$S_3$. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z₂${\mathbb{Z}}_2$ phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.     

Piezoelectric resonance in Rochelle salt: The contribution of diagonal strains

Within the framework of two-sublattice Mitsui model with taking into account the shear strain ε₄${\epsilon }_4$ and the diagonal strains ε₂${\epsilon }_2$ and ε₃${\epsilon }_3$, a dynamic dielectric response of Rochelle salt X-cuts is considered. Experimentally observed phenomena of crystal clamping by high frequency electric field, piezoelectric resonance, and microwave dispersion are described. Analytical expressions for the resonant frequencies of these cuts, associated with the shear vibration mode of ε₄${\epsilon }_4$ and with the extensional in-plane modes of ε₂${\epsilon }_2$, ε₃${\epsilon }_3$, are derived. It is shown that the lowest resonant frequency is always associated with the ε₄${\epsilon }_4$ shear mode.     

Phase diagrams of a spin-1 Ising superlattice

The three-dimensional spin-1 Ising superlattice consisting of two different ferromagnetic materials with two different crystal fields _Δ1${\Delta }_1$ and _Δ2${\Delta }_2$ is considered in the mean field approximation. The phase diagrams are considered in the (t,_d2$t,d_2$) plane for different ranges of variation of _d1(t=T/J,_d1=_Δ1/J$d_1(t=T/J,d_1={\Delta }_1/J$, _d2=_Δ2/J$d_2={\Delta }_2/J$ are the reduced temperature and crystal fields respectively). The phase diagrams exhibit a variety of multicritical points and reentrant and double reentrant behaviours. They are found to depend qualitatively and/or quantitatively on the thicknesses of the materials in a supercell. This has direct consequences on the nature of the magnetic states of superlattices with different thicknesses.     

Cyclic calorons

The Nahm data of periodic instantons, often called calorons, with spatial _CN$C_N$-symmetries are considered, by applying Sutcliffe?s ansatz for the monopoles with _CN$C_N$-symmetries. The bulk data of calorons are shown to enjoy the periodic Toda lattice, and the solutions are given in terms of elliptic theta functions. The case of N=3$N=3$ calorons are investigated in detail. It is found that the “scale parameters” of these calorons have upper bounds in their values, so that they do not have the large scale, or monopole, limits. The instanton limit of the _C3$C_3$-symmetric caloron is obtained.     

Effects of Gd substitution on the structural and magnetic properties of strontium hexaferrites

The effect of Gd substitution in M-type strontium hexaferrites has been examined in two series of samples, (_Sr1-xGdx)O·5.25$({\mathrm{Sr}}_{1-x}{\mathrm{Gd}}_x)\mathrm{O}·5.25$_Fe2O3${\mathrm{Fe}}_2{\mathrm{O}}_3$ and _{Sr1-xGdxFe12-xCoxO19}${\mathrm{Sr}}_{1-x}{\mathrm{Gd}}_x{\mathrm{Fe}}_{12-x}{\mathrm{Co}}_x{\mathrm{O}}_{19}$, both prepared by the ceramic method, where x=0–0.40$x=0–0.40$. The samples have been characterized by XRD, VSM and SEM-EDAX techniques. All substituted samples present primarily the hexaferrite structure. Sample (_{Sr0.95Gdx0.05})O·5.25$({\mathrm{Sr}}_{0.95}{\mathrm{Gd}}_{x0.05})\mathrm{O}·5.25$_Fe2O3${\mathrm{Fe}}_2{\mathrm{O}}_3$ is single phase. Formation of impurity phases is affected by stoichiometry and presence of Co. In Sr–Gd samples, coercivity showed a maximum value of 305 kA/m (3.8 kOe) for x=0.20$x=0.20$, while remanence and saturation magnetization did not decrease. Coercivity and magnetization in the Sr–Gd–Co series decreased steadily with substitution degree.     

How information influences an individual opinion evolution

We propose an opinion formation model which takes an individual’s opinion transition probability into consideration. In the model, each individual updates his/her opinion based on the probability of reception and acceptance. We describe the process of opinion evolution by using individual’s awareness _Wi$W_i$, message intensity _a0$a_0$ and message credibility _b0$b_0$. Results show that if a message’s view stays below 1 and its credibility takes a value around 2, it can win the trust of individuals with a high value of awareness (_Wi≥1$W_i\ge 1$), leading the public opinion to support the message’s own view within 100 steps and then decide the opinion formation. The final average opinion is closely related to the first message’s credibility and individual’s awareness.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Spreading of periodic diseases and synchronization phenomena on networks

In this paper, we investigate numerically the Susceptible–Infected–Recovered–Susceptible (SIRS) epidemic model on an exponential network generated by a preferential attachment procedure. The discrete SIRS model considers two main parameters: the duration _τ0${\tau }_0$ of the complete infection–recovery cycle and the duration _τI${\tau }_I$ of infection. A permanent source of infection _I0$I_0$ has also been introduced in order to avoid the vanishing of the disease in the SIRS model. The fraction of infected agents is found to oscillate with a period T≥_τ0$T\ge {\tau }_0$. Simulations reveal that the average fraction of infected agents depends on _I0$I_0$ and _τI/_τ0${\tau }_I/{\tau }_0$. A maximum of synchronization of infected agents, i.e. a maximum amplitude of periodic spreading oscillations, is found to occur when the ratio _τI/_τ0${\tau }_I/{\tau }_0$ is slightly smaller than 1/2$1/2$. The model is in agreement with the general observation that an outbreak corresponds to high _τI/_τ0${\tau }_I/{\tau }_0$ values.     

Whistler instability in a semi-relativistic bi-Maxwellian plasma

Employing linearized Vlasov–Maxwell system of equations, the whistler instability is discussed for a semi-relativistic bi-Maxwellian distribution. The dispersion relations are analyzed analytically along with the graphical representation and the estimates of the growth rate and instability threshold condition are also presented in the limiting cases i.e., _ξ±=(ω?Ω)/_k∥vt‖?1${\xi }_{\pm }=(\omega ?\Omega )/k_{\parallel }{v}_{t_{\Vert }}?1$ (resonant case) and _ξ±?1${\xi }_{\pm }?1$ (non-resonant case). Further for field free case i.e., _B0=0$B_0=0$, the growth rates for Weibel instability in a semi-relativistic bi-Maxwellian plasma are presented for both the limiting cases.