Dynamic conductivity modified by impurity resonant states in doping three-dimensional Dirac semimetals

The impurity effect is studied in three-dimensional Dirac semimetals in the framework of a T-matrix method to consider the multiple scattering events of Dirac electrons off impurities. It has been found that a strong impurity potential can significantly restructure the energy dispersion and the density of states of Dirac electrons. An impurity-induced resonant state emerges and significantly modifies the pristine optical response. It is shown that the impurity state disturbs the common longitudinal optical conductivity by creating either an optical conductivity peak or double absorption jumps, depending on the relative position of the impurity band and the Fermi level. More importantly, these conductivity features appear in the forbidden region between the Drude and interband transition, completely or partially filling the Pauli block region of optical response. The underlying physics is that the appearance of resonance states as well as the broadening of the bands leads to a more complicated selection rule for the optical transitions, making it possible to excite new electron-hole pairs in the forbidden region. These features in optical conductivity provide valuable information to understand the impurity behaviors in 3D Dirac materials.     

Structural,thermal and electrical properties of polyvinyl alcohol/poly(vinyl pyrrolidone)–sodium nitrate solid polymer blend electrolyte

Sodium ion conducting solid polymer blend electrolyte thin films have been prepared by using polyvinyl alcohol (PVA)/poly(vinyl pyrrolidone) (PVP) with NaNO₃ by solution cast technique. The prepared films were characterized by various methods. The complexation of the salt with the polymer blend was identified by X-ray diffraction (XRD) and Fourier transforms infrared spectroscopy (FTIR), Differential scanning calorimetry was used to analyze the thermal behavior of the samples, and the glass transition temperature is low for the highest conducting polymer material. The scanning electron microscopy gives the surface morphology of the polymer electrolytes. The frequency and temperature dependent of electrical conductivities of the films were studied using impedance analyzer in the frequency range of 1 Hz to 1 MHz. The highest electrical conductivity of 50PVA/50PVP/2 wt% NaNO₃ concentration has been found to be 1.25 × 10^?5 S cm^?1 at room temperature. The electrical permittivity of the polymer films have been studied for various temperatures. The transference number measurements showed that the charge transport is mainly due to ions than electrons. Using this highest conducting polymer electrolyte, an electrochemical cell is fabricated and the parameters of the cells are tabulated.     

Electrochemical polymerization of alizarin and the electrochemical properties of poly(alizarin)

Electrochemical polymerization of alizarin on glassy carbon electrode (GCE) was carried out in acidic solution by cyclic voltammetry (CV), and the polymerization process was monitored by electrochemical quartz crystal microbalance (EQCM). A possible mechanism concerning the polymerization of alizarin was also proposed in this work. The as-synthesized poly(alizarin) was characterized by scanning electron microscopy (SEM) and electrochemical impedance spectroscopy (EIS). The study on electrode reaction process shows that the electrode reaction of poly(alizarin) is controlled by diffusion. Finally, the activation energy (E _a) of the electrode reactions of poly(alizarin) was obtained according to the temperature dependence of the redox peak currents.     

The structure of ion-acoustic waves in a low-frequency three-component electron–ion space plasma with two-electron populations

In the present paper, we have studied the binding energy of the shallow donor hydrogenic impurity, which is confined in an inhomogeneous cylindrical quantum dot (CQD) of \(\hbox {GaAs-Al}_{x}\hbox {Ga}_{1-x}\hbox {As}\). Perturbation method is used to calculate the binding energy within the framework of effective mass approximation and taking into account the effect of dielectric mismatch between the dot and the barrier material. The ground-state binding energy of the donor is computed as a function of dot size for finite confinement. The result shows that the ground-state binding energy decreases with the increase in dot size. The result is compared with infinite dielectric mismatch as a limiting case. The binding energy of the hydrogenic impurity is maximum for an on-axis donor impurity.     

Solitary wave solutions for some nonlinear time-fractional partial differential equations

In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.     

Multiswitching compound–compound synchronisation of six chaotic systems

In this paper, multiswitching combination synchronisation (MSCS) scheme has been investigated in a class of three non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen systems are taken as the drive systems. The combination of multidrive systems is then synchronised with the fractional-order Lü chaotic system. In MSCS, the state variables of the two drive systems synchronise with different state variables of the response system, simultaneously. Based on the stability of fractional-order chaotic systems, the MSCS of three fractional-order non-identical systems has been investigated. For the synchronisation of three non-identical fractional-order chaotic systems, suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method.