In this study, we report on electronic and optical properties of the bulk and primitive structure of A$_2$B$_3$(A = Bi or Sb and B = Se or Te) compounds using FP-LAPW method within density functional theory. The potentials for exchange and correlation is treated within generalized gradient approximation-Perdew Burke Ernzerhof and Tran-Blahamodified Becke–Johnson (TB_mBJ). The inclusion of spin-orbit coupling approximation is used to calculate electronicstructures and optical properties by determining the complex dielectric function, from which the other parameters arederived. The obtained results are in good agreement with the experimental results. Also, Sb$_2$Te$_3$ compounds have beenfound to possess maximum value of absorption and reflection among all the studied compounds. For all the compounds, astrong absorption coefficient ($\alpha$) exists between the energy range 0 and 5 eV, and is greater than 10$^5$ cm$^{–1}$, which makesthem suitable for optoelectronic applications.

Gadolinium-doped bismuth telluride (GBT), ferric-doped bismuth telluride (FBT) and chromium-doped bismuth telluride (CBT) nanocrystals have been synthesized using colloidal hot-injection method with same doping ratio. Field-oriented uniaxial anisotropic ferromagnetic properties for all the samples were analysed from the squareness ratio ($M_r$/$M_s$), $K_1$ (magnetocrystalline anisotropic constant), $K_1$$^v$ (shape anisotropic constant), $K_{eff}$ (effective anisotropy constant) and magnetic energy using vibration sample magnetometer. The magneto-impedance (MI) spectral ratio (${\Delta}$Z/$Z_0$)% has been influenced by rotational magnetization, as well as domain wall motion with respect to applied magnetic field. The results have proven that the GBT thin film sample exhibits the maximum MI effect. Our results may shed light on the simple method of synthesis and development of the effective MI materials based on rare-earth/transition-doped bismuth telluride for the realization of magnetic sensor applications in future.

We investigated the magnetic interaction of carbon (C)-transition (Cr/Fe) and rare-earth Gadolinium (Gd) metal co-doped bismuth telluride (BT) systems (Cr$_x$C$_y$Bi$_{12-x}$Te$_{18-y}$, Fe$_x$C$_y$Bi$_{12-x}$Te$_{18-y}$ and Gd$_x$C$_y$Bi$_{12-x}$Te$_{18-y}$ (x = 1,y = 1) supercell structures) by using the density functional theory based on the full-potential linear augmented plane wave method via inclusion of spin polarized calculation. Addition of metal dopant ions in bismuth telluride enhanced the totalspin magnetic moment of the entire system ($M_{tot}$), which was further increased by the presence of the carbon ion. However, spin magnetic moment of individual dopant ions ($M_S$) was found to be increased or decreased depending upon the position of the metal-carbon dopants relative to each other. This increase in $M_S$ is explained by Zener exchange mechanism. C showed a weak $M_S$, in its addition in the BT system. Gd-C co-doping showed highest $M_{tot}$ and $M_S$ compared to Fe-C doped (BT) system. The spin magnetic moment of the system and that of individual dopant ions is influenced by varying the position of C relative to metal dopant ions in BT system. This understanding over the changes inthe value of magnetic moment with respect to the position of C ion compared to other dopant ions in the material will lead to the future improvement of magnetic data storage devices.