Positron lifetime has been measured in SmS under external pressures from 0 to ∼ 16 kbar, and in (Sm_0·8Gd_0·2)S at temperatures from 10 K to 300 K. An abrupt drop in the lifetime was observed at the valence transition at a pressure of 6·5 kbar in SmS and at a temperature of ∼ 120 K in (Sm_0·8Gd_0·2)S. Measurement of the Doppler broadening of the annihilation photons was made in (Sm_0·8 Gd_0·2)S as a function of temperature. The line shape parameter of the Doppler broadened spectrum also showed an abrupt change at the transition. Angular correlation of annihilation photons was measured in the semiconducting phase of SmS and in the metallic phase of (Sm_0·8Tb_0·2)S. The correlation profile in the mixed valence (metallic) phase was broader than that in the semi-conducting phase. These results have been explained on the basis of the electronic structure of the semiconducting and the metallic phases of these materials.

Here we present an overview of some of our recent experimental investigation on the high conducting topologically protected surface state properties of a 3D topological insulator (TI), Bi$_2$Se$_3$, in both bulk and single-crystals form. Selenium (Se) vacancies in Bi$_2$Se$_3$ are natural bulk charge dopants, hence these vacancies act as non-magnetic defects in these materials. We use Bi$_2$Se$_3$ material as a prototype of a 3D TI) material with the disorder, for exploring the effects of non-magnetic disorder on the topological conducting surface states. Using a sensitive non-contact mutual inductance-based measurement technique, we identify distinct signatures of surface and bulk contributions to electrical conductivity in a TI Bi$_2$Se$_3$. We show a temperature-dependent transformation from surface to bulk dominated electrical conductivity and unravel the unusual resurfacing of a surface-dominated electrical conductivity at high temperatures. We show that the surface to bulk conductivity transformation is related to a unique activation energy scale ${\Delta}$ in the range of tens of meV, which is smaller than the bulk-insulating gap in Bi$_2$Se$_3$. This gap, we believe is related to a defect state created by the charge dopant Se vacancies in Bi$_2$Se$_3$. We also see interesting effects related to disorder-related coupling of the surface states. The Se vacancies which dope the bulk of the Bi$_2$Se$_3$ crystal lead to an unusual inductive-type coupling of the high conducting 2D-like surface states. The coupling leads to a critical thickness feature in bulk TI crystal, which is distinct from the direct coupling limit in TI’s. We find that if the thickness of the Bi$_2$Se$_3$ crystal exceeds this criticalthickness, then the surface states are no longer inductively coupled. To probe the temperature-related surface to bulk transformation in conductivity of Bi$_2$Se$_3$, we use a high sensitivity magneto-optical imaging technique to directly imagethe distribution of current in single crystal and a thin film of Bi$_2$Se$_3$. At low temperatures, we observed a strong sheet current from the topological surface state. Above 80 K, we report that the emergence of a temperature-dependentin homogeneous, grainy current distribution state in Bi$_2$Se$_3$ single crystals. The grainy state has mixed regions with high and low current densities. The observation of the emergence of a temperature-dependent inhomogeneous phase in the TI suggests the possibility of a disorder-driven spontaneous phase separation scenario.