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Pure Topological Insulating materials preserve a unique electronic statecomprising of bulk insulating gap and conducting surface states. Here we usebulk Bi2Se3 single crystals possessing Se vacancy defects as a prototypetopological insulator (TI) material for exploring the effect of non-magneticdisorder on the conducting properties of TIs. We employ a sensitive,non-contact, mutual inductance based technique for measuring the surface andbulk contribution to electrical conductivity in the TI. We discern thedifferent contributions, by observing that predominant surface electricalconduction produces linear frequency dependence of the pickup signal while bulkconductivity gives rise to quadratic frequency dependence. We also see analgebraic temperature dependent surface conductivity while an activated bulkconductivity. Using the above we uncover an interplay between surface and bulkcontribution to electrical conductivity in the TI as a function oftemperatures. In the Bi2Se3 crystals the transformation from surface to bulkdominated electrical transport is found to occur close to 70 K. Thistemperature range matches well with our results from activated bulk electricaltransport results which shows an activation energy scale, delta which is in themillieV range. The gap delta is much less than the bulk band gap in Bi2Se3, andwhich we argue is associated with defect states in the TI material. Tounderstand our results, we propose a model of a TI comprising of aninhomogeneous low electrically conducting medium (bulk) which is sandwichedbetween thin two high electrically conducting sheets (surface). Theinhomogeneous TI state we argue is generated by Selenium vacancies defects inBi2Se3, which is responsible for producing an interplay between bulk andsurface conductivity.

Non-contact mutual inductance based measurement of an inhomogeneous topological insulating state in Bi2Se3 single crystals with defects