Noncontact Mutual-Inductance-Based Measurement of an Inhomogeneous Topological Insulating State in Bi2Se3 Single Crystals with Defects

Pure topological insulating materials preserve a unique electronic state comprised of a bulk insulating gap and conducting surface states. We use bulk Bi2Se3 single crystals possessing Se vacancy defects as a prototype topological insulator (TI) material for exploring the effect of nonmagnetic disorder on the conducting properties of TIs. We employ a sensitive, noncontact mutual-inductance-based technique for measuring the surface and bulk contributions to electrical conductivity in the TI. We discern the bulk and surface contributions by observing that the predominant surface electrical conduction shows a linear frequency dependence of the pickup signal while bulk conductivity gives rise to a quadratic frequency dependence. We also observe an algebraic temperature-dependent surface conductivity and an activated form of bulk electrical conductivity. Using the above, we uncover an interplay between surface and bulk contributions to electrical conductivity in the TI as a function of temperature. In the Bi2Se3 crystals, the transformation from surface to bulk-dominated electrical transport is found to occur close to a temperature of 70 K. This temperature matches well with our results from activated bulk electrical transport results, which show an activation energy scale Δ, which is in the meV range. The gap Δis much less than the bulk band gap in Bi2Se3, which we argue is associated with defect states in the TI material. To understand our results, we propose a model of TI comprised of an inhomogeneous low electrically conducting medium (bulk), which is sandwiched between two thin high electrically conducting sheets (surface). We argue that the inhomogeneous TI state is generated by selenium vacancy defects in Bi2Se3, which are responsible for producing an interplay between bulk and surface conductivities.