  The binary Bi-chalchogenides, Bi2Ch3, are widely regarded as model examples
of a recently discovered new form of quantum matter, the three-dimensional
topological insulator (TI) [1-4]. These compounds host a single spin-helical
surface state which is guaranteed to be metallic due to time reversal symmetry,
and should be ideal materials with which to realize spintronic and quantum
computing applications of TIs [5]. However, the vast majority of such compounds
synthesized to date are not insulators at all, but rather have detrimental
metallic bulk conductivity [2, 3]. This is generally accepted to result from
unintentional doping by defects, although the nature of the defects responsible
across different compounds, as well as strategies to minimize their detrimental
role, are surprisingly poorly understood. Here, we present a comprehensive
survey of the defect landscape of Bi-chalchogenide TIs from first-principles
calculations. We find that fundamental differences in the energetics of native
defect formation in Te- and Se-containing TIs enables precise control of the
conductivity across the ternary Bi-Te-Se alloy system. From a systematic
angle-resolved photoemission (ARPES) investigation of such ternary alloys,
combined with bulk transport measurements, we demonstrate that this method can
be utilized to achieve true topological insulators, with only a single Dirac
cone surface state intersecting the chemical potential. Our microscopic
calculations reveal the key role of anti-site defects for achieving this, and
predict optimal growth conditions to realize maximally-resistive ternary TIs.
