Insulator-metal quantum phase transition in heavy topological insulators

Exponentially localized surface states are the most distinctive property of a crystal with non-trivial band topology. Such surface states play a key role in characterizing topological insulators (TIs), both in theory and experiments. TIs resulting from the hybridization of heavy (or nearly flat) and light (or dispersive) bands are automatically tuned to the vicinity of an insulator-to-metal phase transition (IMT), which is not accompanied by a change in bulk band-topology. By formulating a scaling theory for IMTs in such "heavy" TIs, we show that the proximity to an IMT manifests most dramatically in the behavior of the surface states, viz. (i) the strength of spin-orbital locking is strongly suppressed; (ii) the surface conduction and valence bands support vastly different number of states; (iii) the surface states penetrate deep into the bulk and the penetration depth diverges at the IMT point. Thus, the surface states in heavy TIs coexist with bulk scattered states, and may no longer serve as an useful determinant of their bulk band-topology. The mechanism of degradation of surface states discussed here is generic, and expected to hold in both heavy TIs and semimetals.