Integer quantum Hall transition: An alternative approach and exact results

Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder

“…Technically, this result obtains because the disorder-averaged AIII model is conformally invariant at the Dirac point, and the exact LDOS moment spectra can be extracted using an Abelian bosonization treatment. The exact spectrum 24 is quadratic in q, and takes the form of Eq. (2.3), with…”

“…(3.3)] were originally studied in Ref. 24. In this work, the exact multifractal spectrum τ (q) was calculated for the broken-T , random vector potential (∼ in-plane polarized magnetic impurity) 53 class AIII model, to all orders in ∆ A .…”

“…All three classes exhibit delocalized states in 2D, although this occurs only at the Dirac point for class AIII. 24 In the T -invariant symplectic case, the unpaired single Dirac flavor avoids the usual spinorbit metal-insulator transition, 9 remaining delocalized even for strong disorder due to a topological term. 10 The generic case of broken-T with all three disorder potentials non-zero realizes the unitary class A, and is believed to flow under renormalization to the plateau transition in the integer quantum Hall effect.…”

“…In particular, we extend the pioneering results of Ref. 24 to the generic cases of time-reversal (T ) preserving and breaking impurities. Our calculations are performed in the near-ballistic limit, 25 wherein weak disorder enters as a perturbation to the clean Dirac band structure.…”

“…18,[26][27][28] These appear at strong coupling (many impurities) for dirty Dirac fermions. 9,10,24,29 We consider the case of a single flavor Dirac surface band, relevant to (e.g.) the TIs Bi 2 Se 3 and Bi 2 Te 3 (Refs.…”