Numerical study of localization in the two-state Landau level

Integer quantum Hall effect in double-layer systems

“…This work is motivated by recent experiments hinting at changes in localization properties when two different Landau levels are nearly degenerate [22][23][24][25][27][28][29] , by growing interest in the conditions necessary for the occurrence of the quantum Hall effect in three-dimensional electron systems, and by the need for improved understanding of the disappearance of the quantum Hall effect at weak magnetic fields in high mobility samples. In each case, we believe that double-layer quantum Hall systems offer advantages for both theoretical studies and for the experimental studies which we hope to motivate.…”

Diagrammatic analysis of the two-state quantum Hall system with chiral invariance

“…Thus, we have found the exact value of the longitudinal conductivity at E = ±∆. In the previous numerical work [4], this value was obscure, although it suggested the similar value. We find no particular difference for the conductivity between the extended state at E = ∆ and the E = 0 in the ∆ = 0 case.…”

“…We have evaluated the real part of the Green function numerically by the same method of Ref. [4], and find that the real part vanishes at E = ±∆.…”

“…In the previous paper [4], the Zeeman term has been included, which does not break a chiral invariance. It has been shown that the density of state has a gap less than the Zeeman energy ∆, and the extended state shifts from E = 0 to the Zeeman energy E = ∆.…”

“…This cancellation occurs not only for the Gaussian white noise distribution but also for the general local non-Gaussian random distribution. [1] This model has been examined further by the numerical method [3,4] and the localization exponents have been estimated for these extended states. The localization length exponent at E = 0 seems different from the usual quantum Hall system and belongs a new universality class, although other two extended states at E = E 1 belongs to the conventional quantum Hall universality class with the localization length exponent ν ≃ 2.3 [4].…”