Metallic Phase in Quantum Hall Systems due to Inter-Landau-Band Mixing

Abstract

The electronic eigenstates of a quantum Hall (QH) system are chiral states. Strong inter-Landau-band mixings among these states can occur when the bandwidth is comparable to the spacing of two adjacent Landau bands. We show that mixing of localized states with opposite chirality can delocalize electronic states. Based on numerical results, we propose the existence of a metallic phase between two adjacent QH phases and between a QH phase and the insulating phase. This result is consistent with nonscaling behaviors observed in recent experiments on a quantum Hall liquid-to-insulator transition. DOI: 10.1103/PhysRevLett.87.216802 PACS numbers: 73.43. -f, 71.30. +h, 73.20.Jc Recently there has been a great renewal of interest on transitions from integer quantum Hall effect (IQHE) states to an insulator [1][2][3][4][5]. According to the scaling theory of localization [6], all electrons in a disordered two-dimensional system are localized in the absence of a magnetic field. In the presence of a strong magnetic field, a series of disorder-broadened Landau bands (LBs) will appear, and extended states reside at the centers of these bands while states at other energies are localized. The integrally quantized Hall (QH) plateaus are observed when the Fermi level lies in the localized states, with the value of the Hall conductance, s xy ne 2 ͞h, related to the number of filled LBs ͑n͒. As a function of the magnetic field, the Hall conductance jumps from one QH plateau to another when the Fermi energy crosses an extended-state level. Many previous studies [1][2][3][4][5] have been focused on how such a transition occurs.One overlooked issue regarding IQHE is the nature of a transition from one QH plateau to another. All existing theories assume it to be a continuous quantum phase transition. The fingerprint of a continuous phase transition is scaling laws around the transition point, and this assumption is mainly due to the early scaling experiments [7]. In the case of IQHE, a continuous quantum phase transition means algebraic divergence of the longitudinal Hallresistivity slope in temperature T at the transition point. However, recent experiments [5] showed that such slopes remain finite when they are extrapolated to T 0. This implies a nonscaling behavior around a transition point, contradicting the expectation of continuous quantum phase transitions suggested by the theories. It also means that one should reexamine the nature of plateau transitions.In this Letter we show that a narrow metallic phase may exist between two adjacent IQHE phases and between an IQHE phase and an insulating phase when the effect of interband mixing of opposite chirality is taken into account. Thus, it corresponds to two consecutive quantum phase transitions instead of one when the Hall conductance jumps from one plateau to another, consistent with the nonscaling behavior observed in experiments.According to the semiclassical theory [8], an electronic state in a strong magnetic field and in a smooth potential can be decomposed into a rapid c...

Anti-levitation in integer quantum Hall systems

“…In order to add more quantitative perception, it is vital to elucidate the behavior of extended states in LBs as the magnetic field gradually decreases to zero, or as the disorder gradually increases. Different answers to this question lead to different global phase diagrams [6][7][8] for the IQHE.…”

“…In Refs. [6][7][8] the scenario of Chern number annihilation as B → 0 has been discussed on a qualitative level. In order to add more quantitative perception, it is vital to elucidate the behavior of extended states in LBs as the magnetic field gradually decreases to zero, or as the disorder gradually increases.…”

A possible unified picture for both scaling and non-scaling plateau-to-plateau transitions in quantum Hall systems

“…This means a (a) E-mail: phgxiong@bnu.edu.cn non-scaling behavior around a P-P transition, in contradiction with the expectation of continuous quantum phase transitions [11,12]. In recent studies [13,14] we provided a possible picture for such non-scaling behavior. We showed that an extended-state band is formed near each LB center because of the mixing of states with opposite chiralities, leading to a narrow metallic phase between neighboring QH plateaus.…”

Weakly chiral networks and two-dimensional delocalized states in a weak magnetic field

“…6-15. On the other hand, theoretical numerical studies [16][17][18][19][20][21][22][23][24][25] aimed at revealing levitation on a microscopic level, are less conclusive 26 . The only established fact is the tendency [27][28][29][30][31][32][33] for floating up of delocalized states upon decreasing ω c in the strong-field domain, where Landau levels are still well-defined.…”