Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

Xie, Xin; Wang, Xiang Rong; Liu, Dongzi

doi:10.1103/physrevlett.80.3563

Cited by 59 publications

(75 citation statements)

References 34 publications

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“…Following the method specified in Ref. [26], the 2M vector of wave function amplitudes (ψ n+1 ,ψ n ) T is related to the vector (ψ n ,ψ n−1 ) T according to the relation…”

Section: Model and Methodsmentioning

confidence: 99%

Anti-levitation in integer quantum Hall systems

et al. 2014

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The evolution of extended states of two-dimensional electron gas with white-noise randomness and field is numerically investigated by using the Anderson model on square lattices. Focusing on the lowest Landau band we establish an anti-levitation scenario of the extended states: As either the disorder strength W increases or the magnetic field strength B decreases, the energies of the extended states move below the Landau energies pertaining to a clean system. Moreover, for strong enough disorder, there is a disorder-dependent critical magnetic field B c (W ) below which there are no extended states at all. A general phase diagram in the W -1/B plane is suggested with a line separating domains of localized and delocalized states.

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“…Following the method specified in Ref. [26], the 2M vector of wave function amplitudes (ψ n+1 ,ψ n ) T is related to the vector (ψ n ,ψ n−1 ) T according to the relation…”

Section: Model and Methodsmentioning

confidence: 99%

Anti-levitation in integer quantum Hall systems

et al. 2014

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“…The electron localization length is often obtained from the transfer matrix method. For a two-dimensional system, however, it is well known that, from this quantity, it is difficult to provide a conclusive answer to questions related to the metal-insulator transition (MIT) [10]. On the other hand, level-statistics analysis [11] has been used in studying MIT.…”

Section: -1mentioning

confidence: 99%

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

et al. 2001

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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...

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“…Using the transfer matrix method we calculate λ M (E) by a standard iteration algorithm [4,16]. In our calculations L > 10 6 ≫ λ M (E) and self-averaging requires relatively small data ensembles to achieve good statistics.…”

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Band of Critical States in Anderson Localization in a Strong Magnetic Field with Random Spin-Orbit Scattering

Wang

Avishai

et al. 2015

Phys. Rev. Lett.

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Anderson localization problem for non-interacting two-dimensional electron gas subject to strong magnetic field, disordered potential and spin-orbit coupling is studied numerically on a square lattice. The nature of the corresponding localization-delocalization transition and the properties of the pertinent extended states depend on the nature of the spin-orbit coupling (uniform or fully random). For uniform spin-orbit coupling (such as Rashba coupling), there is a band of extended states in the center of a Landau band as in a "standard" Anderson metal-insulator transition. However, for fully random spin-orbit coupling, the familiar pattern of Landau bands disappears. Instead, there is a central band of critical states with definite fractal structure separated at two critical energies from two side bands of localized states. Moreover, finite size scaling analysis suggests that for this novel transition, on the localized side of a critical energy Ec, the localization length diverges as ξ(E) ∝ exp(α/ |E − Ec|), a behavior which, along with the band of critical states, is reminiscent of a Berezinskii-Kosterlitz-Thouless transition. Traditionally, non-interacting disordered electronic systems subject to disordered potential are classified according to the symmetries of their Hamiltonian with respect to time reversal (TR) and spin rotation (SR) transformations. Considering the Hamiltonian as a random matrix [1-3], its symmetries determine to which random matrix Gaussian ensemble (also referred to as universality class) it belongs, orthogonal (both TR and SR symmetries are satisfied), symplectic (only TR symmetry) or unitary.This classification is intimately related to one of the most fundamental concepts in the physics of disordered electronic systems: the Anderson localization transition (ALT) [4,5] that is a quantum phase transition between localized and extended states in a disordered system. The critical dimension for existence or non-existence of ALT is d = 2. For d < 2 there is no ALT while for d > 2 there is always ALT. Hence, for two-dimensional electron gas (2DEG), ALT (if it exists) is of special interest. The scaling theory of localization [6] (developed before the discovery of the quantum Hall effect) together with calculations based on nonlinear sigma model [7,8], established that for d = 2, ALT does not exist for the orthogonal and unitary classes (zero or finite magnetic field, respectively) and does exist for the symplectic class (finite spin-orbit scattering and zero magnetic field). After the discovery of the integer Quantum Hall effect (IQHE) [9], topology was also recognized as a property determining the pertinent universality class [10]. Mathematically, the role of topology in the IQHE is quantified by the occurrence of a topological term in the action of the corresponding non-linear sigma model [11]. In the presence of the topological term it is established that if SR invariance is respected, the system is in the IQHE universality class characterized by a Hall transition between localized and cr...

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Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

Cited by 59 publications

References 34 publications

Anti-levitation in integer quantum Hall systems

Anti-levitation in integer quantum Hall systems

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

Band of Critical States in Anderson Localization in a Strong Magnetic Field with Random Spin-Orbit Scattering

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