Anti-levitation in integer quantum Hall systems

Wang, Chen; Avishai, Y.; Meir, Yigal; Wang, Xiangrong

doi:10.1103/physrevb.89.045314

Phys. Rev. B

2014

DOI: 10.1103/physrevb.89.045314

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Anti-levitation in integer quantum Hall systems

Chen Wang

Y. Avishai

Yigal Meir

et al.

Abstract: 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 di… Show more

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Cited by 9 publications

(9 citation statements)

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“…However, we find dY L /dL = 0 at WNs for L > 18 within numerical errors, instead of dY L /dL > 0 for an extended state. The merging of Y L (E = 0) indicates E = 0 is a critical point and a novel phase transition between an isolated critical state at WNs and extended states at E 0, very similar to the phase transition from an isolated critical level to localized states in IQH systems [32]. Our data fit well to the one-parameter scaling hypothesis of Y L (E) = f (L/ξ) with ξ = ξ 0 |E| −ν for states near E = 0.…”

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confidence: 72%

Non-Wigner-Dyson level statistics and fractal wave function of disordered Weyl semimetals

2019

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Finding fingerprints of disordered Weyl semimetals (WSMs) is an unsolved task. Here we report such findings in the level statistics and the fractal nature of electron wavefunction around Weyl nodes of disordered WSMs. The nearest-neighbor level spacing follows a new universal distribution P c (s) = C 1 s 2 exp[−C 2 s 2−γ 0 ] originally proposed for the level statistics of critical states in the integer quantum Hall systems or normal dirty metals (diffusive metals) at metal-to-insulator transitions, instead of the Wigner-Dyson distribution for diffusive metals. Numerically, we find γ 0 = 0.62 ± 0.07. In contrast to the Bloch wavefuntions of clean WSMs that uniformly distribute over the whole space of (D = 3) at large length scale, the wavefunction of disordered WSMs at a Weyl node occupies a fractal space of dimension D = 2.18 ± 0.05. The finite size scaling of the inverse participation ratio suggests that the correlation length of wavefunctions at Weyl nodes (E = 0) diverges as ξ ∝ |E| −ν with ν = 0.89 ± 0.05. In the ergodic limit, the level number variance Σ 2 around Weyl nodes increases linearly with the average level number N, Σ 2 = χN, where χ = 0.2 ± 0.1 is independent of system sizes and disorder strengths.Crystal Weyl semimetals (WSMs), characterized by the linear crossings of their conduction and valence bands at Weyl nodes (WNs) and topologically protected surface states, have attracted enormous attention in recent years because of their exotic properties and potentials in applications [1][2][3][4][5][6][7][8]. There is little doubt that WSMs are a new state of matter in nature. However, the characteristics of WSMs for a crystal do not apply to a disordered system since the lattice momentum is not a good quantum number. To fully establish the WSMs as a genuine state of matter, one needs to find their fingerprints in disorders that inevitably exist in all materials. It was originally believed that disordered WSMs are featured by vanishing density of states (DOS) at WNs [9][10][11][12][13]. The divergence of the bulk state localization length at the Weyl-semimetalto-diffusive-metal (WSM-to-DM) transition was also conjectured [14][15][16][17][18]. Nonetheless, these features were challenged in many recent studies [19][20][21][22]. So far, a simple working criterion for disordered WSMs is still lacking. This study aims to search the fingerprints from the random matrices that describe the disordered WSMs.Random matrices have broad applications in many fields of physics [23][24][25][26][27]. In the condensed matter physics, random matrix theory can be used to distinguish different types of metals. The distribution P(s) of nearest-neighbour level spacing s (in the unit of the mean level spacing) of diffusive metals (normal dirty metals) and the level number variance Σ 2 (∆E) = n 2 − n 2 in a given energy range are governed by the Wigner-Dysion distributions [28]. For example, P(s) follows the Wigner surmises, P β (s) = C 1 s β exp[−C 2 s 2 ] (C 1 and C 2 are determined by the probability normalization and the u...

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confidence: 72%

Non-Wigner-Dyson level statistics and fractal wave function of disordered Weyl semimetals

2019

Self Cite

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“…3(c) where E c (W ) is plotted v.s W for B = 1/5 (black squares) and B = 1/2 (red circles). The fact that for W ≥ 6.5 all states are localized (albeit in the absence of SOC), has already been substantiated [17].…”

mentioning

confidence: 79%

“…On both sides of E c , lnλ M (E) decreases with M , indicating that all states away from E c are localized. However, at the critical point E c ,λ M (E) is independent of M , and the corresponding states are critical [17]. The bottom panel displays lnλ M (E) for the same values of B and W as in the upper panel when the constant (Rashba) SOC strength is a = 0.1.…”

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confidence: 99%

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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“…More recently, by using the Anderson model on square lattice with on-site random disorder potentials, a surprising anti-levitation behavior was observed from numerical investigations [12]. 3 There, the energy of the extended states of a LL moves below the "traditional" Landau level center as either the disorder strength increases or the magnetic field strength decreases [12].…”

mentioning

confidence: 99%

“…3 There, the energy of the extended states of a LL moves below the "traditional" Landau level center as either the disorder strength increases or the magnetic field strength decreases [12].…”

mentioning

confidence: 99%

Antilevitation of Landau levels in vanishing magnetic fields

et al. 2016

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We report in this paper an anti-levitation behavior of Landau levels in vanishing magnetic fields in a high quality heterojunction insulated-gated field-effect transistor. We found, in the Landau fan diagram of electron density versus magnetic field, the positions of the magneto-resistance minima at Landau level fillings =4, 5, 6 move below the "traditional" Landau level line to lower electron densities. Moreover, the even and odd filling factors show quantitatively different behaviors in anti-levitation, suggesting that the exchange interactions may be important.

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Anti-levitation in integer quantum Hall systems

Cited by 9 publications

References 38 publications

Non-Wigner-Dyson level statistics and fractal wave function of disordered Weyl semimetals

Non-Wigner-Dyson level statistics and fractal wave function of disordered Weyl semimetals

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

Antilevitation of Landau levels in vanishing magnetic fields

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