Critical parameters for the disorder-induced metal-insulator transition in fcc and bcc lattices

Eilmes, Andrzej; Fischer, Andrea M.; Röemer, Rudolf A.

doi:10.1103/physrevb.77.245117

Cited by 20 publications

(38 citation statements)

References 34 publications

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“…This Hamiltonian belongs to the symmetry class AII [21] (or, DIII for W = 0). The transfer matrix [22,23] is given in terms of the wave function ψ n on a slice at z = n as…”

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confidence: 99%

Disordered Weak and Strong Topological Insulators

2013

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A global phase diagram of disordered weak and strong topological insulators is established numerically. As expected, the location of the phase boundaries is renormalized by disorder, a feature recognized in the study of the so-called topological Anderson insulator. Here, we report unexpected quantization, i.e., robustness against disorder of the conductance peaks on these phase boundaries. Another highlight of the work is on the emergence of two subregions in the weak topological insulator phase under disorder. According to the size dependence of the conductance, the surface states are either robust or "defeated" in the two subregions. The nature of the two distinct types of behavior is further revealed by studying the Lyapunov exponents.PACS numbers: 73.20.Fz, 71.30.+h Robustness against disorder is a defining property of the topological quantum phenomena. Depending on the degree of this robustness, three-dimensional (3D) Z 2 topological insulators (TIs) [1][2][3] are classified into strong and weak (STI and WTI). Bulk-surface correspondence implies that an STI exhibits a single helical Dirac cone that is protected, while a WTI manifests generally an even number (possibly null) of Dirac cones depending on the orientation of the surface [4].Unusual robustness of Dirac electrons (especially in the case of a single Dirac cone) against disorder has been widely recognized in the study of graphene [5,6]. As a consequence of the absence of backward scattering [7], the Dirac electrons do not localize. However, in the presence of valleys (even number of Dirac cones) they do localize mediated by intervalley scatterings [8]. Does this mean that an STI continues to be an STI in the presence of arbitrarily strong disorder, while a WTI simply collapses on the switching on of the short-ranged potential disorder that induces intervalley scattering?Recent studies on the disordered WTI [9,10] seem to suggest that the reality is much different. Our global phase diagram depicted in Fig. 1 finds its way also in this direction. This phase diagram is established by a combination of the study of the averaged two-terminal conductance and of the quasi-1D decay length in the transfer matrix approach. In the actual computation the 3D disordered Z 2 topological insulator is modeled as an WilsonDirac-type tight-binding Hamiltonian with an effective (k-dependent) mass term m(k) = m 0 + m 2 µ=x,y,z (1 − cos k µ ) [11], implemented on a cubic lattice. The topological nature of the model is controlled by the ratio of two mass parameters m 0 and m 2 such that an STI phase with Z 2 (one strong and three weak) indices [4] (ν 0 , ν 1 ν 2 ν 3 ) = (1, 000) appears when −2 < m 0 /m 2 < 0, while the regime of parameters −4 < m 0 /m 2 < −2 falls on a WTI phase with (ν 0 , ν 1 ν 2 ν 3 ) = (0, 111) [12].The obtained "global" phase diagram depicted in Fig. 1 highlights the main results of the Letter. This phase diagram shows how disorder modifies the above topological classification in the clean limit (naturally as a function of the strength of disorde...

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“…This Hamiltonian belongs to the symmetry class AII [21] (or, DIII for W = 0). The transfer matrix [22,23] is given in terms of the wave function ψ n on a slice at z = n as…”

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confidence: 99%

Disordered Weak and Strong Topological Insulators

2013

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“…[19] and extended in Refs. [20][21][22], in order to obtain the localization length index . The LE is believed to have scaling behavior (see, for example, Refs.…”

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“…The function fðMÞ is a decreasing function of M. Usually, a power-law correction is used: fðMÞ ¼ M y , where y < 0 is the irrelevant exponent. We used the following formula to fit the data [14,22]:…”

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confidence: 99%

Numerical Study of the Localization Length Critical Index in a Network Model of Plateau-Plateau Transitions in the Quantum Hall Effect

Amado

Sedrakyan

et al. 2011

Phys. Rev. Lett.

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We calculate numerically the localization length critical index within the Chalker-Coddington model of the plateau-plateau transitions in the quantum Hall effect. We report a finite-size scaling analysis using both the traditional power-law corrections to the scaling function and the inverse logarithmic ones, which provided a more stable fit resulting in the localization length critical index ¼ 2:616 AE 0:014. We observe an increase of the critical exponent with the system size, which is possibly the origin of discrepancies with early results obtained for smaller systems. DOI: 10.1103/PhysRevLett.107.066402 PACS numbers: 71.30.+h, 71.23.An, 72.15.Rn Plateau-plateau transitions in the quantum Hall effect have been one of the most challenging problems in condensed matter physics during the past two decades. It is an interesting example of the localization-delocalization transition in two-dimensional disordered systems, where a quantum critical point appears due to the breaking of time reversal symmetry. One of the important problems in this area of research is the formulation of a quantum field theory describing the transition. The first suggestion in this respect appeared in Ref. [1], where the authors noticed that the presence of the topological term in the nonlinear sigma model formulation of the problem can result in the occurrence of delocalized states under strong magnetic fields.Later, Chalker and Coddington [2] formulated a phenomenological model of quantum percolation based on a transfer-matrix approach (referred to as the CC model hereafter). The numerical value 2:5 AE 0:5 of the critical index of the Lyapunov exponent (LE) calculated within the CC model (see Ref.[3] for a review) was in good agreement with the experimentally measured localization length index ¼ 2:4 in the quantum Hall effect [4]. This success motivated considerable interest in the CC model and stimulated its further investigation until the present day [5][6][7][8][9][10][11][12][13][14]. In early studies the continuum limit of the CC model was related to replicas of ordinary spin chains [6], a Hubbard-like model [7], and supersymmetric spin chains [8,9]. In Refs. [10,11], the continuum limit was also related to the conformal field theory of the Wess-Zumino-Witten-Novikov (WZWN) type. Analyzing the representations of the PSLð2j2Þ conformal field theory, they found one which gives a reasonable value of 16=7 ' 2:286 for the localization length index. Moreover, multifractal scaling indices of the CC model were predicted to depend quadratically on the parameter q of the multifractal analysis within the WZWN model.Most intriguing developments in the plateau-plateau transition problem were reported later in Refs. [15,16], where the multifractal behavior of the CC model was investigated. In both papers, approximately quartic deviation from the exact quadratic dependence of the multifractal indices on the parameter q, predicted in Refs. [10,11], was observed. The latter suggested that the validity of the supersymmetric WZWN approach to plate...

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“…[21][22][23] The extended states always exist close to the band center irrespective of the disorder strength. In addition to the simple cubic lattice, the localization behaviors in more compact body-centered cubic ͑BCC͒ and face-centered cubic lattices have been investigated recently by Eilmes et al 24 The critical exponents are essentially the same among the three different types of lattices of the same universality class and the value of critical disorder W C increases with the coordination number of lattice types. 24 However, in many mixed valence semiconductors or doped perovskites, the primary cell usually contains more than one type of atom.…”

Section: Introductionmentioning

confidence: 99%

“…In addition to the simple cubic lattice, the localization behaviors in more compact body-centered cubic ͑BCC͒ and face-centered cubic lattices have been investigated recently by Eilmes et al 24 The critical exponents are essentially the same among the three different types of lattices of the same universality class and the value of critical disorder W C increases with the coordination number of lattice types. 24 However, in many mixed valence semiconductors or doped perovskites, the primary cell usually contains more than one type of atom. The electronic bands near the Fermi energy are composed of valence and conduction bands resulting from hybridization among the neighboring atoms of different types.…”

Section: Introductionmentioning

confidence: 99%

Disorder-type-dependent phase diagram in a CsCl-type complex Anderson lattice model

Wang

Zhang

2010

Phys. Rev. B

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The investigation on disorder-driven metal-insulator transition of the Anderson lattice model has been extended to a CsCl-type complex lattice to accommodate for the hybridized bands originating from atomic orbitals of inequivalent lattice sites. Using the standard transfer-matrix method and finite-size scaling an asymmetrical mobility edge is found in the energy-disorder phase diagram under site-selective disorder. The critical disorder is larger in the less disorder-affected band than its counterpart in the more disorder-affected band. Moreover, a unique type of delocalized state appears at the edge of the less disorder-affected band. The asymptotic localization length M ͑W͒ increases linearly with the longitudinal sample size, which depends neither on the lateral size M nor on the disorder strength W. Except for this particular energy, metal-insulator transitions exist for all other energies and reduced localization lengths satisfy the single-parameter scaling law. The critical exponent, Ϸ 1.5-1.6, is in good agreement with the previous results. The critical disorder is larger than that of a simple cubic lattice due to increased coordination number. The complex Anderson lattice model considered here has the advantage of simulating the localization disparity between electron-and holedoped bands in the presence of site-selective disorder.

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Critical parameters for the disorder-induced metal-insulator transition in fcc and bcc lattices

Cited by 20 publications

References 34 publications

Disordered Weak and Strong Topological Insulators

Disordered Weak and Strong Topological Insulators

Numerical Study of the Localization Length Critical Index in a Network Model of Plateau-Plateau Transitions in the Quantum Hall Effect

Disorder-type-dependent phase diagram in a CsCl-type complex Anderson lattice model

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