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Keith Slevin

Publications and source records attributed to Keith Slevin.

At least 37 records · Page 2Linked to original sources
arXiv2012

Effect of electron-electron interaction near the metal-insulator transition in doped semiconductors studied within the local density approximation

We report a numerical analysis of Anderson localization in a model of a doped semiconductor. The model incorporates the disorder arising from the random spatial distribution of the donor impurities and takes account of the electron-electron interactions between the carriers using density functional theory in the local density approximation. Preliminary results suggest that the model exhibits a metal-insulator transition.

cond-mat.mtrl-sci↗
arXiv2012

Finite Size Scaling of the Chalker-Coddington Model

In Ref.1 (Physical Review B 80, 041304(R) (2009)), we reported an estimate of the critical exponent for the divergence of the localization length at the quantum Hall transition that is significantly larger than those reported in the previous published work of other authors. In this paper, we update our finite size scaling analysis of the Chalker-Coddington model and suggest the origin of the previous underestimate by other authors. We also compare our results with the predictions of Lütken and Ross (Physics Letters B 653, 363 (2007)).

cond-mat.mes-hall↗
arXiv2011

Multifractal finite-size-scaling and universality at the Anderson transition

We describe a new multifractal finite size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simulations of system sizes up to L^3=120^3 and involving nearly 10^6 independent wavefunctions have yielded unprecedented precision for the critical disorder W_c=16.530 (16.524,16.536) and the critical exponent nu=1.590 (1.579,1.602). We find that the multifractal exponents Delta_q exhibit a previously predicted symmetry relation and we confirm the non-parabolic nature of their spectrum. We explain in detail the MFSS procedure first introduced in our Letter [Phys. Rev. Lett. 105, 046403 (2010)] and, in addition, we show how to take account of correlations in the simulation data. The MFSS procedure is applicable to any continuous phase transition exhibiting multifractal fluctuations in the vicinity of the critical point.

cond-mat.dis-nn↗
arXiv2010

Critical parameters from generalised multifractal analysis at the Anderson transition

We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction amplitudes is sufficient to characterize the transition. In combination with finite-size scaling, this formalism permits the critical parameters to be estimated without the need for conductance or other transport measurements. Applying this method to high-precision data for wavefunction statistics obtained by exact diagonalization of the three-dimensional Anderson model, we estimate the critical exponent $ν=1.58\pm 0.03$.

cond-mat.dis-nn↗
arXiv2010

Finite Size Scaling Analysis of the Anderson Transition

This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are briefly sketched. The finite size scaling method is described. Recent results for the critical exponents of the different symmetry classes are summarised. The importance of corrections to scaling are emphasised. A comparison with experiment is made, and a direction for future work is suggested.

cond-mat.mes-hall↗
arXiv2009

Critical exponent for the quantum Hall transition

We report an estimate $ν= 2.593$ $[ {2.587,2.598} ]$ of the critical exponent of the Chalker-Coddington model of the integer quantum Hall effect that is significantly larger than previous numerical estimates and in disagreement with experiment. We conclude that models of non-interacting electrons cannot explain the critical phenomena of the integer quantum Hall effect.

cond-mat.dis-nn↗
arXiv2009

Point-Contact Conductance in Asymmetric Chalker-Coddington Network Model

We study the transport properties of disordered two-dimensional electron systems with a perfectly conducting channel. We introduce an asymmetric Chalker-Coddington network model and numerically investigate the point-contact conductance. We find that the behavior of the conductance in this model is completely different from that in the symmetric model. Even in the limit of a large distance between the contacts, we find a broad distribution of conductance and a non-trivial power law dependence of the averaged conductance on the system width. Our results are applicable to systems such as zigzag graphene nano-ribbons where the numbers of left-going and right-going channels are different.

cond-mat.mes-hall↗
arXiv2008

Transport properties in network models with perfectly conducting channels

We study the transport properties of disordered electron systems that contain perfectly conducting channels. Two quantum network models that belong to different universality classes, unitary and symplectic, are simulated numerically. The perfectly conducting channel in the unitary class can be realized in zigzag graphene nano-ribbons and that in the symplectic class is known to appear in metallic carbon nanotubes. The existence of a perfectly conducting channel leads to novel conductance distribution functions and a shortening of the conductance decay length.

cond-mat.mes-hall↗
arXiv2007

Chalker-Coddington model described by an S-matrix with odd dimensions

The Chalker-Coddington network model is often used to describe the transport properties of quantum Hall systems. By adding an extra channel to this model, we introduce an asymmetric model with profoundly different transport properties. We present a numerical analysis of these transport properties and consider the relevance for realistic systems.

cond-mat.mes-hall↗
arXiv2005

Quantum transport phenomena in disordered electron systems with spin-orbit coupling in two dimensions and below

Electron transport phenomena in disordered electron systems with spin-orbit coupling in two dimensions and below are studied numerically. The scaling hypothesis is checked by analyzing the scaling of the quasi-1D localization length. A logarithmic increase of the mean conductance is also confirmed. These support the theoretical prediction that the two dimensional metal in systems with spin-orbit coupling has a perfect conductivity. Transport through a Sierpinski carpet is also reported.

cond-mat.mes-hall↗
arXiv2003

The Anderson transition due to random spin-orbit coupling in two-dimension

We report an analysis of the Anderson transition in an SU(2) model with chiral symmetry. Clear single parameter scaling behaviour is observed. We estimate the critical exponent for the divergence of the localization length to be $ν=2.72\pm.02$ indicating that the transition belongs to the symplectic universality class.

cond-mat.dis-nn↗
arXiv2003

The chiral symplectic universality class

We report a numerical investigation of localization in the SU(2) model without diagonal disorder. At the band center, chiral symmetry plays an important role. Our results indicate that states at the band center are critical. States away from the band center but not too close to the edge of the spectrum are metallic as expected for Hamiltonians with symplectic symmetry.

cond-mat.dis-nn↗
arXiv2002

Scaling of the conductance distribution near the Anderson transition

The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is essential to investigate the scaling of the full conductance distribution to establish the scaling hypothesis. We present a clear cut numerical demonstration that the conductance distribution indeed obeys one parameter scaling near the Anderson transition.

cond-mat.dis-nn↗
arXiv2002

The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling

We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent $ν$ for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyse the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent $ν=2.73 \pm 0.02$.

cond-mat.dis-nn↗
arXiv2001

Reply to Suslov

In a recent submission to this archive arXiv:cond-mat/0105325, Suslov has claimed that our recent numerical estimate of the critical exponent of the Anderson transition $ν=1.57\pm.02$ is in error and that the available numerical data are consistent with a value of $ν=1$. We contest this claim and demonstrate using Suslov's own scaling procedure that $ν\ne 1$

cond-mat.dis-nn↗