arXiv subjects

A. Mobius

Publications and source records attributed to A. Mobius.

14 recordsLinked to original sources

arXiv2022

Incorrect sample classification in "Electron localization induced by intrinsic anion disorder in a transition metal oxynitride"

In the recent study of the metal-insulator transition (MIT) in the disordered crystalline solid SrNbO$_{3-x}$N$_x$ by Daichi Oka et al. [Commun. Phys. 4, 269 (2021)], the data evaluation relies on the Al'tshuler-Aronov theory of the interference of electron-electron interaction and elastic impurity scattering of electrons. The present comment shows that this evaluation approach is inappropriate. For that aim, we reconsider data for the samples with $x = 0.96$ and $x = 1.02$ from three different perspectives: (i) analysis of the logarithmic temperature derivative of the conductivity, (ii) study of the deviations of the measured conductivity data from the Al'tshuler-Aronov approximation of the temperature dependence, and (iii) comparison of the measured temperature data with the values obtained treating the sample as secondary thermometer in terms of that approximation. This way, for the sample with $x = 0.96$, classified as metallic by Daichi Oka et al., qualitative contradictions between the measurements and the zero-temperature extrapolation according to the Al'tshuler-Aronov theory are uncovered. Thus, this sample very likely exhibits activated instead of metallic conduction. In consequence, our findings question the continuity of the MIT resulting from the highly cited scaling theory of localization.

cond-mat.dis-nn↗

arXiv2013

The metal-insulator transition in disordered solids: How theoretical prejudices influence its characterization. A critical review of analyses of experimental data

In a recent experiment, Siegrist et al. [Nature Materials 10, 202 (2011)] investigated the metal-insulator transition (MIT) of GeSb_2Te_4 on increasing annealing temperature. The authors conclude that this material exhibits a discontinuous MIT with a finite minimum metallic conductivity. The striking contrast to reports on other disordered substances motivates the present in-depth study of the influence of the MIT criterion used on the characterization of the MIT. First, we discuss in detail the inherent biases of the various available approaches to locating the MIT. Second, reanalyzing the GeSb_2Te_4 measurements, we show that this material resembles other disordered solids to a large extent: according to a widely-used approach, these data may also be interpreted in terms of a continuous MIT. Checking the justification of the respective fits, however, uncovers inconsistencies in the experimental data. Third, comparing with previous experimental studies of crystalline Si:As, Si:P, Si:B, Ge:Ga, CdSe:In, n-Cd_{0.95}Mn$_{0.05}Se, Cd_{0.95}Mn_{0.05}Te_{0.97}Se_{0.03}:In, disordered Gd, and nano-granular Pt-C, we show that such an inconclusive behavior occurs frequently: the analysis of the logarithmic temperature derivative of the conductivity highlights serious inconsistencies in the original interpretations in terms of a continuous MIT. In part, they are common to all these studies and seem to be generic, in part, they vary from experiment to experiment and may arise from measurement problems. Thus, the question for the character of the MIT of these materials has to be considered as yet open. The challenges now lie in improving the measurement precision and in developing a microscopic theory capable of explaining the seemingly generic features.

cond-mat.dis-nn↗

arXiv2009

Indications for a line of continuous phase transitions at finite temperatures connected with the apparent metal-insulator transition in 2d disordered systems

In a recent experiment, Lai et al. [Phys. Rev. B 75 (2007) 033314] studied the apparent metal-insulator transition (MIT) of a Si quantum well structure. Tuning the charge carrier concentration n, they measured the conductivity sigma(T,n) for a very dense set of n values. They observed linear T dependences of sigma around the Fermi temperature and found that the corresponding T -> 0 extrapolation sigma_0(n) exhibits a sharp bend just at the MIT. Reconsidering the data by Lai et al., it is shown here that this sharp bend is related to a peculiarity of sigma(T=const.,n), which is clearly detectable in the whole T range up to 4 K, the highest measuring temperature in that work. It may indicate a sharp continuous phase transition between the regions of apparent metallic and activated conduction to be present at finite temperature. This interpretation is confirmed by a scaling analysis without fit, which illuminates similarities to previous experiments and provides understanding of the shape of the peculiarity and of sharp peaks found in dlog_{10}sigma/dn(n). Simultaneously, the scaling analysis uncovers a strange feature of the apparent metallic state.

cond-mat.str-el↗

arXiv2009

Comment on "Density of States and Critical Behavior of the Coulomb Glass"

In a recent numerical investigation of the Coulomb glass, Surer et al. [Phys. Rev. Lett. 102, 067205 (2009)] concluded that their simulation results are consistent with the Efros Shklovskii prediction for the density of states in the three-dimensional case. Here, we show that this statement has no relevance concerning the problem of the asymptotic behavior in the Coulomb gap since it is based on unjustified assumptions. Moreover, for the random-displacement Coulomb glass model, we demonstrate that a part of the density of states data by Surer et al. erroneously exhibit a broad gap. This is related to the staggered occupation being instable contrary to their findings.

cond-mat.dis-nn↗

arXiv2009

Critical behavior of the Coulomb-glass model in the zero-disorder limit: Ising universality in a system with long-range interactions

The ordering of charges on half-filled hypercubic lattices is investigated numerically, where electroneutrality is ensured by background charges. This system is equivalent to the $s = 1/2$ Ising lattice model with antiferromagnetic $1/r$ interaction. The temperature dependences of specific heat, mean staggered occupation, and of a generalized susceptibility indicate continuous order-disorder phase transitions at finite temperatures in two- and three-dimensional systems. In contrast, the susceptibility of the one-dimensional system exhibits singular behavior at vanishing temperature. For the two- and three-dimensional cases, the critical exponents are obtained by means of a finite-size scaling analysis. Their values are consistent with those of the Ising model with short-range interaction, and they imply that the studied model cannot belong to any other known universality class. Samples of up to 1400, $112^2$, and $22^3$ sites are considered for dimensions 1 to 3, respectively.

cond-mat.stat-mech↗

arXiv2008

Indications for sharp continuous phase transitions at finite temperatures connected with the apparent metal-insulator transition in two-dimensional disordered systems

In a recent experiment, Lai et al. [Phys. Rev. B 75, 033314 (2007)] studied the apparent metal-insulator transition (MIT) of a Si quantum well structure tuning the charge carrier concentration $n$. They observed linear temperature dependences of the conductivity $σ(T,n)$ around the Fermi temperature and found that the corresponding $T \to 0$ extrapolation $σ_0(n)$ exhibits a sharp bend just at the MIT. Here, reconsidering the data published by Lai et al., it is shown that this sharp bend is related to a peculiarity of $σ(T=const.,n)$ clearly detectable in the whole $T$ range up to 4 K, the highest measuring temperature in that work. Since this peculiarity seems not to be smoothed out with increasing $T$ it may indicate a sharp continuous phase transition between the regions of apparent metallic and activated conduction to be present at finite temperature. Hints from the literature of such a behavior are discussed. Finally, a scaling analysis illuminates similarities to previous experiments and provides understanding of the shape of the peculiarity and of sharp peaks found in $d log_{10} σ/ d n (n)$.

cond-mat.str-el↗

arXiv2005

Optimization by thermal cycling

An optimization algorithm is presented which consists of cyclically heating and quenching by Metropolis and local search procedures, respectively. It works particularly well when it is applied to an archive of samples instead of to a single one. We demonstrate for the traveling salesman problem that this algorithm is far more efficient than usual simulated annealing; our implementation can compete concerning speed with recent, very fast genetic local search algorithms.

cond-mat.dis-nn↗

arXiv2005

Optimization by thermal cycling

Thermal cycling is an heuristic optimization algorithm which consists of cyclically heating and quenching by Metropolis and local search procedures, respectively, where the amplitude slowly decreases. In recent years, it has been successfully applied to two combinatorial optimization tasks, the traveling salesman problem and the search for low-energy states of the Coulomb glass. In these cases, the algorithm is far more efficient than usual simulated annealing. In its original form the algorithm was designed only for the case of discrete variables. Its basic ideas are applicable also to a problem with continuous variables, the search for low-energy states of Lennard-Jones clusters.

cond-mat.dis-nn↗

arXiv2003

Short-range type critical behavior in spite of long-range interactions: the phase transition of a Coulomb system on a lattice

One- to three-dimensional hypercubic lattices half-filled with localized particles interacting via the long-range Coulomb potential are investigated numerically. The temperature dependences of specific heat, mean staggered occupation, and of a generalized susceptibility indicate order-disorder phase transitions in two- and three-dimensional systems. The critical properties, clarified by finite-size scaling analysis, are consistent with those of the Ising model with short-range interaction.

cond-mat↗

arXiv2002

Possible persistence of the metal-insulator transition in two-dimensional systems at finite temperatures

For the immediate vicinity of the metal-insulator transition (MIT), data on the dependence of the resistivity rho on the charge carrier concentration n from an Si MOSFET experiment by Kravchenko et al. and from an AlAs quantum well study by Papadakis and Shayegan are reanalyzed. In both cases, the rho(T=const.,n) curves for various values of the temperature T seem to exhibit an offset concerning n, where the related resistivity is close to h/e^2. This offset may result from a peculiarity in rho(T=const.,n) indicating the MIT to be present also at finite T. More detailed experiments are imperative.

cond-mat.dis-nn↗

arXiv2001

Metal-insulator transition in amorphous alloys

We focus on the central problem of discriminating between metallic and insulating behaviour in amorphous alloys formed between a semiconductor and a metal. For this, the logarithmic temperature derivative of the conductivity, w = d ln sigma / d ln T, has proved over recent years to be very helpful in determining the critical value x_c of the metal content x for the metal-insulator transition (MIT). We show that, for various amorphous alloys, recent experimental results on w(T,x) are qualitatively inconsistent with the usual assumptions of continuity of the MIT at T = 0 and of sigma(T,x_c) being proportional to a power of T. These results suggest that w(T,x_c) tends to 0 as T -> 0, in which case the MIT should be discontinuous at T = 0 (but only there), in agreement with Mott's hypothesis of a finite minimum metallic conductivity.

cond-mat.dis-nn↗

arXiv2001

Specific heat of the Coulomb glass

The specific heat of the Coulomb glass is studied by numerical simulations. Both the lattice model with various strengths of disorder, and the random-position model are considered for the one- to three-dimensional cases. In order to extend the investigations down to very low temperatures where the many-valley structure of the configuration space is of great importance we use a hybrid-Metropolis procedure. This algorithm bridges the gap between Metropolis simulation and analytical statistical mechanics. The analysis of the simulation results shows that the correlation length of the relevant processes is rather small, and that multi-particle processes yield an essential contribution to the specific heat in all cases except the one-dimensional random-position model.

cond-mat.dis-nn↗

arXiv2001

The metal-insulator transition in amorphous Si_{1-x}Ni_x: Evidence for Mott's minimum metallic conductivity

We study the metal-insulator transition in two sets of amorphous Si_{1-x}Ni_x films. The sets were prepared by different, electron-beam-evaporation-based technologies: evaporation of the alloy, and gradient deposition from separate Ni and Si crucibles. The characterization included electron and scanning tunneling microscopy, glow discharge optical emission spectroscopy, and Rutherford back scattering. Investigating the logarithmic temperature derivative of the conductivity, w = d ln sigma / d ln T, we observe that, for insulating samples, w(T) shows a minimum increasing at both low and high T. Both the minimum value of w and the corresponding temperature seem to tend to zero as the transition is approached. The analysis of this feature of w(T,x) leads to the conclusion that the transition in Si_{1-x}Ni_x is very likely discontinuous at zero temperature in agreement with Mott's original views.

cond-mat.dis-nn↗

arXiv1999

Combinatorial Optimization by Iterative Partial Transcription

A procedure is presented which considerably improves the performance of local search based heuristic algorithms for combinatorial optimization problems. It increases the average `gain' of the individual local searches by merging pairs of solutions: certain parts of either solution are transcribed by the related parts of the respective other solution, corresponding to flipping clusters of a spin glass. This iterative partial transcription acts as a local search in the subspace spanned by the differing components of both solutions. Embedding it in the simple multi-start-local-search algorithm and in the thermal-cycling method, we demonstrate its effectiveness for several instances of the traveling salesman problem. The obtained results indicate that, for this task, such approaches are far superior to simulated annealing.

cond-mat.dis-nn↗