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 $\sigma(T,n)$ around the Fermi temperature and found that the corresponding $T \to 0$ extrapolation $\sigma_0(n)$ 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 $\sigma(T=const.,n)$ 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 $d log_{10} \sigma / d n (n)$.Comment: Revised version (quantitative determination of exponent beta added), accepted for publication by Physical Review B. Revtex, 10 pages, 9 figure

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

In a recent experimental study, Siegrist et al. [Nature Materials 10, 202–208 (2011)] investigated the metal-insulator transition (MIT) induced by annealing in GeSb 2 Te 4 . The authors concluded that this phase-change material exhibits a discontinuous MIT with finite minimum metallic conductivity. The striking contrast between their work and reports on many other disordered substances from the last decades motivates the present in-depth study of the influence of the MIT criterion used on the character of the MIT derived. First, we discuss in detail the inherent biases of various approaches to locating the MIT. Second, reanalyzing GeSb 2 Te 4 data, we show that this material resembles other disordered solids to a large extent: according to a widely-used approach, its temperature dependences of the conductivity, σ(T), may likewise be interpreted in terms of a continuous MIT. Third, examining 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 nanogranular Pt-C, we detect substantial problems in the interpretations of σ(T) in numerous studies which claim the MIT to be continuous: Evaluating the logarithmic derivative d ln σ/d ln T highlights serious inconsistencies. In part, they are common to all such studies and seem to be generic, in part, they vary from experiment to experiment. Fourth, for four qualitatively different phenomenological models of the temperature and control parameter dependence of the conductivity, we present the respective flow diagrams of d ln σ/d ln T. In consequence, the likely generic inconsistencies seem to originate from the MIT being discontinuous, in contradiction to most of the original interpretations. Because of the large number and diversity of the experiments considered, these inconsistencies provide overwhelming evidence against the common, localization theory motivated interpretations. The primary challenges now lie in improving measurement precision and accuracy, rather than in extending the temperature range, and in developing a microscopic theory which explains the seemingly generic features of d ln σ/d ln T. © 2018, © 2018 The Author(s). Published with license by Taylor & Francis. © 2018, © Arnulf Möbius

Accuracy and Precision in Electronic Structure Computation: Wien2k and FPLO

Electronic structure calculations in the framework of density functional theory are based on complex numerical codes which are used in a multitude of applications. Frequently, existing experimental information is used as a gauge for the reliability of such codes. However, their results depend both on the chosen exchange-correlation energy functional and on the specific numerical implementation of the Kohn-Sham equations. The only way to disentangle these two items is a direct comparison of two or more electronic structure codes. Here, we address the achievable numerical accuracy and numerical precision in the total energy computation of the two all-electron density-functional codes Wien2k and FPLO. Both codes are based on almost independent numerical implementations and largely differ in the representation of the Bloch wave function. Thus, it is a highly encouraging result that the total energy data obtained with both codes agree within less than 10−6. We here relate the term numerical accuracy to the value of the total energy E, while the term numerical precision is related to the numerical noise of E as observed in total energy derivatives. We find that Wien2k achieves a slightly higher accuracy than FPLO at the price of a larger numerical effort. Further, we demonstrate that the FPLO code shows somewhat higher precision, i.e., less numerical noise in E than Wien2k, which is useful for the evaluation of physical properties based on derivatives of E