Exotic multifractal conductance fluctuations in graphene

Abstract

In quantum systems, signatures of multifractality are rare. They have been found only in the multiscaling of eigenfunctions at critical points. Here we demonstrate multifractality in the magnetic-field-induced universal conductance fluctuations of the conductance in a quantum condensed-matter system, namely, high-mobility single-layer graphene field-effect transistors. This multifractality decreases as the temperature increases or as doping moves the system away from the Dirac point. Our measurements and analysis present evidence for an incipient Anderson-localization near the Dirac point as the most plausible cause for this multifractality. Our experiments suggest that multifractality in the scaling behaviour of local eigenfunctions are reflected in macroscopic transport coefficients. We conjecture that an incipient Anderson-localization transition may be the origin of this multifractality. It is possible that multifractality is ubiquitous in transport properties of lowdimensional systems. Indeed, our work suggests that we should look for multifractality in transport in other low-dimensional quantum condensed-matter systems. * aveek@iisc.ac.in arXiv:1804.04454v1 [cond-mat.mes-hall]

High-temperature superconductivity as viewed from the maximum hardness principle

“…*The DOS(E F ) values strongly depend on the fine details of parameters used to describe band occupation and convergence algorithms; the system is on the verge of a metal [32] and being a narrow band gap semiconductor…”

“…2 is energetically uphill (section “Methods”) since it corresponds to a formation of electronically soft metals or narrow-gap semiconductors (though the metallic behaviour is more likely for La-doped system [32]) starting from much harder insulators . Progress of reaction (Eq.…”

Multifractal Magnetoconductance Fluctuations in Mesoscopic Systems

“…Differently from the experimental observations of fractality, as in Ref. [3], where the number of propagating wave modes in the leads are large (semiclassical regime), the multifractal behavior emerges when there is just one propagating wave mode in the leads (extreme quantum regime), more specifically, close to the charge-neutrality (Dirac) point of single-layer graphene [20]. Besides, the authors of Ref.…”

“…Recently, the fractal nature of UCF came up again after a somewhat unexpected experimental detection of multifractality in the conductance fluctuations of a single-layer graphene sample [20]. In practical terms, multifractality means that it is not enough to determine just a single scaling exponent, such as γ, which is related to the usual fractal dimension [19] (see above), to describe fluctuations, but instead an infinite number of scaling exponents becomes necessary to fully characterize the fluctuation statistics.…”

“…Besides, the authors of Ref. [20] conjectured that the experimental observation of multifractality might be an evidence of an incipient Anderson localization near the Dirac point, since this appears to be the most plausible cause for the multifractal behavior. However, as we will show with the results of this paper, this conjecture deserves a deeper analysis.…”