Zero-bias anomaly in a two-dimensional granular insulator

Abstract

We compare tunneling density of states (TDOS) into two ultrathin Ag films, one uniform and one granular, for different degrees of disorder. The uniform film shows a crossover from Altshuler-Aronov (AA) zero bias anomaly to Efros Shklovskii (ES) like Coulomb gap as the disorder is increased. The granular film, on the other hand, exhibits AA behavior even deeply in the insulating regime. We analyze the data and find that granularity introduces a new regime for the TDOS. While the conductivity is dominated by hopping between clusters of grains and is thus insulating, the TDOS probes the properties of an individual cluster which is "metallic".PACS numbers: 73.40. Rw; 72.80.Ng; 72.20.Ee; The metal-insulator transition (MIT) in disordered electronic systems renders their transport properties one of the most exciting topics in condensed matter physics. The effects of Coulomb interaction in the vicinity of the MIT are particularly strong, and despite major theoretical and experimental efforts are not yet fully understood [2]. Much of the work is focused on 2D metallic films. While infinite 2D systems are insulators [1], samples shorter than the localization length ξ exhibits metallic behavior. This enables to utilize thin dirty metals to study both metallic and insulating regimes.For weakly disordered metallic films with relatively high conductivity the interplay between electron-electron interaction and disorder has a pronounced influence on the electronic properties, as shown by Altshuler and Aronov (AA) [3]. Both conductivity and the tunneling density of states (TDOS) are significantly modified (relatively to the non-interacting values) and acquire temperature dependent corrections. The theory predicts the depletion of the TDOS around the Fermi level, a phenomenon that became known as zero bias anomaly (ZBA), which was indeed observed experimentally in disordered metals [4].For strongly disordered systems, electronic states are localized, and transport at low temperatures is achieved via variable range hopping (VRH). For non-interacting electrons there is no gap in the TDOS at the Fermi level and the electric conductivity is given by Mott's law [5]. Electron interactions open a Coulomb gap at the Fermi energy, affecting the TDOS and the electric conductivity as shown by Efros and Shklovskii (ES) [6]. The Coulomb gap in the 2D density of states is given byand the conductivity as a function of temperature is where κ is a dielectric constant and T 0 = e 2 /κξ. Though the ZBA and the Coulomb gap both result from the long range Coulomb interaction and lead to a depletion of the TDOS at the Fermi energy, a unified theory of both effects is still absent [8].Most theoretical and experimental works deal with homogeneously disordered systems in which the degree of disorder controls the vicinity to the MIT. A different system that may provide a natural and convenient arena for experimental and theoretical study of strongly interacting systems is a granular metal [9] i.e. a disordered array of metallic islands with typical size ...

Normal-state gap in the parent cuprate Pr2CuO4±δ

“…The zero bias anomaly in tunneling spectra may stem from various reasons, such as electron-electron interactions [18], Coulomb blockade [19], hopping dominated conductance between the clusters of disordered metal grains [20], Kondo scattering from magnetic moments, Giaever-Zeller two-step tunneling process, etc. In electron-doped cuprates, Alff et al studied the tunneling spectra of Pr 2−x Ce x CuO 4 and La 2−x Ce x CuO 4 , and reported a T * that is smaller than T c , pointing to a competing order below the superconducting dome [15].…”