Hard Correlation Gap Observed in Quench-Condensed Ultrathin Beryllium

Abstract

We report on the tunneling density of states (DOS) in ultrathin and strongly disordered Be films quench-condensed at 20 K. Above 5 K, the DOS shows the well-known logarithmic anomaly at the Fermi level. Only in a narrow temperature range near 2 K is the DOS linearly dependent on energy, as predicted by Efros and Shklovskii. However, both the zero-bias conductance and the slope of the linear DOS are found to decrease drastically with decreasing temperature. Tunneling measurements at mK temperatures have revealed conclusively that a hard correlation gap opens up in the DOS.PACS numbers: 73.40. Gk, 72.15.Rn, 71.30.+h, 74.40+k It is known that electron-electron (e-e) Coulomb interactions can drastically alter the density of states (DOS) near the Fermi energy in disordered electronic systems. In the weakly disordered limit, Altshuler et al.[1] have predicted that interactions lead to a singular depletion of the DOS with a |ǫ| 1/2 dependence in three dimensions (3D) and a ln|ǫ| dependence [2] in two dimensions(2D), where ǫ is the energy measured from the Fermi level. These corrections have been observed in tunneling studies of the DOS in disordered metals in 3D [3] and 2D [4,5]. In the strongly insulating regime, Efros and Shklovskii (ES) have predicted [6,7] that Coulomb interactions lead to a soft Coulomb gap in the single-particle DOS, with a vanishing DOS at the Fermi level. This soft gap is quadratic in energy in 3D and linear in energy in 2D. In both 2D and 3D, the Coulomb gap is predicted [7] to lead to a variable-range hopping resistance of R ✷ (T) = R 0 exp [(T 0 /T ) ν ], where ν = 1/2 and T is the temperature.Although it was predicted over two decades ago, the Coulomb gap is by no means an understood subject. The existence of the ES Coulomb gap had mainly been inferred from transport experiments such as glassy electronic relaxation [8] and hopping conduction [9,10]. The ES Coulomb gap in 3D was directly observed a few years ago by tunneling in Si:B [11]. Direct evidence for the ES Coulomb gap in 2D has been reported only during the past year by Butko et al. [12], but no temperature dependence and magnetic field dependence have been reported. The Coulomb gap predicted by Efros and Shklovskii [6,7] describes the DOS for adding an extra electron to the ground state without allowing relaxation. Later theoretical studies [13] of the Coulomb gap, taking into consideration multi-electron processes, have found a further reduction of the DOS near the Fermi energy, leading to a much harder gap with effectively no states within a narrow but finite range of energy. In fact, a change in the hopping exponent with decreasing temperature from ν = 1/2 to ν = 1 was reported a few years ago in Si:B[10], suggesting that a hard gap might exist at low temperatures. Most recently, the Coulomb gap in 2D has become a subject of renewed interest [14] with the unexpected discovery of a metal-insulator transition in the 2D electron gas in semiconductor devices [15].

Electron Glass in Ultrathin Granular Al Films at Low Temperatures

“…Thus it is not clear what role, if any, the Coulomb gap plays in the observed glassy relaxation. In addition, we did not find any hysteresis in quench-condensed Li films of R ✷ ∼ 10 kΩ/✷ and Be films of R ✷ = 3 ∼ 500 kΩ/✷, even though a true Coulomb gap has been observed in Be films [16]. While we were not able to investigate the morphology of the Li films, which become unstable in air, scanning force microscopy studies of the Be films warmed up to room temperature did not find any granular structure down to 1 nm.…”

Zero bias anomaly in the density of states of low-dimensional metals

“…What is the true low-frequency behavior of the DOS of disordered metals in reduced dimensions? The answer to this question is relevant for a number of recent tunneling experiments [2,3,4], where a strong suppression of the tunneling conductance G(V ) as a function of the applied voltage has been observed (zero bias anomaly). The tunneling conductance is related to the DOS via G(V ) ∝ ν(ω = eV ), so that the experimentally observed zero bias anomaly in the tunneling conductance reflects the strong suppression of the average DOS at the Fermi energy.…”

Nanopattern-stimulated superconductor-insulator transition in thin TiN films

“…We find that nanopatterning enhances the role of the two-dimensional Coulomb interaction in the system transforming the originally insulating film into a more pronounced insulator. We observe magnetoresistance oscillations reflecting collective behaviour of the multiconnected nanopatterned superconducting film in the wide range of temperatures and uncover the physical mechanism of these oscillations as phase slips in superconducting weak link network.That a thin film of the same material can be a superconductor but can very well turn an insulator, is one of the most remarkable aspects of disordered superconductors [1][2][3][4][5][6][7]. The engine driving the transition between the superconducting and insulating states is disorder the effect of which is two-fold.…”

“…That a thin film of the same material can be a superconductor but can very well turn an insulator, is one of the most remarkable aspects of disordered superconductors [1][2][3][4][5][6][7]. The engine driving the transition between the superconducting and insulating states is disorder the effect of which is two-fold.…”