Anomalous suppression of the transition temperature of superconducting nanostructured honeycomb films: Electrical transport measurements and Maekawa-Fukuyama model

Deepak K. Singh, Sigfrid Yngvesson, Thomas P. Russell, and Mark T. Tuominen

Phys. Rev. B 77, 174512 – Published 16 May 2008

Abstract

We report electrical transport measurements made on thin superconducting niobium films perforated by an etched array of nanoscopic holes. The hole diameter in these “honeycomb” network films is comparable to the coherence length of the parent superconducting material. A series of 12 films, with varying hole depths, were measured. As the film thickness is decreased, an unusually large reduction of transition temperature is observed for the honeycomb films as compared to plain etched films of similar thicknesses. We report on a $T_{c}$ reduction in superconducting network films that is not due to an applied magnetic field. These observations are in contrast to previous reports based on Ginzburg-Landau theory analysis, which does not allow for any change in the transition temperature for perforated films in comparison to plain films. The Maekawa-Fukuyama (MF) model for two-dimensional (2D) superconductors is used to fit the sheet resistance data. The MF-2D model fits very well to the lightly etched samples, but an anomaly in $T_{c}$ reduction is observed for heavily etched samples. These deviations are analyzed on the basis of change in dimensionality using the Aslamozov-Larkin model.

Received 2 July 2007

DOI:https://doi.org/10.1103/PhysRevB.77.174512

Authors & Affiliations

Deepak K. Singh^1,*, Sigfrid Yngvesson², Thomas P. Russell³, and Mark T. Tuominen^1,†

¹Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
²Department of Electrical Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
³Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA

^*Present address: Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
^†Corresponding author. tuominen@physics.umass.edu

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Vol. 77, Iss. 17 — 1 May 2008

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Images

Figure 1
(Color online) Schematic description, in 2D, of “honeycomb” film fabrication for different etching times. As we can see in this schematic picture, the thickness of the lightly etched honeycomb film is same as the original film (10 nm), but as the etching time is increased, holes become deeper as well the constriction (film connecting two neighboring holes) gets thinner. Eventually after certain amount of time, the holes are etched all the way (open holes) through and create a multiply connected system of lower thickness than the original film.Reuse & Permissions
Figure 2
(Color online) AFM images of diblock template and honeycomb films (before imaging, samples are cleaned in sulfuric acid at $70 °$ centigrade). (a) Diblock template, (b) 15-s etched sample, (c) 105-s etched sample (note that constrictions are getting thinner, as discussed in the text, possibly because of undercuts), and (d) 140-s etched sample (complete etching results in the exposure of a Si wafer).Reuse & Permissions
Figure 3
(Color online) Sheet resistance data for different time etched samples. (a) Different time etched honeycomb films. This plot clearly shows that as the sheet resistance value increases, transition temperature decreases. (b) For comparison purposes, plain Nb film sheet resistance data are also plotted. In the inset, sheet resistance data for 75-s etched plain Nb film is shown. As we can see here superconductivity is destroyed in plain Nb film after 75 s of etching time.Reuse & Permissions
Figure 4
(Color online) The variation of normalized transition temperature as a function of etching time for both plain Nb films and honeycomb films. As the etching time increases, sample thickness decreases linearly (see text). In this figure we observe two very different behaviors in $T_{c}$ reduction for films of similar thicknesses, in the absence of magnetic field. Just a guide to the eye, the dashed line shows a linear variation of $T_{c}$ with increasing etching time for plain Nb film.Reuse & Permissions
Figure 5
(Color online) Maekawa-Fukuyama 2D model fitting to sheet resistance data for honeycomb films. As we can see in this figure the MF-2D model (green, solid gray, curve) does not fit well to the all data points. But if we fit the MF-2D model to the lightly etched honeycomb films data, then, as we can see in this figure (blue, dashed gray, curve), a very good fitting is obtained. The fitting value of the coupling constant, in this case, is 0.8.Reuse & Permissions
Figure 6
(Color online) Fitting to the excess conductivity data using the Aslamazov-Larkins model. As we can see in this figure, the superconducting dimensionality of the original film is 2D, which was expected because the thickness of the Nb film is of the order of coherence length for the superconductor. (a) In the case of honeycomb film, dimensionality changes from 2D to a fractional value for increased etching time. (b) In the case of plain Nb film, dimensionality does not change.Reuse & Permissions

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