Quantum transport in three-dimensional metalattices of platinum featuring an unprecedentedly large surface area to volume ratio

Three-dimensional (3D) electronic nanomaterials are less explored than their counterparts in the lower dimensions because of the limited techniques for the preparation of high-quality materials. Here we report characterization of and quantum transport measurement on 3D metalattices of Pt grown in the voids of self-assembled templates of silica nanospheres by confined chemical fluid deposition. These Pt metalattices featuring an unprecedentedly large surface area to volume ratio were found to show positive magnetoresistance (MR) at low temperatures, changing from positive to negative in low magnetic fields within a narrow temperature window as the temperature was raised. The low-field MR was attributed to the effect of quantum interference of electronic waves in the diffusive regime in three dimensions, processes known as weak localization and antilocalization. We argue that the presence of the large surface area to volume ratio results in such a strong enhancement in the electron-phonon scatterings that a change in the sign in the MR is enabled.

Figure 1

Preparation of metalattices of Pt with a varying periodicity. Scanning electron microscope images for 30-nm (a), (b), 75-nm (c), (d), and 125-nm (e), (f) Pt metalattices, showing the top and cross-section view, respectively. All images were taken on samples with silica nanospheres left inside the samples.

Figure 2

Characterization of 30-nm Pt metalattices. (a) Electron-diffraction pattern from transmission electron microscopy (TEM) studies showing that the Pt metalattice is polycrystalline. (b) High-angle annular dark field (HAADF) scanning TEM (STEM) image of the cross section of the Pt metalattice. (c) Energy dispersive x-ray spectroscopy image showing uniform Pt composition in the same area as in (b). (d) Cross-sectional TEM shows that the Pt metalattice is well ordered over a length scale of 1 μm. (e) HAADF-STEM tomography image of a Pt metalattice, tilted to show the 3D shape of the tetrahedral site (TS) and octahedral site (OS). The defects seen in this image were likely introduced by the high-energy focused ion-beam preparation of the ultrathin sample for this paper.

Figure 3

Electrical transport measurements on the metalattice and a film of Pt. (a) Temperature dependence of the resistivity of 30-nm Pt metalattices. The inset shows an optical image of a sample. (b) Normalized values of magnetoresistance (MR) at fixed temperatures below 20 K for sample 1. (c) MR of sample 1 between 18 and 30 K. The temperatures for the curves from top to bottom are $T=30$, 28, 26, 24, 22, 20, and 18 K. All curves except that obtained at 18 K were shifted vertically for clarity. (d) Temperature dependence of the resistivity of a planar film of Pt. A 5-nm-thick Ti underlay was used to promote adhesion. The substrate is Si with 300-nm thermally grown $\mathrm{Si}{\mathrm{O}}_2$. The inset shows an optical image of the device. (e) Values of transverse MR with the field perpendicular to the measurement current and the plane of the film. (f) Values of longitudinal MR with the field parallel to the measurement current.