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One-dimensional Silicon and Germanium Nanostructures With No Carbon Analogues

In this work we report new silicon and germanium tubular nanostructures with no corresponding stable carbon analogues. The electronic and mechanical properties of these new tubes were investigated through ab initio methods. Our results show that the structures have lower energy than their corresponding nanoribbon structures and are stable up to high temperatures (500 and 1000 K, for silicon and germanium tubes, respectively). Both tubes are semiconducting with small indirect band gaps, which can be significantly altered by both compressive and tensile strains. Large bandgap variations of almost 50% were observed for strain rates as small as 3%, suggesting possible applications in sensor devices. They also present high Young's modulus values (0.25 and 0.15 TPa, respectively). TEM images were simulated to help the identification of these new structures.

Carbon nanostructures present very interesting electronic and mechanical properties. The discovery of fullerenes [1], carbon nanotubes [2], and more recently graphene [3], has created a new era in materials science. In particular, the discovery of new and very unusual graphene properties has led to a renewed interest in the search for other similar structures.
A natural question is whether other atoms in the same column of the periodic table as carbon (such as, silicon and germanium) could produce similar structures. This has motivated many studies [4][5][6][7], which produced many interesting results. It has been demonstrated that silicon and germanium are able to produce many analogues of the carbon nanostructures, such as: closed cage structures [4], nanotubes [7][8][9][10][11][12][13][14], and even two-dimensional honeycomb graphene-like sheets, the so-called silicene and germanene, the former which has been already experimentally realized [15][16][17].
However, despite all these similarities, there are important and significant differences among carbon and silicon and/or germanium structures. Due to the pseudo Jan-Teller effect (PJTE) [18][19][20], silicon and germanium nanostructures tend to form buckled geometries, as a consequence of a stronger sp 3 character, in comparison to carbon ones. The PJTE is responsible for the instability of multi-layered silicon nanostructures [12]. In principle, due to these differences, it is possible that unique silicon and germanium structures can exist, with no corresponding carbon counterpart. In this work we present one example of theses cases. We present new silicon and germanium nanotube structures, with no corresponding stable carbon analogues and which cannot be described by any integer chiral indices.
The electronic and mechanical properties of these new structures were investigated through ab initio density functional theory (DFT) methods using the DMol3 [21] package, as smallest possible nanotubes which can be formed from a two-ring wide zigzag nanoribbon parent. One unique aspect of the tubes is that they cannot be described by any integer chiral indices (see Figure 1 (a)). These structures can be generated moving the three atomic chains that compose the nanoribbon into a tubular configuration (see Figure 1). The tube unit cell contains six atoms and exhibits a P1 structural symmetry.
No stable corresponding carbon structures could be obtained, with the structures collapsing and returning to its planar nanoribbon conformation. This can be explained by the PJTE, since silicon and germanium p orbitals are much closer in energy than the corresponding carbon ones [19]. This is reflected into a stronger sp 3 hybridization character, to maintain the system in the elastic region. In this regime, from the curves in Figure 5 we can estimate the Young modulus values for both structures by using where Y is the Young's modulus, V 0 is the equilibrium volume, U is the total strain energy and ε is the strain. Using this equation we obtain values of 0.25T P a and 0.15T P a for the silicon and germanium tubes respectively. These values are quite high and comparable to the values found in strong metals, although not as high as that of graphene, indicating these novel structures present promising mechanical properties. We have also calculated the Poisson's ratios along the directions shown in Figure 1. The electronic and mechanical properties are summarized in Table I.
Concomitantly with the total energy analysis as a function of strain, we have also analysed