Understanding the coupling between onedimensional (1D) materials and their protective materials is essential for developing nanodevices. Herein, we investigate the effect of the size, chirality, and type of nanotubes [such as carbon/boron nitride nanotubes (CNTs/BNNTs)] on the atomic and electronic structures of confined Te chains using density functional theory. We find that the optimal configurations of the Te chains confined in CNTs/BNNTs depend strongly on the size of the nanotubes but weakly on their chirality and type. Furthermore, the Te@BNNTs exhibit giant Rashba splitting with a Rashba constant of up to 2.65 eV Å, while the Te@CNTs show no splitting. This is mainly due to the large bandgap of the BNNTs, as well as the enhanced symmetry breaking of the Te chains when confined. Our findings provide a basis for the design of nano spin devices through protective materials.
In recent years, tellurium has attracted the interest of researchers because of its excellent transport properties and ability to form largearea airstable twodimensional (2D) thin films^{[14]}. 2D Te films are composed of Te chains with van der Waals (vdW) interactions between the chains^{[57]}, which are expected to separate Te chains, even to the limit of the singlechain scale^{[810]}. Single Te chains are expected to exhibit interesting physical properties that largely differ from the bulk^{[11]}. For example, helical Te chains have a bandgap of ~1.53 eV at room temperature^{[12]}, in contrast to the value of 0.35 eV for the bulk. The symmetry breaking of Te chains due to their unique chiral characteristics leads to strong spinorbit interactions and Rashba splitting. An isolated single Te chain was predicted to have a large Rashba constant of up to 2.17 eV with 23.13% strain^{[12]}. However, single Te chains are inaccessible experimentally because they can easily crimp and adsorb small molecules from the environment, thereby degrading their performance. Nanotubes, such as carbon/boron nitride nanotubes (CNTs/BNNTs), serve as excellent protective materials for these nanochains, due to their unique 1D hollow structure and chemical stability^{[810,1315]}. For instance, Pham
Previous works have mainly focused on the influence of the size of the nanotubes on the confined Te chains. For example, the number of Te chains decreases from triple, double to even single, with decreasing the diameter of the nanotubes^{[16]}. In smallsized nanotubes, these 1D atomic chains undergo a structural change^{[17,18]} and phase transition. S and Se encapsulated in CNTs adopt linear, zigzag, or helical structures depending on the inner diameter of the CNTs^{[19,20]}. The Peierls structural distortion occurs for single Te chains^{[8]}. Apart from the above structural change, Qin
Therefore, herein, we systematically explore the effect of nanotube size and chirality on the atomic and electronic structures of Te chains confined in CNTs/BNNTs by density functional theory. We find that the tube size predominates in determining the configurations of the confined Te chains. The Te@BNNTs show giant Rashba splitting with a Rashba constant of up to 2.65 eV Å, which is the highest among known pure 1D systems, while the Te@CNTs show no Rashba splitting. This is because the large bandgap of the BNNTs accommodates and maintains the band edges of the Te chains, while the CNTs with a zero bandgap cannot. Our findings provide a basis for the construction of nano spin devices and lay a foundation for the design of new nanoelectronic devices.
All calculations were performed using the CASTEP code with ultrasoft pseudopotentials^{[22]}. We employed a sequence of Te@CNT and Te@BNNT structures that were periodic along the caxis direction [
Top and side views of atomic structures of (A) Te@(6, 6) CNTs, (B) Te@(10, 0) CNTs, (C) Te@(6, 6) BNNTs, (D) Te@(10, 0) BNNTs, (E) Te@(7, 7) CNTs, (F) Te@(12, 0) CNTs, (G) Te@(7, 7) BNNTs and (H) Te@(12, 0) BNNTs.
We adopt the adsorption energy (
where
To systematically study how the size, chirality, and type of the nanotubes affect the atomic and electronic structures of the single Te chains confined in nanotubes, we consider two groups of CNTs/BNNTs with different sizes, namely, (6, 6)/(10, 0) and (7, 7)/(12, 0), each of which contains armchair and zigzag nanotubes, thereby helping us to study the size and chirality effects individually. The smallsized group [i.e., (6, 6) and (10, 0)] represented the smallest nanotubes that can accommodate a single Te chain, given that the vdW radii of C/B/N (
Due to the different lattice constants of the Te chains and nanotubes, their combination is inevitably accompanied by stretching or compression of the softer Te chains. To find the optimal mismatch, we consider a wide range of strains from 20% to 60%, given that the unique helical structure of the Te chains can bear a large strain without breaking. With increasing strain, we find that the helical Te chains in the range of small strains transform to zigzag chains and then to straight chains in the range of large strains, which is similar to the scenario of free chains under various stresses^{[12]}. The global minima of the adsorption energy curve refer to the optimal configurations of Te chains confined in CNTs and BNNTs.
We first focus on the group of nanotubes with smaller sizes, i.e., the (6, 6) and (10, 0) CNTs. In
Adsorption energy (
Despite the similarity of their crystallographic structures, CNTs and BNNTs differ largely with regard to their electronic structures. For example, BNNTs have a large bandgap, while CNTs have no bandgap^{[28]}. The large bandgap of BNNTs is expected to not interfere with the conduction band minimum (CBM) and valence band maximum (VBM) characteristics of the confined Te chains. Therefore, we next focus on the Te chains confined in the (6, 6), (10, 0), (7, 7) and (12, 0) BNNTs.
In
Adsorption energy (
In both
For the heavy Te element, the band structure calculations must account for the SOC effect. For the Te@CNTs systems, we tentatively computed the band structures of the straight Te chain, (6, 6) CNTs and Te@(6, 6) CNTs [
Band structures of Te@(10, 0) CNTs with/without SOC (A)/(B) and Te@(10, 0) BNNTs with/without SOC (C)/(D). The Rashba splitting is highlighted, where the green and red lines are for the spinup and spindown bands, respectively.
The band splitting observed in the BNNTs after considering SOC is known as Rashba splitting. We employ the three most critical Rashba splitting parameters (
Rashba energy (





Te@(6,6) BNNTs  11.06  0.02  1.31  This work 
Te@(10,0) BNNTs  20.64  0.02  2.65  This work 
Te@(7,7) BNNTs  20.29  0.02  1.91  This work 
Te@(12,0) BNNTs  20.60  0.02  1.76  This work 
Isolated Te chains  24  0.057  0.84  Ref^{[12]} 
Distorted23.13% stretched Te  111  0.102  2.18  Ref^{[12]} 
InGaAs/InAlAs  < 1  0.028  0.51  Ref^{[31]} 
SiAu nanowire  N/A  0.05  N/A  Ref^{[32]} 
Pt/Si(111)nanowire  81  0.12  1.36  Ref^{[33]} 
Q2 Bi on In/Si(111)  78.2  0.073  2.1  Ref^{[34]} 
The Te@CNTs do not have Rashba splitting, while Te@BNNTs do, indicating that the electronic structures of the internal Te chains depend on the type of nanotubes. Compared with the Te@CNTs, all the Te@BNNTs have large Rashba splitting, which is mainly due to the large bandgap of the BNNTs. For this reason, the CBM and VBM of the Te chains can reside in the large bandgap of the BNNTs and the Rashba splitting of the Te chains is maintained. The large bandgap of the BNNTs can, therefore, completely expose the band edge of the Te chains, while the zero band gap of the CNTs limits this performance. Apart from the intrinsic atomic SOC, the structural origin, i.e., the symmetry breaking, contributes to the large Rashba splitting. The bond length of the Te chains in the free state is 2.76 Å and the bond angle is 100.9°. When confined in nanotubes, the confinement induces a change in bond length and angle. For example, with the strain of 16.10%, the bond lengths of the Te chains in BNNTs are 2.742.75 Å and the bond angles are 116.1116.3°. The comparison between free Te chains and confined Te demonstrates that confinement enhances the Rashba splitting through symmetry breaking.
Materials with large Rashba constants and energies provide us with more leeway in the choice of their spintronic properties. The free Te chains have already excelled over other 1D materials, such as 1D atomic Te chains and the distorted 23.13% stretched Te [
In this study, we have established how the size and chirality of CNTs/BNNTs affect the atomic and electronic structures of confined Te chains. The optimal structures of Te chains confined in CNTs and BNNTs are predominately determined by the size of the nanotubes rather than their chirality or type. Remarkably, the Te@BNNTs show even superior Rashba splitting, compared with the isolated Te chains, while the Te@CNTs show no splitting at all. The striking contrast is mainly due to the large bandgaps of BNNTs that accommodate and maintain the band edges of Te chains where the Rashba splitting emerges. Our results reveal an interesting conclusion: the relative independence of the electronic structure between the confined and protective materials is an essential prerequisite for protective realization without degrading the performance of confined materials. These results are expected to shed light on the development of nano spin devices.
Made substantial contributions to the conception and design of the study and performed data analysis and interpretation: Han J, Ma C, Gao W
Provided administrative, technical, and material support: Qi L, Gao W
Supplementary materials are available from the Journal of Materials Informatics or the authors.
This work is supported by the National Natural Science Foundation of China (Nos. 21673095, 11974128, 51631004, 11774084, and 91833302), the Opening Project of the State Key Laboratory of High Performance Ceramics and Superfine Microstructure (SKL201910SIC), the Program for JLU (Jilin University) Science and Technology Innovative Research Team (Number 2017TD09), and the computing resources of High Performance Computing Center of Jilin University.
All authors declared that there are no conflicts of interest.
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© The Author(s) 2022.
Supplementary Materials