Theoritical Study On Magneto-and Electro-Properties Of Helical Structures

Helical structures with diverse functions are widespread in nature. As the core content of helical electronics, the relationship between helical structures and physical properties was studied in this paper. Due to the continuous development of micro-and nano-technology, the materials with helical structures in molecular, nano-and micro-scale have been synthesized in recent years, and they all display a number of unique physical phenomena which non-helical structure does not have. However, the model of single electron constrained in a helix which only could be used to describe the movements along the helix can not fully reflect the actual behavior of electrons constrained in helical structures. The lack of more accurate models restricts the progress of helical electronics. Furthermore, the correlation between helical structures and physical properties is still unknown because it still lacks theoretical researches in this field. In the view of current situation, we studied the behavior of electrons constrained in one-dimensional and three-dimensional helical structures by quantum mechanics and DFT. In order to construct the relationship between helical structures and physical properties, the Schrodinger equations of electrons with various constrained potential field are presented and solved by analytical or numerical methods. The effect on the behavior of electrons induced by helical structure parameters and the response to the applied fields of electrons in helical structures are also investigated in this paper. Our achievements and conclusions are as follows:The behavior of electrons constrained in a coil is studied under an applied magnetic field both experimentally and theoretically. The analytical solution to the Schrodinger equations of electrons constrained in a coil with an applied magnetic field is given by Byers-Yang gauge transformation and introduces the induced magnetic moment. The calculation results show that the induced magnetic moment responds to the applied magnetic field positively and it is also closely related with the parameters of helical structure. In addition, the observation of experiments illustrates that the diamagnetic signal is enhanced after the helical structure of the sample destroyed at3K. It is proved that the existence of paramagnetic response of helical structures is caused by the polarization of angular momentum which is from the movements of electrons along the coil. Our results indicate the association between helical structure and paramagnetism.In order to be more close to the real situation, we improved the model of electron constrained in helix. In the new model, single electron is set in a three-dimensional space and constrained by a helix with positive charges. Under a confined potential which is an inverse proportion function of radius, a Schrodinger equation in helical cylindrical coordinates was given to study the energy levels and wave functions of electrons. Using series method, the analytical solution of the Schrodinger equation is obtained under two variable substitutions. The calculation shows that in the case of an opened boundary it is possible to separate the movement of the electron into axial, angular and radial movement which is described by three ordinary differential quantum numbers, respectively. Axial quantum number describes the movements along the helix, which is agreement with the traditional model of single electron constrained in helix. Angular quantum number describes rotation around the helix, the absolute value of which determines the measure of the area of the orbit. Radial quantum number describes the movements along the perpendicular direction of the helix, the value of which determines the number of the nodes of orbit and the measure of the area of the orbit.On the basis of these above results, we also calculated spin-orbit coupling wave functions of the electron in the helical cylindrical coordinates, fine structures of the energy spectrum with spin-orbit interaction and Zeeman effect in the helical cylindrical space with an applied magnetic field. These results show that the degeneracy of the energy level reduces by spin-orbit interaction and eliminates by spin-orbit coupling under applied magnetic field. In addition, the concern is that all the energy levels are manipulated by the parameters of helical structure, and a phase transition of paramagnetic to diamagnetic occurs in several levels as the helical angle increasing. Meanwhile, the change of energy levels shows magneto-chiral anisotropy in the whole processes.In the molecular scale of helical structure, we explored changes of band structures of lithium single-wall nanotubes (LiSWNTs) after a chirality-breaking and under different tensile states by the first principle calculations based on DFT. After a chirality-breaking, the two-dimensional space group of the network changes into C1from C1h, and two types of chirality-breaking exist in LiSWNTs which are horizontal and vertical helicalization. The calculations on the band structures of LiSWNTs within first-principle, pseudopotential self-consistent local density approximation approach adapted for helical symmetry are reported in this paper. The chirality-breaking induced the bands split, which provide more transport channels for electrons. As the helical LiSWNTs being stretched, the band structures changed from metallic type to quasi-metallic type. This transition caused by configuration of helical structures indicates that manipulation to the electrons constrained helical single-wall nanotubes is available.In summary, the behavior of electrons constrained in helical structures is studied in this paper through theoretical calculation and computer simulation, for the purpose to construct the association between helical structure and physical properties. Above all these results, the mechanism of quantum manipulation is studied and analyzed in order to provide new effective methods on manipulation to the physical properties of materials with helical structure, such as micro-and nano-sensors. Our findings may also have new applications in the developments of materials science in helical electronics.