A THEORETICAL STUDY ON ELECTRONIC PROPERTIES OF SOME TRANSITION METAL NANOWIRES

Abstract

Nanoscale science/technology is a rapidly flourishing field that encompasses almost every area of science and engineering. It has witnessed the onset of entirely new class of low dimensional materials such as fullerenes, nanocomposites, nanoclusters, quantum wells, nanowires, quantum dots etc. These materials lay the foundation for building advanced materials with unique properties and enhanced performance. Various properties, like electronic, magnetic, optical and vibrational, get altered with respect to the bulk in a unique way in these materials. On the experimental front, electronic, magnetic, optical and magneto-optical properties have been studied for the 2-dimensional and 1-dimensional lattices, gratings, monolayers, and nanowires etc., and tailoring of electronic and magnetic properties has been explored for these. In this context, monolayer and bilayer graphene and its doped systems have also drawn much attention. Transition metal (TM) nanorods, nanowires, nanoparticles and nanoclusters have been synthesized and characterized to understand their electronic, magnetic and optical properties. Theoretical calculations to understand and predict the properties of nanomaterials can greatly help in streamlining the experimental research and hence in designing suitable materials with enhanced performance. Density functional theory (DFT) is one such powerful theoretical technique used in physics, chemistry, material science and engineering for performing ab-initio calculations to investigate many-body systems, in particular atoms, molecules, condensed phases and the bulk materials. DFT has proved to be a very effective and reliable tool for study of electronic structure, magnetic and optical properties. It has been successfully applied for the study of electronic structure and optical properties of various TMs and rare earth compounds. Many experimental and theoretical studies have focused on structural, electronic and magnetic properties and compositional disorder in TM alloys. First principle DFT calculations have also been successfully employed for study of electronic structure, magnetic and transport properties of nanowires, nanotubes, nanoribbons and nanoclusters, and for study of atomic scale mechanisms and atomic scale modeling. In this thesis the focus is on the study of some TM nanowires (NWs). TM NWs are of fundamental physical interest because of their unusual electronic and magnetic properties e.g. appearance of magnetism, quantized conductance, spin dependent transport etc. Research on NWs of these elements has gained momentum because of their tremendous technological iii applications as molecular electronic devices, magnetic storage and as potential interconnects between nanodevices. We have carried out first-principles DFT calculations to evaluate the electronic, magnetic, optical and vibrational properties of some TM NWs. Projector Augmented Wave method, as incorporated in the Vienna ab initio simulation package, has been employed for calculations. Some calculations have also been carried out using the full potential linearized augmented plane wave method for the sake of comparison or for use as reference. Three different types of systems are the subject of this study: Free standing elemental NWs of TMs V and Pd; free standing equiatomic binary NWs of V and C; substrate supported 3-d TM (V and Cr) and 4-d TM (Nb and Mo) NWs. The whole work of the thesis is presented through Chapters 1 to 6 as briefly described below: Chapter 1 is an introductory chapter which gives a brief description of the theory underlying the work carried out. Topics like electronic structure problem, density functional theory, exchange and correlation, electronic structure methods, Brillouin zone integrations, magneto-crystalline anisotropy energy, linear optical theory, basics of phonon dispersion, elementary formulae for basic low-dimensional systems, and the supercell approach are discussed briefly. Finally, the motivation and outline of the thesis close the curtains on this chapter and usher the readers to the main work of the thesis. Chapter 2 heralds the presentation of the work embodied in this thesis. It presents detailed study of the electronic, magnetic and optical properties of free-standing and supported NWs of vanadium. In an effort to evaluate the effect of structure on these properties, we have studied five different structures of ultrathin NWs of V: linear, zigzag, dimerized, ladder and helical. Further, the study of optical response for NWs, in general, is important from application point of view and has hardly been reported in the past. This gap is bridged by also studying the optical properties for these V NWs. For dimerized NWs, we show that besides the usual alternate up and down arrangement of spins (as reported earlier), other configurations are also possible for the AFM state. One of these turns out to be energetically more favored. We find that linear chains (LCs) have a cusp in the cohesive energy vs. atomic separation curve marking the embarkment of the “high-spin” state and leading to the metastable state. The electronic density of states (DOS) vs. energy curve nicely illustrates this iv transition. Study of optical properties of these NWs unfurls a nice impact of the spatial dimensions of these structures on imaginary part of dielectric function for different polarizations of the incident electric field. In addition to free standing NWs, we have also studied the NWs supported on substrate since the latter are more realistic. We chose noble metal copper as substrate mainly because it is less likely to influence the properties of the NWs. Properties of bulk V and of Cu substrate alone have also been studied for a better interpretation of the results. The influence of the substrate on the NW has been studied with the help of electronic DOS, charge density, magnetic and optical properties. Finally, we have also made a preliminary study on the thicker NWs of vanadium. Having studied elemental NWs of vanadium, we advanced one step ahead in Chapter 3 by considering NWs of “alloy” of vanadium with carbon. Interesting properties of metal carbides, in particular VC, inspired us to explore this system at nanoscale. Chapter 3 deals with the study of various structures of thin and thick equiatomic vanadium-carbide NWs, and presents the electronic, magnetic, optical and vibrational properties of these. The vibrational properties of NWs, which have been explored very little in the past, and have hardly been studied theoretically for binary NWs, have been calculated and discussed for VC NWs. We have also studied some elemental NWs of constituents vanadium (Chapter 2) and carbon to compare with VC binary NWs. The cohesive energy/formula-unit shows a nice systematic trend for these NWs. We find an encouraging result that magnetic moment at the V site is hardly compromised in the VC ultrathin wires. Interestingly, the cohesive, mechanical and vibrational properties of these wires are found to be dictated by the lighter C atoms while the electronic and magnetic properties are governed by the V atoms. The anisotropy in the optical properties is found to have a nice association to the structure of the NWs. Results are also presented for electron localization function, difference charge density and heat capacity. Chapter 4 focuses on a NW structure, we call “2x2” structure, which has been realized experimentally for silver NWs in Mechanically Controllable Break Junction experiments identified through High Resolution Transmission Electron Microscopy. It has been found to be one of the “magic structures” for Ag NWs during the thinning process. However, it has sparsely been studied theoretically: only for Ag and Fe NWs. We chose the element Pd for the study of 2x2 structured NWs since Pd linear chains are known to display v enhanced DOS in magnetic regime and also because Pd being a 4d TM is a fairly good candidate for studying spin-orbit coupling. Furthermore, previous reports on Pd zigzag NWs seem to be mutually inconsistent, with the results differing much. This prompted us to study the zigzag NWs of Pd to resolve the inconsistency. For a systematic study, we also studied the most elementary structure i.e. the linear chain: the ideal one-dimensional structure. Thus we have studied the gradual evolution of the electronic, magnetic, optical and vibrational properties of ultrathin NWs of Pd as we go from linear chain (having no expanse in transverse plane) to zigzag structure (having expanse along only one direction in the transverse plane) to 2x2 structure (having expanse in two directions in the transverse plane). Through this systematic study, we have resolved the discrepancies in the results reported earlier for zigzag Pd NWs. We also studied the magneto-crystalline anisotropy constants for these NWs of Pd and determined their easy axis of magnetization. This study unfurls nicely the impact of spin magnetization direction on the atomic magnetic moments through the 2x2 structure. Furthermore, charge density, difference charge density and electron localization function have also been studied. We find that, when properly aligned, these Pd NWs can serve as very effective polarizers of light. Free standing NWs offer ease of computational handling of 1-dimensional materials. However due to transient nature of NWs, these are more utopian than real. In this respect, substrate supported NWs fare better. These are the ones that are more realistic, can be/ are realized experimentally and can be harnessed for various applications. Hence it becomes relevant to study substrate supported NWs. Therefore, Chapter 5 is devoted to substrate supported NWs. For this we studied 3d TM (V and Cr) and 4d TM (Nb and Mo) NWs on the substrate Cu. These calculations involve a large number of substrate atoms and hence are highly CPU expensive. For this reason, and also for lack of computational facility required for larger systems, we confined to simple structure of NWs on the substrate: like LC and zigzag structure. For the sake of having an almost complete picture, we have studied three different orientations of the surface i.e. (001), (110) and (111) oriented copper substrates. Free standing elemental NWs of these TMs have also been studied on equal footing for sake of comparison and thus to understand the influence of the substrate on the properties of the NWs. In addition to this, we have studied Cu(001), Cu(110) and Cu(111) substrates alone also, to facilitate in the understanding of results for the system of substrate supported NWs. To the best of our vi knowledge, results on substrate supported 4d TM chains have not been reported earlier. Also, the optical properties have not been reported so far for free-standing as well as supported NWs of these TMs. The atomic positions are analyzed after atomic relaxation and the results are discussed accordingly. Impact of the substrate, as also the orientation of the substrate, has been discussed. Chapter 6 on conclusions summarizes the entire work presented in the thesis and also presents future scope of the work. There is a vast range of possibilities for working in this area; literally speaking, sky is the limit. We suggest some ways in which the present work can be extended further