Sharif Digital Repository

In 2002 Baskaran and Jafari published an article that was about a spin-1 collective mode. Similarity between carbon nanotubes and graphene was a motivation for working on this project, in order to find another spin mode by considering random phase approximation as a simple way of finding collective motion of a physical systems. Moreover rolling graphene sheet induce diffrent physical properties as a result of chiral axis . In this project we focus only on achiral nanotubes and at last find two collective modes in this structures  

In this thesis we have been mainly interested in studying Single Impurity Anderson model (SIAM) in Dirac fermions. Although this model seems to be simple, the rich physics of SIAM can not be underestimated. In this thesis we were interested in Dirac materials, systems which their low energy excitations are described by Dirac equation.Therefore, considering Dirac material in two dimensions(2D), we briefly review the distinct features of one atom thick layer of carbon. In addition, we will explain the effective Hamiltonian of Bismuth near L point which is considered a three dimensional(3D) Dirac material. Because of very strong spin-orbit interaction, bismuth is a key element in topological... 

We study the quantum transport properties of three dimensional Dirac materials within the framework of Landauer–Büttiker formalism. Charge carriers in normal metal satisfying the Schrödinger equation, can be split into four-component with appropriate matching conditions at the boundary with the three dimensional Dirac material (3DDM).We calculate the conductance and the Fano factor of an interface separating 3DDM from a normal metal, as well as the conductance through a slab of 3DDM. Under certain circumstances the 3DDM appears transparent to electrons hitting the 3DDM. We find that electrons hitting the metal-3DDM interface from metallic side can enter 3DDM in a reversed spin state as soon... 

The ability to determine the nature of the low temperature state of the interacting quantum system is one of the main goals of condensed matter theory. Nevertheless, despite ongoing efforts, no single method has proved to work perfectly for interacting systems. In this thesis, we employ the strong-coupling perturbation theory which corresponds to an expansion in powers of the hopping t around the atomic limit. So, first the strong-coupling perturbation theory is introduced. Next we apply this approach to the half-filled Hubbard model on honeycomb lattice. Within this approach, we are able to obtain an analytical form for single-particle gap, extracted from density of state, as a function of... 

In this thesis, we have investigated the plasmon dispersion on the Dirac matter. The Dirac matters which we consider to this end are graphene and borophene allotrope.The borophene allotrope has smaller anisotropic Fermi velocity and tilted Dirac cone in comparison with graphene. We briefly give a short introduction to these materials and then we study the propagation of electromagnetic modes in them. We begin with graphene as a well known two dimensional Dirac material. It has been found that two kinds of plasmon modes named as plasmon mode and transverse electric filed mode are allowed to propagate in graphene but just the plasmon mode can be affected by interaction. As the correlated... 

Recently, some materials, such as Weyl and Dirac semimetals, have been found in condensed matter physics whose band structure behaves like Weyl fermions of elementary particles near some points of the first Birillouin zone. The Weyl equation that governs these materials, have boundary because they are finite. By applying proper boundary conditions, two-dimensional surface states have been emerged. these states are called fermi arc sates because the surface corresponding to the fermi energy is not a closed surface. Surface states are mixed with bulk states because by getting close to the end of fermi arcs, surface states tend to bulk states con-tinuously. Being able to distinguish between... 

8−Pmmn Borophene is a single layer 2D material made or Boron atoms. This material is a Dirac material with anisotropic tilted Dirac cones (Unlike Graphene). In study, We will exploit Group theory and representation theory to investigate the space group of this material namely Pmmn space group. Then representation theory and basis functions of the irreducible representations of space group will be used to find the allowed couplings between electronic and phononic states; hence we will derive the most general hamiltonian of Electron-Phonon coupling allowed by symmetry  

Since concepts in quantum information theory has recently been applied to characterize states in many-body systems, we survey entanglement of the ground states in the S = 1/2 antiferromagnetic Heisenberg ladder systems and 2D square lattices. The Lancz¨os method for exact diagonalization of quantum spin models are used to find the ground states. Moreover, effect of defect in ladder on entanglement and ground state energy are studied  

Disorders with creating the localized states, which are the states with limited spatial distribution, cause carriers of these states become limited to small part of space and cannot participate in the transport. If energy of these states is near the Fermi energy, the Anderson metal-insulator phase transition occurs. In this thesis,we studied type of disorders and determining their Hamiltonian and by studying definition of localization from different aspects, we attained a better explanation of disorders effects on materials. With studying the localization scaling theory, we ex-amined conditions of localization in different dimensions. Then for determining the green function and therefor the... 

In this thesis, we investigate the effect of disorder on Majorana fermions at the boundary of one-dimensional topological superconductor. Starting from one-dimensional spin model nXY and then applying the Jordan-Wigner transformation result in one-dimensional topological superconductor. The Majorana fermions are found in the topological superconductor boundaries, protected by particle-hole and time-reversal symmetries. On the other hand, these fermions are highly localized at the boundary. Owing to non-trivial topology, the Majorana fermions are not affected by weak disorder. Increasing the disorder strength, the localization length of the Majorana fermions increases. Upon further increase in... 

The zero-energy excitations of topological superconductor promising the design of quantum computers have received a great deal of attentions in recent years. But the materialization has remained to be elusive. Our focus in this thesis is on the one- and two-dimensional systems where the necessary ingredients may conspire to realize topological superconductors. In particular, we will focus on the role of reduction of spatial symmetries near the interfaces. We will start with a one-dimensional system at the boundary of a two-dimensional system with particular orientation so that the full translational symmetry is replaced with a quasi-periodic symmetry. We show that the Fibonacci sequence... 

The ionic Hubbard model is an extended version of the Hubbard model in which an ionic potential term is added to the original Hubbard model. This model was proposed to describe the neutral-ionic transition in the charge transfer of salts, and later attention to this model increased due to its potential application in ferroelectric perovskites. Considering the realization of the ionic Hubbard model in cold atoms in the study of the invention of superlattice modulation spectroscopy to investigate the bond order and a very attractive recent study for the realization of the one-dimensional ionic Hubbard model in the twisted GeSe bilayer, existence of an exact solution and accurate results for... 

In this thesis, we study different aspects of tilted Dirac materials from hydrodynamics and holography approach. Dirac materials are among the most important structures which have been introduced in recent years in condensed matter physics where graphene is the simplest of them. Classification of space groups allows nonsymmorphic structures where the low energy electronic degrees of freedom can be described by tilted Dirac cones. In the long wavelength and time limit, these materials can be effectively described by a metric which is called tilted metric. Dirac materials are usually strongly coupled and cannot be studied using the common perturbative techniques; therefore hydrodynamics and... 

In this thesis, first of all we introduce the Anderson model, Multifractality, and conformal field theory. Then we try to determine some critical and scaling quantities for the critical wave functions in the 2D systems with spin-orbit interactions We implement a correction-to-scaling analysis by introducing an irrelevant exponent which leads to a proper and sharp evaluation of the critical parameters including correlation exponent, rescaled localization length and the critical disorder. Then, we survey the multifractal properties of this model and obtain some multifractal exponent in the critical point. Finally, we will survey the existence of the conformal invariance symmetry in it. Our... 

In this project, we investigate the influence of angular momentum of Light on the Dirac matter. We show that polarization or spin of light can change the population of [pseudo-]spins. In graphene, pseudo-spins indicate the probability of existing elec-trons in each sub-lattice. However, the two different sub-lattices are the same and the contribution from two distinct Dirac cones cancel out. Therefore, the change in the population of pseudo-spins does not happen. On the other hand, in topological insulators we have just one Dirac cone; thus, polarization of light can change the population of [pseudo-]spins  

In this thesis, physical properties and gas sensing application of three-dimensional graphene-based structures are studied. The three-dimensional structures of reduced graphene oxide and relative hybrids were synthesized through reducing graphene oxide aqueous solution. The arrangement of two-dimensional graphene layers in three-dimensional architectures has some advantages such as high surface area, hence increasing available adsorption sites. These properties result in changing electrical parameters of the structure, such as electrical impedance and phase angle in the presence of different mediums and alteration of temperature and pressure. Various characterization techniques like atomic... 

Quantum thermodynamics is a new field of study in physics, which by considering the fundamentals of statistical mechanics, open quantum system, quantum information and mesoscopic system aims at the investigation of quantum systems from a thermodynamical point of view. To achieve these aims, a better understanding of the relations between quantum and thermodynamics fundamentals is essential. Energy and correlation are two key concepts in statistical mechanics and quantum thermodynamics (and information), respectively, that studying the relation between them will shed light on the fundamentals of quantum thermodynamics. As generating any correlation in quantum systems with initial heat state... 

Titanium alloy Ti-6Al-4V ELI with high biocompatibility and corrosion resistance, has a lot of applications in biomedical engineering. Disadvantage of this alloy is it’s disability to create a fast and good contact with the host/bone environment, after implanting in the body. Beside that it has low wear resistance. Nowadays to optimize the wear resistance, bioactivity and osteoconduction of surface of implants which are made from this alloy, the surface morphology are optimized in size and distribution. Different surface treatments are used for producing rough and porous surfaces to improve bioactivity along with wear resistance. In this study, surface modification of Ti-6Al-4V ELI was done... 

Commercially pure titanium (CP-Ti) is an important groups of titanium family and because of high strength, low density, high corrosion resistance and biocompatibility, this group of titanium is a suitable choice for application at chemical, petrochemical and medicine industry. Nowadays surgeons have a tendency toward use of CP-Ti instead of Ti-6Al-4V alloy. Moreover, because of body anatomy limitation, use of thick sheets result in high volume and damage soft tissue. Therefore, for sheet thickness reduction, study of the effects of metallurgical and geometrical parameter on fracture behavior of thin sheets is important. In this study, the fracture behavior of CP-Ti thin sheets investigated....