Sharif Digital Repository

In this thesis, we analyze the Higgs mode in one-dimensional Kitaev topological superconductor. We first review the macroscopic (Ginzburg-Landau Theory) and microscopic (BCS Theory) derivation of oscillations of the energy gap in conventional superconductor in the presence of an electromagnetic field as a perturbation. We explain both analytical (based on Anderson pseudospins) and numerical (Density Matrix Formalism) approaches for calculations. The goal is to find the temporal evolution of the superconductor energy gap which is the order parameter of the system. In our investigation, we will see that we could reduce our problem to studying the amplitude of the energy gap in the Kitaev... 

Dirac-Weyl semimetals are new topological phases hosting the coexistence of Dirac and Weyl points in momentum space. Due to the different symmetry requirements of Weyl and Dirac semimetals, one may wonder whether these phases can coexist in real materials. Based on first principles calculations the noncentrosymmetric compounds SrHgPb and CaHgSn have band structure with the Dirac-Weyl crossings. In this thesis we introduce four band minimal lattice models which preserve n-fold rotation along z axis and break inversion symmetry. The obtained models use the minimum number of degrees of freedom, spin and orbital, and proper symmetries relevant to real materials yielding a four-band model where... 

In this thesis, we consider a simple layered structure grown along [001] direction. Based on the previous works we show that the energy spectrum contains linear Dirac spectrum of type II tilted in some direction. We also investigate the anomalous transport phenomena in the bilayer structures grown along [111] direction of a class of perovskites. The crystal field splits the d orbitals into two classes dubbed as eg and t2g described by different Hamiltonians within each manifold. An applied magnetic field breaks the time reversal symmetry and we show that the tight-binding bands acquire non-zero Chern numbers underlying the existence of non-trivial band topology in these structures. Again... 

Genetically the equilibrium and nonequilibrium collective properties of the electron system depend upon the strength of interaction between electrons, and of course between electrons and other degrees of freedom such as phonons. One of the collective states is the so-called exciton, a bound state of electron and hole in narrow-band semiconductors. The bound states give rise to absorption peaks below the gap in optical conductivity measurements.Excitonic insulator is an interesting phase of matter where the ground state is characterized by a coherent ondensation of exciton, much like the condensation of Cooper pairs in superconductors. Despite being introduced and theorized more than five... 

In this thesis, we study the tunneling transport at the interface of superconducting states in Bismuth-Nickel bilayer systems . The electron states on the surface of Bismuth are described by Dirac fermions due to strong inversion symmetry breaking near the surface and strong spin-orbit coupling . The magnetic fluctuations of underneath Nickel give rise to an attractive interaction between electron states of Bismuth and formation of superconducting states . The latter states cann't be described by conventional singlet and triplet pairing symmetries due to lack of spin degeneracy in Bismuth . In previous works, it's shown that the superconducting states break the time-reversal symmetry... 

The nature of the Cooper pairing in the paradigmatic unconventional superconductor Sr2RuO4 is an outstanding puzzle in condensed matter physics. Despite the tremendous efforts made in the past twenty-seven years, neither the pairing symmetry nor the underlying pairing mechanism in this material has been understood with clear consensus. This is largely due to the lack of a superconducting order that is capable of interpreting in a coherent manner the numerous essential experimental observations. At this stage, it may be desirable to reexamine our existing theoretical descriptions of superconducting Sr2RuO4.This thesis focuses on the experiments that have been carried out so far on Sr2RuO4 and... 

Notwithstanding massive efforts put forward in the last few decades, the experimental realization of quantum states with topological orders in a controlled way and accessible conditions has remained elusive. The realization of such states in fractional quantum Hall states requires extreme conditions like the cryogenic temperatures and strong magnetic fields. Also, the existence of a pure topological order in spin liquid materials is limited by disorder, subleading interactions, or lack of enough experimental information. Alternatively, we may think of extrinsic models to simulate the exotic phases by combining a set of naturally accessible quantum systems. Our approach involves the... 

In this work we introduce a new proposal to realize topological superconductivity. In this model we use a ferromagnetic material with high curie temperature like Nickel in proximity to the surface of a three dimensional topological insulator or equivalently Bismuth which has surface states with strong spin-orbit coupling which makes its surface Hamiltonian similar to the surface of a three dimensional topological insulator.The surface electrons of Bismuth are Dirac fermions with strong spin-orbit interaction. The interaction of surface electrons with magnetic fluctuations in the ferromagnet induces an effective attractive electron-electron interaction among surface electrons upon integration... 

In this thesis, first we study superconductivity and its mechanisms then classify different types of that based on symmetry of gap function. After that, we shall discuss metallic systems that have impurities in them and propose two successful model describing this phenomenon, Anderson’s model and Kondo’s model. In the next step, by introducing Kondo lattice model which is an ordered array of impurities in system, try to solve it by mean-field approximation and will be seen a phase transition in a characteristic temperature known as Kondo’s temperature. Then generalize these models to situation when background system is a superconductor and study it’s behavior and quantum phases. Although... 

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... 

Quantum spin liquids are characterized by the lack of long range magnetic order at zero temperature due to strong quantum fluctuations in frustrated magnets, emergent fractionalized excitations coupled to gauge fields, pattern of long-range entanglements, and topological orders. Since the theoretical predictions dated back to the seventies, a huge amount of both theoretical and experimental efforts put forward to explore these emerging phenomena in real materials. Besides the organic compounds with spin liquid ground states, recent years have witnessed the dawn of new oxide materials such as α - RuCl3 and Na2IrO3 which may host spin liquid at low temperatures. The ground states of the latter... 

The concept of topology has underlined the discovery of new phases of matter since the eighties. Meanwhile the material growth, synthesis, and measurements have enabled us to examine the theoretical predictions. Amongst all, the anomalous thermal Hall and Nernst effects result from the non-trivial topological properties of lowenergy carriers. In this thesis our objection is to study some of these phases in two-dimensional magnetic layers such as honeycomb and Kagome lattices and their heterostructures.First, we consider heterostructures of a pyrochlore lattice along the [111] directions: triangular-kagome (TK), triangular-kagome-triangular (TKT), and kagometriangular-kagome (KTK) lattices.... 

We are interested in the relation between entanglement and quantum phase transitions. We have presented a formulation on how the entanglement of a very large the system is related to the entanglement of a small part of system. The renormalization of entanglement is an indicator of the critical behavior of the models. The framework of our approach is introduced about the Ising model. In particular, we show that derivative of entanglement developes a minimum close to the critical point. We further clarify that this minimum point approaches to the exact critical point of the system as the system becomes thermodynamic. This phenomenon is governed by an exponent that is closely related to the... 

The lubricating oil is commonly used to cool down the moving parts of turbine gas systems. In many applications, this oil is cooled down using a recirculating water circuit. The water is then cooled down using an air-cooled heat exchanger. Any deficiency in aerothermodynamic design of such heat exchanger would result in high temperature of gas turbine moving parts such as bearings. Obviously, this mal-performance has adverse effect on the lifetime of these parts and their maintanence aspects. Since the good performance of air-cooled heat exchanger has numerous advantages for the performance of related gas turbine unit, it is mandatory to design these heat exchangers in minimum sizes and...