Topological Hallmarks And Spin-Valley Based Phenomena In Van Der Waals Layered Materials

As the title reflects,the central theme of this thesis is to present our recent investigations on the non-trivial topological anomalies and spin-valley based phenomena in two-dimensional van der Waals layered materials.Topology is concerned with the characteristics conserved under smooth or adiabatic deformations,and thus,it can be described by two principal hallmarks:globality and robustness.Certain material classes the so-called topological materials show strange behavior such as insulating response in bulk with robust conducting surface states.They have a robust immune system,for instance,when carriers hit a defect or some impurity in these materials,they simply ripple around it,instead of being scattered or experiencing resistance as in conventional wires.And are,therefore,considered,a game-changing class of materials as may have the ability to lead low power-consumption materials with more efficient energy,circuits for spin manipulations,and fast processing quantum computing.Based on time-reversal(TR)symmetry,topological materials may be divided into two major classes:one is the so-called TR preserving topological materials described by Z2 topological invariant and the other is TR broken topological materials characterized by Chern number or Z number.This thesis intends to include both these topological phases and its fate in the layered materials on his agenda.One sub-class of topological materials,the so-called magnetic topological insulators or quantum anomalous Hall(QAH)insulators,where the TR symmetry spoiled through exchange magnetization is highly efficient for low-dissipation power transmission,also supporting the exploration of a variety of new physics.Prior investigation proposed that magnetic topological insulators may be realized by depositing heavy-element layers on top of the surface of non-van der Waals(non-vdW)magnetic insulators.However,such a strategy has several experimental complications,such as surface reconstruction due to the existence of dangling bonds on the surface of the substrates.Owing to the presence of strong chemical bonding between constituent layers,it is experimentally not easy to downsize the vertical dimension of non-vdW three-dimensional(3D)ferromagnetic/anti-ferromagnetic insulators while preserving the lateral surface geometry(or only changing it slightly).To push away all these practical barriers and make the ideal environment more realistic,here in Chapter-4 of this thesis,we suggest a versatile experimental welcoming platform based on 2D vdW ferromagnetic insulators as a substrate for the deposition of heavy spin-orbit coupling components.Unlike a non-vdW substrate,2D vdW ferromagnetic insulators,in principle,possess a natural cleav-age plane with a perfect surface geometry free from dangling bonds,have no surface reform complication,are free of spin alignments,and are more accessible to being synthesized experimentally with excellent stability.This may attract the experimental community to invest their efforts in probing magnetic topological insulators.In addition,this thesis in Chapter-4 aims to address the following key queries to advance new,and possibly superior,routes for magnetic topological insulators.(i)Can the addition of spin-orbit coupling drive trivial 2D vdW ferromagnetic systems to become large-bandgap magnetic topological insulators in a fundamental and controlled way?(ii)Can they improve the ferromagnetic properties of 2D vdW ferromagnetic insulators,such as the Curie temperature in these systems?By employing the state-of-art first-principles calculation methods,we find that the quantum anomalous Hall effect can be realized by placing the heavy-element atomic layer on top of monolayer CrI3 with a natural cleavage surface and broken time-reversal symmetry.We showed that CrI3/X(X=Bi,Sb,or As)systems could open up a sizable bulk gap to harbour quantum anomalous Hall effect,e.g.,CrI3/Bi is a natural magnetic insulator with a bulk gap of 30 meV,which can be further enlarged via strain engineering or adjusting spin orientations.We also found that the ferromagnetic properties(magnetic anisotropic energy and Curie temperature)of pristine Crl3 can be further improved due to the presence of heavy atomic layers,and the spin orientation can be utilized as a useful knob to tune the band structure and Fermi level of CrI3/Bi system.The topological nature,together with the enhanced ferromagnetism,can unlock new potential applications for CrI3-based materials in spintronics and electronics.In Chapter-5,this thesis's agenda turns to our recent developments describing the surface-related features of the 3D topological insulators with or without considerable thickness as thought as the furthermost demandable in the field of condensed matter physics because of its rich technological applications.In particular,we focus on a subclass of thin films,the so-called ultrathin films with a sufficiently small thickness around?4-5QLs(Quintuple Layers)or thinner.To reduce bulk contribution or decouple the surface contribution from the bulk,the 3D topological insulators are usually grown in ultra-thin film geometry.However,the massless Dirac spectrum at the surface of topological materials converts into a gapped spectrum due to the considerable interaction between the top and bottom surfaces in ultra-thin film geometry.The size of this bandgap can be controlled through many external means such as the thickness of the sample and breaking the underline symmetries of the system.We will study the tuning of this bandgap by breaking the TR symmetry with circularly polarized light.The shining laser light reconstructs the electronic structure of 3D topological films by birthing the so-called Floquet-engineered topological band structure.By evaluating the surface psedu-spin Chern number analytically,we find that 3D topological insulators in ultra-thin film geometry pass through a phase transition from quantum pseudo spin Hall(QPSH)state to a photo-induced quantum Hall(P-QH)state when the effective energy induced by the circularly polarized light becomes greater in magnitude than the effective energy induced by the coupling between the top and bottom surfaces.We find that both the QPSH and P-QH states present a pronounced step-wise character.The phase-transition between these two topological states can be controlled by the degree of hybridization and off-resonant circularly polarized light.In contrast to magnetic doping,our approach is more realistic as circular polarized is a clean perturbation which can break the TR symmetry without hurting the system geometry.Additionally,we analyze the topological structure of QPSH and P-QH states by mapping the 3D unit vector on a unit sphere and revealing that they display merons-like or anti-merons-like configurations in the real spin space.Consequently,we will also address the flowing querries in this Chapter-5;(i)Is the light interact equally with each 2D(kx-ky)slice in the kz direction?(ii)Is there any possibility of topological phase transition along kz direction?To address all these queries,we will treat the momentum k in the z-direction as a parameter and will calculate the kz-dependent Chern number.The light-matter interaction in our model would be treated through the well-established theory,the so-called Floquet theory.Diverting our attention,in Chapter-6,we aim to measure the topological behavior of bilayer silicene(BLS),owing buckled type structure,significant spin-orbit(SO)coupling,and strong interlayer atomic interactions.To be more explicit,using the low energy effective continuum model together with the Kubo formalism and Floquet theory,we address the following questions(i)Can the application of laser light with circular or linear polarization,modify the electronic and topological nature of AB BLS in a notable and controlled fashion?(ii)Can the adjustment of antiferromagnetic(AFM)exchange magnetization ordering in BLS revise the electronic and topological signatures of BLS?(iii)What new conclusions are possible in BLS due to the combined employment of laser light,AFM exchange magnetization,and vertical electric field and the interplay among them?What would be the feature-rich phase diagrams for all these circumstances?Exploring such queries may be advantageous to push the boundary of our understanding of topological phases in real materials,which can provide a platform for a real quantum computer that shows intrinsic immunity against decoherence,which is the primary barrier in fabricating a scalable quantum computer.Finally,an endeavor has been made to devise a topological domain wall of BLS equipped with circularly polarized light and gatted voltage,which could propagate perfectly valley polarized channels without worrying from the environment.Spintronic device based on conventional semiconductors generically needs an unevenness between up and down spin electrons(or holes)apparently proposing that ferromagnetism may be a necessary and essential ingredient of any semiconductor spintronic devices.However,recent developments proposed advance and may be superior unconventional strategies to semiconductor spintronics—one that does not require any ferromagnetism and is free from the worries such as unwanted local magnetic fields that hinder the high densification of devices.The growth of this alternating route for designing semiconductor spintronic devices—"spintronics without magnetism"—based on the so-called SO coupling in the materials allowing the generation and manipulation of spins solely by the gate voltage.Most importantly,in spintronics without magnetism,the direction of spin polarization can be controlled via the Rashba SO coupling.In this context,materials with considerable Rashba SO coupling strength may help to drive the paradigm from less favorable magnetic-spintronic to most demandable nonmagnetic spintronic.In this context,in Chapter-7,we describe our recent developments where we have explored a set of promising 2D materials crystalized in MX(M=Mo/W,X=C/S/Se)chemical composition which exhibits a large and electrically switchable anisotropic Rashbalike and non-magnetic Zeeman-type spin splitting.In the paraelectric phase,these monolayers give a topological response with robust helical edge states protecting by time-reversal symmetry.The amplitude of the spin splitting can be further tuned with the application of external means such as strain,applying an external electric field,or switching the direction of polar-ization.Additionally,we establish a connection between the strength of Rashba splitting and lattice distortion by operating the asymmetrical strain along the zigzag or armchair direction.Interestingly,these MX monolayers can be turned into a non-magnetic half-metallic phase with the application of lightly electron/hole doping mechanism,which could generate electric field controlled spin-polarized currents where only one spin character crosses the Fermi level and may be useful in spin injection or spin filtering devices.Considering graphene/WC as a prototype example,we show that these MX monolayers can boost the relativistic effects by coupling with the systems exhibiting extremely weak spin-orbit coupling.Finally,we uncovered that these MX monolayers could also be grown on substrates such as WS2(001)and GaTe(001)with type-II band alignment.For practical applications,a multilayer graphene system is recognized as superior to single-layer graphene because the importance of sample defects that influence the spin and charge carrier transport is supposed to be smaller in multilayer graphene system due to its stiffness,leading to comparatively large mean free-path A and spin relaxation time.Furthermore,multilayer structures such as bilayer and trilayer of graphene support additional possibilities to host promising properties due to the so-called layer's degree of freedom.Very recently,trilayer graphene with ABC stacking has drawn significant interest in solid-state physics due to its unique properties such as flat bands near the Fermi level,high Chern numbers with multiple affording robust conducting edge channels,and superconducting states.In the first part of Chapter-8,this thesis aims to demonstrate feature-rich topological behavior of trilayer graphene(ABC stacking)in the presence of a spin degree of freedom by considering various symmetry breaking terms such as bias voltage which break the inversion symmetry,Rashba SO coupling which breaks the sz-symmetry,circularly polarized light and exchange magnetization which break the TR symmetry.The individual,as well as the combined effects of these external stimuli on the topological hallmarks,would be the part of the discussion.In the second part of Chapter-8,the discussion is extended to bilayer transition metal dichalcogenides(TMDCs),where we address the following quarriers(i)How can the electric and optical properties be modified by breaking the spatial inversion and TR symmetries in the bilayer TMDCs?(ii)Is the presence of off-resonant circularly polarized light,bias voltage,and their interplay can tune the Berry curvature in the vicinity of the valley points?Due to the recent experimental progress in bilayer MoS2,we use it as a prototype example to systematically address the above questions.In our model,the inversion symmetry will upset by employing the bias voltage across the bilayer MoS2 system,whereas the TR symmetry will spoil by shining the off-resonant circularly polarized light.Unlike the bilayer graphene,where the intralayer contribution in the Berry curvature is vanishing,and only the interlayer coupling contributes to the Berry curvature,the Berry curvature in bilayer TMDCs has both contributions originating from intralayer and interlayer coupling.Thus in this sense,the Berry curvature of bilayer TMDCs is more interesting and may exhibit different features when both TR and space inversion symmetries are broken.As the bilayer of TMDCs exist in different stacking patterns such as the so-called 2H and 3R stacking with different electronic proper-ties such as bandgaps and spin-splitting etc.,and thus according to our estimations,different stacking correspond to different Berry curvature properties and may seem useful to boost the spintronics and valleytronics technology.