Study Of Disorder And Light Induced Topological Phase Transitions And Transport Properties In Topological Materials

Topological materials are newly discovered quantum materials,in which exist topo-logically protected boundary states.In the past decade,topological materials have been attracted much attention,and theoretically predicted and experimentally observed in a variety of materials.Recently,more new topological materials have been proposed,including the topological semimetal,topological line-node semimetal,topological super-conductor,and topological superfluid.In this thesis,we investigated disorder and light induced topological phase transitions in several topological materials through analytic and numeric approaches.This paper is organized as followsIn chapter 1,we briefly introduce development history of topological materials in-cluding the Hall effect,the anomalous Hall effect,the quantum Hall effect,the quantum anomalous Hall effect and the quantum spin Hall effect.Then we introduce the re-search contents and development including a one-dimensional topological SSH model and a two-dimensional topological BHZ model.After introducing the Dirac and Weyl equa-tion,we introduce the topological semimetal materials,including Weyl semimetal,Dirac semimetal,and the line-node semimetal.At the mean time,we introduce the methods in calculating the topological number,such as the winding number and Chern numberIn chapter 2,we introduce some approaches which can characterize a disordered topological system,such as the Bott index and the real space Chern number.We also describes the method to calculate the two-terminal conductance through the Landauer-Buttiker equation and the recursive Green's function.In addition,we introduce the self consistent Born approximation,which requires the disorder strength is weak.Moreover,we introduce the transfer matrix method to calculate the localization length of a disordered system.At last,the comparision of the above mentioned methods show they have their own strong and weak pointsIn chapter 3,we investigate effects of disorder in thin films of Dirac semimetal.The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter.Topological Dirac semimetals can be viewed as three dimensional analogues of graphene,in which the Dirac nodes are protected by crystalline symmetry.It has been found that quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator.The band insulator is either normal insulator or quantum spin Hall insulator depending on the thin film thickness.We present the study of disorder effects in thin film of Dirac semimetals.It is found that moderate Anderson disorder strength can drive a topological phase transition from normal band insulator to topological Anderson insulator in Dirac semimetal thin film.The numerical calculation based on the model parameters of Dirac semimetal Na3Bi shows that in the topological Anderson insulator phase a quantized conductance plateau occurs in the bulk gap of band insulator,and the distributions of local currents further confirm that the quantized conductance plateau arises from the helical edge states induced by disorder.Finally,an effective medium theory based on Born approximation fits the numerical dataIn chapter 4,we study the topological phase transitions driven by Anderson-type disorder on spin-orbit coupled Lieb lattices in the presence of spin-independent and de-pendent staggered potentials.By combining the recursive Green's function and self-consistcnt Born approximation methods,we found that both time-reversal-invariant and time-reversal-symmetry-broken spin-orbit coupled Lieb lattice systems can host the disorder-induced gapful topological phases,including the quantum spin Hall insulator(QSHI)and quantum anomalous Hall insulator(QAHI)phases.For the time-reversal-invariant case,the disorder induces a topological phase transition directly from a normal insulator(NI)to the QSHI.While for the time-reversal-symmetry-broken case,the disorder can induce either a QAHI-QSHI phase transition or a NI-QAHI-QSHI phase transition,depending on the initial state of the systemIn chapter 5,we study the combined effect of intra-and inter-orbital disorders on WSMs by adopting a tight-binding model that supports the WSM,three-dimensional quantum anomalous Hall insulator(3D QAHI)and normal insulator(NI)phases in the clean limit.Basing on the calculation of the localization length and the Hall conductivity,we present rich phase diagrams due to the interplay of intra-and inter-orbital disorders We find that the WSM with well-separated Weyl nodes is stable to both weak intra-and inter-orbital disorders.However,weak intra-orbital disorder can gap out a WSM close to the 3D QAHI phase in the clean phase diagram,forming a 3D QAHI,and it can also drive a NI near the WSM phase to a WSM.By contrast,weak inter-orbital disorder can cause a 3D QAHI-WSM transition for a 3D QAHI in proximity to the WSM phase in the clean limit,and it can annihilate a WSM near the NI phase,bringing about a WSM-NI transition.In chapter 6,we present here a study on the circularly polarized light-induced Floquet states in type-? LNSMs,as well as those in hybrid LNSMs that have a partially over-tilted linear dispersion in the vicinity of the nodal ring.We illustrate that two distinct types of Floquet Weyl semimetal(WSM)states can be induced in periodically driven type-? and hybrid LNSMs,and the type of Floquet WSMs can be tuned by the direction and the intensity of the incident light.We construct phase diagrams of light irradiated type-? and hybrid LNSMs which are quite distinct from those of light irradiated type-?LNSMs.Moreover,we show that the photoinduced Floquet type-? and type-? WSMs can be characterized by the emergence of different anomalous Hall conductivitiesIn chapter 7,we investigate the effects of periodic fields and disorder on topological properties of a Weyl-semimetal thin film.The two periodic fields,i.e.,a periodic magnet-ic field and elliptically polarized light,are discussed respectively.By use of the Floquet theory,we find that both the two periodic drives can resonantly induce the topological transitions from normal insulator(NI)phases to Floquet topological insulator(FTI)phas-es.The Floquet topological transitions are characterized by variation of Chern number Moreover,we show that the Floquet topological transitions can be explained by a combi-nation of the quantum well approximation and the rotating wave approximation.In the disordered Weyl-semimetal thin film model under periodic fields,we calculate the Bott index to characterize topological phase.It is found that the FTI phase is robust against weak disorder,and collapses for strong disorder strength.Interestingly,we find that dis-order can also induce a topological transition from a topological trivial phase to an FTI phase,establishing the Floquet topological Anderson insulator(FTAI)phase.Finally,an effective-medium theory based on the Born approximation further confirms the numerical conclusions.At last,we give a brief summary and prospect.