Theoretical Studies Of Topological States

In condensed matter physics,states of matter are usually classified by symmetry.At low temperature,topological states of matter describe new quantum states of matter that cannot adia-batically connect to conventional states of matter even though they share the same symmetry.Thus,the discovery of topological states of matter has opened a new research era and attracted intensive research interests in recent years both theoretically and experimentally.This dissertation is devot-ed to the theoretical and numerical study of topological states of matter,mainly focusing on two systems:one is InAs/GaSb quantum wells which gives rise to quantum spin Hall effect;the other one is Bi2Te3/NbSe2 heterostructure which hosts Majorana zero mode inside the superconducting-ow:vortex.The contents and results of the thesis are list below:(1)In chapter 1,we review the background and history of topological states of matter,and summarize our work in this dissertation.(2)In chapter 2,we firstly introduce the basic concept and property of topological phases;then analysis four representative models of 2D topological phases.Secondly,we describe how to calculate the Landauer-Biittiker-Fisher-Lee formulism by using recursive Green's function's method.Thirdly,we review the standard Ginzburg-Landau theory to study the superconduc-tivity.(3)In chapter 3,we study the effect of electric field to InAs/GaSb quantum wells.Based on the eight-band Kane model,we explore the dependence of the hybridization gap and inversion band gap as a function of external electric fields.As a result,we find two regimes via varying the electric fields:(1)Both inverted and hybridization gaps increase and(2)the inverted gap increases while the hybridization gap decreases.Finally,we reduce Kane model to Bernevig-Hughes-Zhang(BHZ)model,to understand the physical insight.Because we can calculate all the parameters in BHZ model which helps us analyze the relationship between inverted gap and hybridization gap.(4)In chapter 4,we study the effect of in-plane magnetic field and strain to InAs/GaSb quan-tum wells(2D topological insulator).Based the double-layer-BHZ model,we theoretically study the quantization of longitudinal conductance by using Landauer-Biitikker-Fisher-Lee formalism.Firstly,our calculation predicts a robustness of the conductance quantization a-gainst the in-plane magnetic field,and find that the gapless edge states can survive as long as the magnetic field is less than 20 T.Secondly,we use a disordered hopping term to model the strain effect(lattice distortion),and show that the strain may help the quantization of the conductance.Finally,the relevance to the experiments will also be discussed.(5)In chapter 5,we study topological superconductor on the interface of the TI/SC heterostruc-ture.Theoretically,we solve the Fu-Kane Hamiltonian and its corresponding Bogoliubov-de-Gennes(BdG)equation,thus investigate the in-gap excitations inside a vortex.The spin wave function of the MZM at the vortex core center(r = 0),is parallel to the magnetic field,and the local Andreev reflection of the MZM is spin selective.When the scanning tunneling microscope(STM)tip is laid above the vortex core center,the total local differential tunnel-ing conductance consists of the normal term proportional to the local density of states and an additional term arising from the Andreev reflection.Finally,we apply our theory to examine the recently reported spin-polarized STM experiments and show good agreement with the experiments.(6)In chapter 6,we theoretically study bilayer superconducting topological insulator film,in which superconductivity exists for both top and bottom surface states.We show that an in-plane magnetic field can drive the system into Larkin-Ovchinnikov(LO)phase,where electrons are paired with finite momenta.Finally,we realize that the LO phase is topologi-cally non-trivial and characterized by a Z2 topological invariant,leading to a Majorana zero mode chain along the edge perpendicular to in-plane magnetic fields.(7)In chapter 7,a summary and the prospect of our work is provided.