Electron Transport Properties Of Disordered Topological Insulator In Two Dimension

Topological band insulator (TBI) that attracts much interest and research effort has established new classifications of matter which has non-trivil topo-logical properties. The topological invariant used to describe the2D TBI is an index called Z2-When it is zero, the system has even pairs of edge states which is topologically equivalent to ordinary insulator. Another non-trivil value is one which indicates odd paris of edge states exsisted. A remarkable fact of TBI is that it can comprises a single pair of spin-filtered edge states which means that electon spin is tied to propagation direction in the conduct-ing channel. Thus, the word "helical" or "crural" is offten seen in describing the edge states. The peculia configuration of the edge states which is distinct from either an ordinary insulator or quantum Hall state (it also has chiral edge state, but electons of both spins go in one direction) enable a2D TBI to have inherently non-dissipative quantum spin Hall effect (QSHE) which says that electon conduction can generate accompanying spin angular momentum transportation because the spin density is directly related to charge density.Time reversal (TR) symmetry is present in TBI systems. The counter-propagating edge states with opposite spins are also TR counterpart of each other. The edge states are believed to be robust against non-magnetic impu-rities for it does not break TR symmetry. The electon in the spin up channel is forbidden to scatter into the spatially overlapping spin down channel in a opposite direction for the process violates TR symmetry. When TBI system is subjected to random disorder potential, we can expect that the edge states will not be easily localized. It is natural to ask how disorder may affect the stability of edge states in2D TBI systems which is the subject of the the-sis. In the computer simulations of2D disordered TBI strip, it is found that edge conducting channel is unaffected under weak disorder. When the disor-der strength increases, a surprising conductance plateau occurs which is due to the topologically protected edge states while the bulk conducting channels are shutted down completely. The unexpected phenomenon is called topo-logical Anderson insulator (TAI) phenomenon and the corresponding phase is called TAI phase.The thesis is divided into three chapters. In the first one, the well known Landauer-Biitticker framework which is used in the calculation of conduc-tance of nano structures is reviewed. The formalism is based on quantum ballistic transport that the inelastic backscattering process is ignored. In chapter two, the elaborate numerical details especially the KNIT algorithm is presented. Tight-binding Hamiltonian is adopted to calculate Green fun-tion through which the transmission funtion in Landau-Buttiker framework can be obtained. In the last chapter, we perform our numerical calculation of a modified Dirac model on a square lattice to generate and discuss the TAI phenomenon.