Nonlocal Transport In A Hybrid Two-dimensional Topological Insulator

A topological insulator is a special quantum matter, which is one of the attractive areas incondensed matter physics in recent years. Both the topological insulator and ordinary insulatorbelong to the insulator, which have the bulk band gap. But, different from ordinary insulator,topological insulator has the gapless metal edge state protected by topological structure.According to the chern number, the topological insulator is divided into two categories: one is thequantum hall system which has a set of chern numbers. This system is also divided into thequantum anomalous hall system with the unique chern number and the quantum hall system withnon-unique chern number. Generally speaking, the topological insulators in this category are notprotected by time-reveral symmetry; The other is the quantum spin hall systems with two sets ofchern numbers, which is protected by time-reveral symmetry. This thesis will study nonlocaltransport characters of the quantum spin hall system in the presence of impurity scattering.For thequantum devices, the completely spin polarized edge states are important. So the examine on thetopological insulator of quantum spin hall system, especially the transport characters is beneficialfor the quantum devices in the future. In the real quantum devices, the impurity is inevitable. So itis needful to study the impurity scattering in the topological insulators. Based on a four-bandtight-binding model and aid by the Keldysh nonequilibrium Green’s function, this thesis study thespecial H-shape topological insulator system. This H-shaped structure can distinguish whether thesystem has completely spin polarized edge state. In this thesis, two types of impurities areconsidered: two types of impurity: the static impurities and non-static impurities. It is found thatthe quantum spin hall edge state is robust against the static impurities and non-static impuritieswith spin conservation. When the spin scattering happen, the quantum spin hall edge state is easilybroken and the quantized nonlocal resistance won’t be hold.In chapter one, the basic conceptions closely relevant to the mesoscopic system andtopological insulator are introduced. In chapter two, the transport theory of the nonequilibriumGreen’s function is derived in detail. The chapter three and four is key point of the whole paper,studying that how the static impurities and non-static impurities impact the nonlocal resistance.The last is a conclusion.