Transport Properties Of The Topological Anderson Insulators

Two dimensional topological insulator, also known as quantum spin hall insulator, was conceptually formulated and predicted in 2005-2006, and was experimentally measured in HgTe/CdTe quantum well in 2007. This is the cornerstone of the development of topological insulator area, which forms the new page of modern condensed matter physics.In the past ten years, there has been great achievements in the topological insulator area. One branch among them is that the disorder effect upon electronic structure was restudied and people found that disorder can play an important role in the topological property of systems. People found that in the topologically trivial system, disorder can induce an Anderson phase transition, result in a topologically nontrivial state. In the so called topological Anderson insulator, the bulk states are Anderson localized yet there is topologically protected edge states.In addition to the disorder,The transport properties of topological Anderson insularors also under the influence of other parameters of the system such as the size of system,Fermi energy,quality parameters,etc.We study the size effect on the transport properties in metal-insulator phase transition.Our work expands the scope of previous investigations which found that quantized conductance which appeared at some disorder strength would disappear with the decrease of the size of system.Based on the HgTe/CdTe quantum well of the 2D topological insulator material,Using recursive nonequilibrium green’s function method to calculate the transport properties of tetragonal model.Comparing the transport properties of the system under different sizes,We find that with the decreasing of size of system,the region of quantized conductance is no longer continuous,but a few separation region. With the increasing of size,separate regions of the quantized conductance is preferentially into a region.The limit of size could make the band different from topologically nontrivial insulator.Further study find that the width of gap of the small size system is greater than 2|M| theoretically. With the increasing of system size,the gap will gradually become the theoretical value.Accroding to this conclusion We can explain the previous work mentioned before:The quantized conductance is not really disappear but its position has been change as the gap become larger. We make a reasonable explanation of phenomena that in different areas of the phase diagram. We also show some interesting changes such as the original small Anderson quantized conductance region will become larger with the increasing of size.In addition we discussed the influence of the relevance,found that under the influence of relevance the topology quality parameters will become positive renormalization and the stability of the system will be reduced.