Quantum Transport in Two-dimensional Topological Systems PDF Download

Author: Jianxiao Zhang
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Languages : en
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Book Description
The discovery of topological states of matters has sparked intense interests amongresearchers in the past decade. Topologically non-trivial band structure in thesequantum states can give rise to a variety of topological phenomena, the experimentaldemonstration of which can have a huge impact on our understandingof fundamental states of matter. Transport measurement is one of the majorexperimental techniques to probe these topological phenomena. This dissertationis devoted to theoretical and numerical studies of quantum transport phenomenain a variety of topological materials, including magnetic topological insulator films,the quantum anomalous Hall insulator/superconductor hetero-structures, the kinkstates in bilayer graphene and the photonic crystal of topological mirror insulatorphase in the optical regime. The numerical simulations of transport phenomenaand the analytical understanding of the underlying physical mechanism in thisdissertation will provide guidance for the future transport measurements.The numerical methods to simulate quantum transport in this dissertation arebased on Landauer-Bttiker formalism and Greens function method, which willbe introduced in Chapter 2. The transmission through certain sample regionscan be extracted from the Greens function method and serves as the input forthe Landauer-Bttiker formalism to compute conductance tensor that is directlymeasured in transport experiments. Physical understanding of the transportmechanism can be provided by analyzing different components of the transmissionmatrix, in combination with other analytical methods for transport phenomena.Defects and impurities can be incorporated in numerical simulations by includingrandom potentials into the model Hamiltonian, and thus this method can be appliedin different transport regimes, from ballistic to diffusive transport.Chapter 3 to 5 of the dissertation is to apply the above numerical methodsto three different topological mesoscopic systems: magnetic topological insulator(MTI) films, quantum anomalous Hall insulator (QAHI) - superconductor (SC)junctions, and bilayer graphene devices.Chapter 3 is dedicated to the study of quantum transport through magnetictextures in a thin film of MTI. We focus on both the longitudinal and Hall transports,which reveal complicated features due to the coexistence of strong spin-orbit couplingfrom TI materials and magnetic non-colinearity from magnetic textures in thissystem. The manifested Hall transport can be induced by different topologicalmechanisms, including the intrinsic anomalous Hall effect from strong SOC and thetopological Hall effect (or known as geometric Hall effect) from magnetic textures.Thus, this system provides a nice platform to understand the interplay betweenspin-orbit coupling and real-space magnetic texture, as well as disorder scatterings.Our numerical simulations have shown different roles of spin-orbit coupling in theclean and disordered limits for this system. In the clean limit when SOC strengthis increased, the topological Hall conductance (THC) almost remains constant butthe topological Hall resistance (THR) can increase by an order of magnitude dueto the reduction of longitudinal conductance, caused by SOC-induced spin flips.However, in the disordered limit, both the THC and THR increase with increasingSOC, while longitudinal conductance is not influenced much by SOC.In Chapter 4, we study the transport of chiral edge channels in a QAHI/superconductorjunction. This type of hetero-junction has been recently fabricated andmeasured in experiments, in pursue of topological superconductivity and Majoranafermions. We focus on the disorder effect in the weak superconductor proximitylimit. Our results show that the quantized valued of conductance remains robustfor a single chiral edge channel even in the presence of disorder in the zero-biaslimit. However, such quantization is broken down for a finite bias, or for multiplechiral edge modes, or for the coexistence of a single chiral edge mode with othertrivial metallic modes, when disorders are present. Our theory provides guidanceto understand transport phenomena in these systems for future experiments.Chapter 5 is a simulation of transport behaviors through the so-called kinkstates in a bilayer graphene device under external electric and magnetic fields. Thedevice, known as a valley valve and electron beam splitter, has been fabricatedby our experimental collaborators and its unusual transport properties have beenmeasured experimentally. Our numerical simulations provide a justification of theguiding center physical picture for topological transport through this device.Chapter 6 goes beyond electronic systems and concerns topological phase inphotonic systems. We utilize a method of dynamic evolution of states to studya topological crystalline insulator phase in a photonic system. The crystallineprotection, achieved by the fine manufacturing of emulated atoms in a photoniclattice, selectively pumps incident states with a certain parity while reflects theother.The studies in the dissertation are in close collaboration with experimentalgroups, including Prof. Moses Chans and Prof. Cui-zu Changs group for the transportmeasurements in MTI films and QAHI/SC junctions, Prof. Jun Zhus groupfor the experiments on the bilayer graphene device, and Prof. Mikael Rechtsmansgroup for the photonic topological systems.