Quantum Transport in two-dimensional topological systems
Open Access
- Author:
- Zhang, Jianxiao
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- April 25, 2019
- Committee Members:
- Chaoxing Liu, Dissertation Advisor/Co-Advisor
Chaoxing Liu, Committee Chair/Co-Chair
Jainendra Jain, Committee Member
Moses H. W. Chan, Committee Member
Zi-Kui Liu, Outside Member - Keywords:
- Quantum transport
topological system
topological superconductor
Quantum anomalous Hall
Green's function - Abstract:
- The discovery of topological states of matters has sparked intense interests among researchers in the past decade. Topologically non-trivial band structure in these quantum states can give rise to a variety of topological phenomena, the experimental demonstration of which can have a huge impact on our understanding of fundamental states of matter. Transport measurement is one of the major experimental techniques to probe these topological phenomena. This dissertation is devoted to theoretical and numerical studies of quantum transport phenomena in a variety of topological materials, including magnetic topological insulator films, the quantum anomalous Hall insulator/superconductor hetero-structures, the kink states in bilayer graphene and the photonic crystal of topological mirror insulator phase in the optical regime. The numerical simulations of transport phenomena and the analytical understanding of the underlying physical mechanism in this dissertation will provide guidance for the future transport measurements. The numerical methods to simulate quantum transport in this dissertation are based on Landauer-Büttiker formalism and Green’s function method, which will be introduced in Chapter 2. The transmission through certain sample regions can be extracted from the Green’s function method and serves as the input for the Landauer-Büttiker formalism to compute conductance tensor that is directly measured in transport experiments. Physical understanding of the transport mechanism can be provided by analyzing different components of the transmission matrix, in combination with other analytical methods for transport phenomena. Defects and impurities can be incorporated in numerical simulations by including random potentials into the model Hamiltonian, and thus this method can be applied in different transport regimes, from ballistic to diffusive transport. Chapter 3 to 5 of the dissertation is to apply the above numerical methods to 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 magnetic textures 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 coupling from TI materials and magnetic non-colinearity from magnetic textures in this system. The manifested Hall transport can be induced by different topological mechanisms, including the intrinsic anomalous Hall effect from strong SOC and the topological Hall effect (or known as geometric Hall effect) from magnetic textures. Thus, this system provides a nice platform to understand the interplay between spin-orbit coupling and real-space magnetic texture, as well as disorder scatterings. Our numerical simulations have shown different roles of spin-orbit coupling in the clean and disordered limits for this system. In the clean limit when SOC strength is increased, the topological Hall conductance (THC) almost remains constant but the topological Hall resistance (THR) can increase by an order of magnitude due to the reduction of longitudinal conductance, caused by SOC-induced spin flips. However, in the disordered limit, both the THC and THR increase with increasing SOC, while longitudinal conductance is not influenced much by SOC. In Chapter 4, we study the transport of chiral edge channels in a QAHI/superconductor junction. This type of hetero-junction has been recently fabricated and measured in experiments, in pursue of topological superconductivity and Majorana fermions. We focus on the disorder effect in the weak superconductor proximity limit. Our results show that the quantized valued of conductance remains robust for a single chiral edge channel even in the presence of disorder in the zero-bias limit. However, such quantization is broken down for a finite bias, or for multiple chiral edge modes, or for the coexistence of a single chiral edge mode with other trivial metallic modes, when disorders are present. Our theory provides guidance to understand transport phenomena in these systems for future experiments. Chapter 5 is a simulation of transport behaviors through the so-called kink states in a bilayer graphene device under external electric and magnetic fields. The device, known as a valley valve and electron beam splitter, has been fabricated by our experimental collaborators and its unusual transport properties have been measured experimentally. Our numerical simulations provide a justification of the guiding center physical picture for topological transport through this device. Chapter 6 goes beyond electronic systems and concerns topological phase in photonic systems. We utilize a method of dynamic evolution of states to study a topological crystalline insulator phase in a photonic system. The crystalline protection, achieved by the fine manufacturing of emulated atoms in a photonic lattice, selectively pumps incident states with a certain parity while reflects the other. The studies in the dissertation are in close collaboration with experimental groups, including Prof. Moses Chan’s and Prof. Cui-zu Chang’s group for the transport measurements in MTI films and QAHI/SC junctions, Prof. Jun Zhu’s group for the experiments on the bilayer graphene device, and Prof. Mikael Rechtsman’s group for the photonic topological systems.