Anderson Localization In Three-dimensional Quantum Hall Systems

The discovery of the quantum Hall effect(QHE)has given topology a central role in condensed-matter physics.The QHE in two-dimensional(2D)electron systems originates from discrete Landau levels forming under a strong perpendicular magnetic field.While the phys-ical picture underlying QHE seems specific to 2D,the generalizations of the QHE to three-dimensional(3D)systems have also been considered.The distinct feature of a 2D quantum Hall system is its chiral edge states,which are topologically protected by the quantum Hall gap and robust against disorder.In the 3D case,the chiral edge state of each layer is coupled to neighboring edge states,forming a 2D chiral surface state.Experimentally,the 3D QHE was first realized in an engineered multilayer quantum well system.In real materials,signatures of the 3D QHE have been found in several anisotropic layered materials,such as Bechgaard salts,?-Mo4O11,n-doped Bi2Se3,EuMnBi2,and most recently,ZrTe5 and BaMnSb2.These mate-rials offer us great opportunities to study the 3D QHE and its novel surface states.This thesis introduces three work on the 3D QHE that I completed during my Ph.D.:(1)Effect of bulk disorder on 3D quantum Hall systems,(2)Effect of surface disorder on the chiral surface states of a 3D quantum Hall system,(3)3D quantum Hall effect induced by charge density waves(CDW):surface,hinge and edge states.(1)We investigate the effect of bulk disorder on 3D quantum Hall systems.Using nu-merical Thouless conductance calculations,we investigate the longitudinal conductance of a disordered 3D quantum Hall system within a tight-binding lattice model.For the bulk,we con-firm that the mobility edges are independent of the propagating directions in this anisotropic system.As disorder increases,the conductance peak of the lowest subband in the horizontal direction floats to the central subband as in the 2D case,while there is no clear evidence of floating in the vertical direction.Inside the quantum Hall gap,we study the novel 2D chiral surface states at the sidewalls of the sample.We demonstrate the crossover of the surface states between the quasi-one-dimensional(1D)metal and insulator regimes,which can be achieved by modifying the interlayer hopping strength and the disorder strength in the model.Finally,in or-der to predict the regime of the surface states for arbitrary parameters,we determine an explicit relationship between the localization length of surface states and the microscopic parameters of the model.(2)We investigate the effect of surface disorder on the chiral surface states of a 3D quan-tum Hall system.Utilizing a transfer-matrix method,we find that the localization length of the surface state along the magnetic field decreases with the surface disorder strength in the weak disorder regime,but increases anomalously in the strong disorder regime.In the strong disor-der regime,the surface states mainly locate at the first inward layer to avoid the strong disorder in the outmost layer.The anomalous increase of the localization length can be explained by an effective model,which maps the strong disorder on the surface layer to the weak disorder on the first inward layer.We also investigate the effect of surface disorder on the full distri-bution of conductances P(g)of the surface states in the quasi-1D regime for various surface disorder strengths.In particular,we find that P(g)is Gaussian in the quasi-1D metal regime and log-normal in the quasi-1D insulator regime.In the crossover regime,P(g)exhibits highly nontrivial forms,whose shapes coincide with the results obtained from the Dorokhov-Mello-Pereyra-Kumar equation of a weakly disordered quasi-1D wire in the absence of time-reversal symmetry.(3)We investigate various topological states in a 3D quantum Hall system induced by CDW,including the 2D chiral surface states,the 1D chiral hinge states,and the top and bottom edge states.These rich topological states are originated from the interplay between the CDW and the magnetic field.Under open boundary conditions,a 1D CDW system hosts topologi-cally protected edge states at both ends.In a 3D quantum Hall system,the CDW in the vertical direction interplays with the bulk states of the system to produce the top and bottom edge states;it interplays with the 2D chiral surface states to produce the 1D chiral hinge states.Observing these topological states experimentally can help to clarify the current controversial mechanisms behind the 3D QHE in ZrTe5.