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Register a new userThe Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
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The chiral hinge modes are the key feature of a second order topological insulator in three dimensions. Here we propose a quadrupole index in combination of a slab Chern number in the bulk to characterize the flowing pattern of chiral hinge modes along the hinges at the intersection of the surfaces of a sample. We further utilize the topological field theory to demonstrate the correspondent connection of the chiral hinge modes to the quadrupole index and the slab Chern number, and present a picture of three-dimensional quantum anomalous Hall effect as a consequence of chiral hinge modes. The two bulk topological invariants can be measured in electric transport and magneto-optical experiments. In this way we establish the bulk-hinge correspondence in a three-dimensional second order topological insulator.
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The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner states gather at corners in the two-dimensional first-order and second-order topological insulators, respectively. Here, we report two kinds of topological states hosting anomalous bulk-boundary correspondence in the extended two-dimensional dimerized lattice with staggered flux threading. At 1/2-filling, we observe isolated corner states with no fractional charge as well as metallic near-edge states in the C = 2 Chern insulator states. At 1/4-filling, we find a C = 0 topologically nontrivial state, where the robust edge states are well localized along edges but bypass corners. These robust topological insulating states significantly differ from both conventional Chern insulators and usual high-order topological insulators.
We show that a thin film of a three-dimensional topological insulator (3DTI) with an exchange field is a realization of the famous Haldane model for quantum Hall effect (QHE) without Landau levels. The exchange field plays the role of staggered fluxes on the honeycomb lattice, and the hybridization gap of the surface states is equivalent to alternating on-site energies on the AB sublattices. A peculiar phase diagram for the QHE is predicted in 3DTI thin films under an applied magnetic field, which is quite different from that either in traditional QHE systems or in graphene.
The Hall effect, the anomalous Hall effect and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The quant
An intriguing observation on the quantum anomalous Hall effect (QAHE) in magnetic topological insulators (MTIs) is the dissipative edge states, where quantized Hall resistance is accompanied by nonzero longitudinal resistance. We numerically investigate this dissipative behavior of QAHE in MTIs with a three-dimensional tight-binding model and non-equilibrium Greens function formalism. It is found that, in clean samples, the geometric mismatch between the detecting electrodes and the MTI sample leads to additional scattering in the central Hall bar, which is similar to the effect of splitting gates in the traditional Hall effect. As a result, while the Hall resistance remains quantized, the longitudinal resistance deviates from zero due to such additional scattering. It is also shown that external magnetic fields as well as disorder scattering can suppress the dissipation of the longitudinal resistance. These results are in good agreement with previous experimental observations and provide insight on the fabrication of QAHE devices.
Even at the lowest accessible temperatures, measurements of the quantum anomalous Hall (QAH) effect have indicated the presence of parasitic dissipative conduction channels. There is no consensus whether parasitic conduction is related to processes in the bulk or along the edges. Here, we approach this problem by comparing transport measurements of Hall bar and Corbino geometry devices fabricated from Cr-doped (BiSb)$_2$Te$_3$. We identify bulk conduction as the dominant source of dissipation at all values of temperature and in-plane electric field. Furthermore, we observe identical breakdown phenomenology in both geometries, indicating that breakdown of the QAH phase is a bulk process. The methodology developed in this study could be used to identify dissipative conduction mechanisms in new QAH materials, ultimately guiding material development towards realization of the QAH effect at higher temperatures.
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