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Register a new userProposal for engineering 3D quantum Hall effect in an electronic superlattice
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The three-dimensional (3D) quantum Hall effect (3DQHE) was initially proposed to be realized in systems with spontaneous charge-density-wave (CDW) or spin-density-wave (SDW), which has stimulated recent experimental progress in this direction. Here, instead of such intrinsic scenarios, we propose to realize the 3DQHE in a synthetic semiconductor superlattice. The superlattice is engineered along one direction, which is modeled by the Kronig-Penney type periodic potential. By applying a magnetic field along this direction, quantized 3D Hall conductivity can be achieved in certain parameter regimes, along with a vanishing transverse conductivity. We show that such results are robust against the disorder effect and can be hopefully realized by state-of-the-art fabrication techniques. Our work opens a new research avenue for exploring the 3DQHE in electronic superlattice structures.
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A device is proposed that is similar in spirit to the electron turnstile except that it operates within a quantum Hall fluid. In the integer quantum Hall regime, this device pumps an integer number of electrons per cycle. In the fractional regime, it pumps an integer number of fractionally charged quasiparticles per cycle. It is proposed that such a device can make an accurate measurement of the charge of the quantum Hall effect quasiparticles.
The analog of two seminal quantum optics experiments are considered in a condensed matter setting with single electron sources injecting electronic wave packets on edge states coupled through a quantum point contact. When only one electron is injected, the measurement of noise correlations at the output of the quantum point contact corresponds to the Hanbury-Brown and Twiss setup. When two electrons are injected on opposite edges, the equivalent of the Hong-Ou-Mandel collision is achieved, exhibiting a dip as in the coincidence measurements of quantum optics. The Landauer-Buttiker scattering theory is used to first review these phenomena in the integer quantum Hall effect, next, to focus on two more exotic systems: edge states of two dimensional topological insulators, where new physics emerges from time reversal symmetry and three electron collisions can be achieved; and edges states of a hybrid Hall/superconducting device, which allow to perform electron quantum optics experiments with Bogoliubov quasiparticles.
The quantum Hall effect is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a wormhole tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution, giving an example of (d-2)-dimensional boundary states. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall conductivity evolves from the 1/B dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd$_3$As$_2$, or Na$_3$Bi. This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.
We show here a series of energy gaps as in Hofstadters butterfly, which have been shown to exist by Koshino et al [Phys. Rev. Lett. 86, 1062 (2001)] for anisotropic three-dimensional (3D) periodic systems in magnetic fields $Vec{B}$, also arise in the isotropic case unless $Vec{B}$ points in high-symmetry directions. Accompanying integer quantum Hall conductivities $(sigma_{xy}, sigma_{yz}, sigma_{zx})$ can, surprisingly, take values $propto (1,0,0), (0,1,0), (0,0,1)$ even for a fixed direction of $Vec{B}$ unlike in the anisotropic case. We can intuitively explain the high-magnetic field spectra and the 3D QHE in terms of quantum mechanical hopping by introducing a ``duality, which connects the 3D system in a strong $Vec{B}$ with another problem in a weak magnetic field $(propto 1/B)$.
Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically-doped topological insulator completed a quantum Hall trio---quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time reversal symmetry broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as topological insulators and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.
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