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Register a new user3D quantum Hall effect of Fermi arcs in topological semimetals
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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.
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Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit 1D higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an $s-d$-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw-Rebbi formulation of QIs and HOFA states. Employing $ab initio$ calculations, we demonstrate HOFAs in both the room- ($alpha$) and intermediate-temperature ($alpha$) phases of Cd$_{3}$As$_2$, KMgBi, and rutile-structure ($beta$-) PtO$_2$.
It is well known that on the surface of Weyl semimetals, Fermi arcs appear as the topologically protected surface states. In this work, we give a semiclassical explanation for the morphology of the surface Fermi arcs. Viewing the surface states as a two-dimensional Fermi gas subject to band bending and Berry curvatures, we show that it is the non-parallelism between the velocity and the momentum that gives rise to the spiraling Fermi arcs. We map out the Fermi arcs from the velocity field for a single Weyl point and a lattice with two Weyl points. We also investigate the surface magnetoplasma of Dirac semimetals in a magnetic field. In this case, the surface states obtains chiral nature from both drift motion and the chiral magnetic effect, resulting in Fermi arcs. We also discuss the important role played by the Imbert-Fedorov shift in the formation of surface Fermi arcs.
The Fermi arcs of topological surface states in the three-dimensional multi-Weyl semimetals on surfaces by a continuum model are investigated systematically. We calculated analytically the energy spectra and wave function for bulk quadratic- and cubic-Weyl semimetal with a single Weyl point. The Fermi arcs of topological surface states in Weyl semimetals with single- and double-pair Weyl points are investigated systematically. The evolution of the Fermi arcs of surface states variating with the boundary parameter is investigated and the topological Lifshitz phase transition of the Fermi arc connection is clearly demonstrated. Besides, the boundary condition for the double parallel flat boundary of Weyl semimetal is deduced with a Lagrangian formalism.
The nonlinear optical responses from topological semimetals are crucial in both understanding the fundamental properties of quantum materials and designing next-generation light-sensors or solar-cells. However, previous work was focusing on the optical effects from bulk states only, disregarding topological surface responses. Here we propose a new (hitherto unknown) surface-only topological photocurrent response from chiral Fermi arcs. Using the ideal topological chiral semimetal RhSi as a representative, we quantitatively compute the topologically robust photocurrents from Fermi arcs on different surfaces. By rigorous crystal symmetry analysis, we demonstrate that Fermi arc photocurrents can be perpendicular to the bulk injection currents regardless of the choice of materials surface. We then generalize this finding to all cubic chiral space groups and predict material candidates. Our theory reveals a powerful notion where common crystalline-symmetry can be used to induce universal topological responses as well as making it possible to completely disentangle bulk and surface topological responses in many conducting material families.
The quantum anomalous Hall (QAH) state is a two-dimensional bulk insulator with a non-zero Chern number in absence of external magnetic fields. Protected gapless chiral edge states enable dissipationless current transport in electronic devices. Doping topological insulators with random magnetic impurities could realize the QAH state, but magnetic order is difficult to establish experimentally in the bulk insulating limit. Here we predict that the single quintuple layer of GdBiTe3 film could be a stoichiometric QAH insulator based on ab-initio calculations, which explicitly demonstrate ferromagnetic order and chiral edge states inside the bulk gap. We further investigate the topological quantum phase transition by tuning the lattice constant and interactions. A simple low-energy effective model is presented to capture the salient physical feature of this topological material.
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