Weyl orbits without an external magnetic field

Valerio Peri, Tena Dubček, Agnes Valenti, Roni Ilan, and Sebastian D. Huber

Phys. Rev. B 101, 235117 – Published 4 June 2020

Abstract

Weyl semimetals in a magnetic field give rise to interesting nonlocal electronic orbits: the ballistic transport through the bulk enabled by the chiral Landau levels is combined with a momentum-space sliding along the surface Fermi-arc driven by the Lorentz force. Bulk chiral Landau levels can also be induced by axial fields whose sign depends on the chirality of the Weyl point. However, the microscopic perturbations that give rise to them can be described in terms of gauge fields only in the low-energy sectors around the Weyl points. In addition, since pseudofields are intrinsic, there is no apparent reason for a Lorentz force that causes sliding along the Fermi arcs. Therefore, the existence of nonlocal orbits driven exclusively by pseudofields is not obvious. Here we show that for systems with at least four Weyl points in the bulk spectrum, nonlocal orbits can be induced by axial fields alone. We discuss the underlying mechanisms by a combination of analytical semiclassical theory, the microscopic numerical study of wave-packet dynamics, and a surface Green's function analysis.

Received 8 April 2020
Accepted 14 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.235117

Physics Subject Headings (PhySH)

Electronic structure Landau levels Transport phenomena

Dirac semimetal Weyl semimetal

Green's function methods Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Valerio Peri ^1,*, Tena Dubček ¹, Agnes Valenti ¹, Roni Ilan ², and Sebastian D. Huber ¹

¹Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
²Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel

^*periv@phys.ethz.ch

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Vol. 101, Iss. 23 — 15 June 2020

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Images

Figure 1
(a) Schematic of a Weyl orbit. Green lines represent real space motion through the bulk, while red ones show the sliding on the Fermi arcs in the surface Brillouin zone. (b) Chiral channels induced in the model of Eq. (1) by the axial field of Sec. 3b. The red dashed lines indicate the Fermi arc connectivity that allows for Weyl orbits. The tuple $(χ, ξ)$ (see main text) entirely characterizes each of the four Weyl points in the system and it is shown for each chiral channel.
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Figure 2
Surface Brillouin zone with Fermi arcs for the model of Eq. (1). The grey dots represent the location of the Weyl points for $b_{y} = b_{z} = π / 2$ . The dashed lines show the analytical prediction of Eq. (27), while the colormap is the effective surface spectral density obtained from a finite slab. Different panels present results for different values of $φ$ : in (a) $φ = 1.5 π$ , in (b) $φ = 1.3 π$ , in (c) $φ = 1.2 π$ , in (d) $φ = π$ .
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Figure 3
In the first row: real space trajectory of a wave packet in the presence of an axial gauge field and different values of $φ$ . In (a) $φ = 1.5 π$ (green), in (b) $φ = 1.4 π$ (yellow), and in (c) $φ = 1.2 π$ (red). Weyl orbits can be clearly seen in (a) and (b). In the second row the trajectories of the kinetic momentum components $p_{y}$ and $p_{z}$ during the wave-packet evolution. The values of $φ$ are the same as in the first row. The black dashed lines show the analytical form of the Fermi arcs as given by Eq. (27).
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Figure 4
Evolution of wave packets in a finite sample $L_{x} = 70$ , $L_{y} = 30$ and $L_{z} = 110$ with axial field $B_{5} = π / 60$ and different values of $φ$ . The first column has $φ = 1.5 π$ , the second one $φ = 1.4 π$ and for the rightmost $φ = 1.2 π$ . The first rows present the real space motion of the wave-packet center of mass. The second row shows the center-of-mass motion in momentum space. Both the kinetic and canonical $z$ component of momentum are shown. Finally, the third row shows how the energy of the wave packet evolves during the evolution. In particular, we show the expectation value of the unperturbed Hamiltonian as computed from the wave packet and the eigenvalue of a slab Hamiltonian evaluated at the kinetic momentum. The grey areas in the first two columns indicate the regions where the wave packet is mainly localized at the sample's surface.
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Figure 5
Surface spectral function $S (ω_{n}, k_{z})$ integrated over $k_{z}$ as a function of $1 / B_{5}$ for different values of $φ$ . In (a) $φ = 1.5 π$ , in (b) $φ = 1.4 π$ and in (c) $φ = 1.2 π$ . The slab is characterized by $L_{x} = 11$ , $L_{y} = 50$ , $τ = 2$ , and $ε_{0} = 0$ . The field values vary between $π / 250$ and $π / 65$ . The discrete energy levels in (a) and (b) arise from the hybridization of surface Fermi arcs and bulk chiral channels confirming the presence of Weyl orbits. In (a) the black dashed line indicates the prediction of the Bohr-Sommerfeld energy quantization of Eq. (42) with $λ = 0.5$ and no free parameters.
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