Large nonreciprocal absorption and emission of radiation in type-I Weyl semimetals with time reversal symmetry breaking

Yoichiro Tsurimaki, Xin Qian, Simo Pajovic, Fei Han, Mingda Li, and Gang Chen

Phys. Rev. B 101, 165426 – Published 24 April 2020

Abstract

The equality between the spectral directional emittance and absorptance of an object under local thermodynamic equilibrium is known as Kirchhoff's law of radiation. The breakdown of Kirchhoff's law of radiation is physically allowed by breaking time reversal symmetry and can open opportunities for nonreciprocal light emitters and absorbers. Large anomalous Hall conductivity and angle recently observed in topological Weyl semimetals, particularly type-I magnetic Weyl semimetals and type-II Weyl semimetals, are expected to create large nonreciprocal electromagnetic wave propagation. In this work, we focus on type-I magnetic Weyl semimetals and show via modeling and simulation that nonreciprocal surface plasmon polaritons can result in pronounced nonreciprocity without an external magnetic field. The modeling in this work begins with a single pair of Weyl nodes, followed by a more realistic model with multiple paired Weyl nodes. Fermi-arc surface states are also taken into account through the surface conductivity. This work points to the promising applicability of topological Weyl semimetals for magneto-optical and energy applications.

Received 29 December 2019
Revised 25 March 2020
Accepted 26 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.165426

Physics Subject Headings (PhySH)

Surface plasmon polariton Topological materials

Weyl semimetal

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yoichiro Tsurimaki ^1,*, Xin Qian ^1,*, Simo Pajovic¹, Fei Han², Mingda Li², and Gang Chen^1,†

¹Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*These authors contributed equally to this work.
^†gchen2@mit.edu

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Vol. 101, Iss. 16 — 15 April 2020

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Images

Figure 1
(a) A black hemispherical enclosure and a small nonblack surface in thermodynamic equilibrium. Positions of two surface elements $d A_{i}$ and $d A_{j}$ are shown in the spherical coordinate. (b) Paths of radiative heat exchange between a nonblack element and two black elements: (1) direct radiative heat exchange between black surfaces (black lines), (2) radiation emitted from $d A_{i}$ and reflected by nonblack element toward $d A_{j}$ (blue line), and (3) radiation emitted from nonblack element to $d A_{j}$ (green line). Radiation emitted from $d A_{j}$ to $d A$ is partially absorbed and reflected toward $d A_{i}$ (red line).
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Figure 2
(a) Electronic band structure of the effective Hamiltonian on the surface of $k_{z}$ = 0, and (b) at the projection to the $k_{y} = k_{z} = 0$ plane. The occupied electron states are illustrated in the solid blue region. (c), (e) Real and (d), (f) imaginary parts of local dielectric tensor and surface optical conductivity of the magnetic Weyl semimetal modeled by the effective Hamiltonian for $E_{F} = 60 meV$ . The Fermi velocity, the Weyl node separation, and the dissipative loss are $v_{F} = 1.0 \times 10^{5} m / s$ and $2 b = 0.45 Å$ , and $γ = 1.5 meV$ , respectively.
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Figure 3
Optical grating structure made of a low-loss dielectric with $ɛ_{d} = 10 + i 0.01$ on top of a semi-infinite magnetic Weyl semimetal with its Weyl node separation 2b in the $k_{x}$ direction. The period, width, height, and thickness of the gratings are $Λ$ , $w$ , $h$ , and $t$ , respectively. The light is incident at angle $θ$ and p polarized (the magnetic field is along the x direction).
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Figure 4
(a), (c) Dispersion relation of SPPs for the angles of incidence $θ = - 60^{\circ}$ (blue) and $θ = + 60^{\circ}$ (red), respectively. The dispersion of the grating for the diffracting order $m = \pm 1$ (green) as well as that of bulk plasmons (blue region) are shown. With the shared y axis, spectral absorptance of the semi-infinite Weyl semimetal for the incident angle $θ = \pm 60^{\circ}$ is shown. (b), (d) Spectral directional absorptance of the grating structure for the incident angles of $θ = \pm 60^{\circ}$ . All simulations do not include the Fermi-arc surface states. The upper (a), (b) and lower (c), (d) panels are for $E_{F} = 60 meV$ and $E_{F} = 100 meV$ , respectively. The geometrical parameters of the grating structure are (b) $Λ = 20 μ m, w = Λ / 2$ , $h = 1.6 μ m$ , $t = 3 μ m$ ; (d) $Λ = 5.9 μ m, w = Λ / 2$ , $h = 0.95 μ m$ , $t = 1.2 μ m$ .
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Figure 5
Spectral directional absorptance of the grating structure with (solid line) and without (dashed line) the presence of the Fermi-arc states for the incident angles of $θ = \pm 60^{\circ}$ . The Fermi energies are (a) $E_{F} = 60 meV$ and (b) $E_{F} = 100 meV$ , respectively. The structure's geometrical parameters are the same as in Fig. 4.
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Figure 6
Comparison of (a) diagonal and (b) off-diagonal elements of dielectric tensor with and without the consideration of relative orientation of Weyl node pairs for $E_{F} = 60 meV$ . Inset of (a): Bulk Brillouin zone of rhombohedral cell and six Weyl nodes with positive and negative chirality. One of the pair of Weyl nodes is aligned along the $k_{x}$ axis. (c), (d) Spectral absorptance of the grating structure on the Weyl semimetal with three oriented Weyl node pairs with (solid line) and without (dashed line) the presence of the Fermi-arc states for the incident angles of $θ = \pm 60^{\circ}$ . The Fermi energies are (c) 60 meV and (d) 100 meV, respectively. The geometrical parameters of the grating structure are (c) $Λ = 14.2 μ m, w = Λ / 1.5$ , $h = 1.4 μ m$ , $t = 2.85 μ m$ ; (d) $Λ = 5.3 μ m, w = Λ / 2$ , $h = 0.7 μ m$ , $t = 1.0 μ m$ .
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