Controllable nonreciprocal optical response and handedness-switching in magnetized spin-orbit coupled graphene

Mohammad Alidoust and Klaus Halterman

Phys. Rev. B 105, 045409 – Published 12 January 2022

Abstract

Starting from a low-energy effective Hamiltonian model, we theoretically calculate the dynamical optical conductivity and permittivity tensor of a magnetized graphene layer with Rashba spin-orbit coupling (SOC). Our results reveal a transverse Hall conductivity correlated with nonreciprocal longitudinal conductivity. Further analysis illustrates that for intermediate magnetization strengths, the relative magnitudes of the magnetization and SOC can be identified experimentally by two well-separated peaks in the dynamical optical response (both the longitudinal and transverse components) as a function of photon frequency. Moreover, the frequency-dependent permittivity tensor is obtained for a wide range of chemical potentials and magnetization strengths. Employing experimentally realistic parameter values, we calculate the circular dichroism of a representative device consisting of magnetized spin-orbit coupled graphene and a dielectric insulator layer, backed by a metallic plate. The results reveal that this device has different relative absorptivities for right-handed and left-handed circularly polarized electromagnetic waves. It is found that the magnetized spin-orbit coupled graphene supports strong handedness-switchings, effectively controlled by varying the chemical potential and magnetization strength with respect to the SOC strength.

Received 16 August 2021
Revised 29 November 2021
Accepted 3 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.045409

Physics Subject Headings (PhySH)

Optical conductivity Optoelectronics Spin-orbit coupling

Graphene

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Mohammad Alidoust ¹ and Klaus Halterman ²

¹Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
²Michelson Laboratory, Physics Division, Naval Air Warfare Center, China Lake, California 93555, USA

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Vol. 105, Iss. 4 — 15 January 2022

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Images

Figure 1
The representative setup for revealing handedness-switching predicted in this paper. The graphene layer is deposited on top of an insulator layer with strong SOC and a thickness of $d$ . A perfectly conducting back plate accompanies the system to generate strong reflection of the electromagnetic wave, which is incident upon the graphene side of the structure. The reflected wave is then collected by a detector. We assume that the graphene sheet is located in the $x y$ plane. The small arrows show the orientation of magnetization on the carbon sites. The blue and red regions indicate the $A$ and $B$ sublattices of graphene, respectively. The carrier density and chemical potential can be controlled by a gate voltage, $V$ .
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Figure 2
The components of the optical conductivity as a function of frequency. (a) and (b) are the real part of $σ_{x x} (ω)$ and imaginary part of $σ_{y x} (ω)$ , respectively. The magnetization is oriented along the $z$ axis, i.e., $h = (0, 0, h_{z})$ . The chemical potential is set to zero, $μ = 0$ , and various values of magnetization strength are considered: $h_{z} = 0, 8, 40, 80 meV$ . The strength of the SOC is set to $α = 20 meV$ .
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Figure 3
The band structure of graphene in the presence of SOC and magnetization plotted as a function of the normalized momentum $k Å / π$ . The chemical potential is set to zero, $μ = 0$ , and the strength of the SOC is fixed at $α = 20 meV$ . The magnetization is oriented along the $z$ axis and its magnitude increases (from left to right) with the following values (in meV): (a) $h_{z} = 0$ , (b) $h_{z} = 8$ , (c) $h_{z} = 40$ , and (d) $h_{z} = 80$ .
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Figure 4
Permittivity tensor components for the graphene sheet with finite SOC and magnetization. Both the real and imaginary components are shown for several different chemical potentials $μ$ . The Zeeman field is set to $h_{z} = 20 meV$ . From symmetry considerations, $ε_{x y} (ω) = - ε_{y x} (ω)$ , the other off-diagonal permittivity components can be deduced.
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Figure 5
The circular dichroism $Ψ (ω)$ as a function of frequency. Several out-of-plane Zeeman fields $h_{z}$ are considered (as shown). Through variations in the gate voltage, the reflected EM energy can exhibit dominant right-handed (positive curves) or left-handed (negative curves) behavior.
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Figure 6
The circular dichroism factor $Ψ (ω)$ against the frequency of the incident circularly polarized EM wave. A broad range of magnetizations $h_{z}$ at two different values of chemical potential are considered: $μ = 0, 20 meV$ .
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