Shear-strain controlled high-harmonic generation in graphene

Letter

Shear-strain controlled high-harmonic generation in graphene

Tomohiro Tamaya, Hidefumi Akiyama, and Takeo Kato

Phys. Rev. B 107, L081405 – Published 28 February 2023

Abstract

We propose a method for controlling the high-harmonic generation (HHG) with a high dynamic range in single-layer graphene. We find that, by utilizing shear strain, a significant enhancement or quenching of HHG is possible over a range of several orders of magnitude. This feature is made possible by the resonance mechanism at a van Hove singularity. Therein, the shear strain controls the configurations of the two Dirac cones, resulting in changes in the energy and dipole moment at the saddle point of the band dispersion. Our findings provide a way for modulating or switching light by using a nano-optomechanical device composed of single-layer graphene.

Received 3 January 2023
Revised 9 February 2023
Accepted 13 February 2023

DOI:https://doi.org/10.1103/PhysRevB.107.L081405

Physics Subject Headings (PhySH)

High-order harmonic generation Nonlinear optics Optoelectronics Strain van Hove singularity

Graphene

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tomohiro Tamaya ^1,2,*, Hidefumi Akiyama ¹, and Takeo Kato ¹

¹Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
²JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan

^*tamaya@g.ecc.u-tokyo.ac.jp

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Issue

Vol. 107, Iss. 8 — 15 February 2023

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Images

Figure 1
(a) Schematic figure of lattice structure of graphene under shear strain. The amplitude of the shear strain is represented by $ζ$ and the vector potential of the incident light is denoted as $A (t)$ , whose tilt angle measured from the armchair axis is described by $θ$ (see the inset). (b1)–(b3) Variation in band structures of graphene for the three shear-strain parameters: (b1) $ζ = 0$ , (b2) $ζ = 0.12$ , and (b3) $ζ = 0.2$ . The white arrows in (b2) indicate the direction of the change in position of the Dirac points induced by the strain.
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Figure 2
(a1) and (b1) Shear-strain dependence of the third- and fifth-order harmonics for $ω_{0} = 90 THz$ . The red and green lines indicate the high-harmonic intensities for the incident-light angles $θ = 120^{\circ}$ and $θ = 30^{\circ}$ , respectively. The polarization angle dependences of the third and fifth harmonics for $ζ = 0.12$ are shown in the insets. The critical strength of the shear strain for a band gap to form is described by $ζ_{c}$ . (a2) and (b2) Shear-strain dependence of the third- and fifth-order harmonics for the different incident-light frequencies, 30 THz (blue lines), 60 THz (orange lines), 90 THz (red lines), and 120 THz (green lines). The dotted black arrows indicate the variation in the double peaks.
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Figure 3
Contour plots of distribution of carrier density in $k$ space after photoirradiation. The incident-light polarization angle is (a) $θ = 30^{\circ}$ and (b) $θ = 120^{\circ}$ . The shear-strain parameter and incident-light frequency are $ζ = 0.12$ and $ω_{0} = 90 THz$ .
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Figure 4
(a) Absorption coefficients of graphene for $ζ = 0.12$ . The green, blue, and red lines show those for different incident-light polarization angles $θ = 30^{\circ}$ , $θ = 95^{\circ}$ , and $θ = 120^{\circ}$ , respectively. Each peak corresponds to different $vHSs$ , induced by the saddle points at $k_{α}$ , $k_{β}$ , and $k_{γ}$ shown in (b). (b) Contour plot of the energy band in graphene for $ζ = 0.12$ . Here, $k_{α}$ , $k_{β}$ , and $k_{γ}$ indicate the positions of the saddle points in $k$ space, each of which induces ${vHS}_{α}$ , ${vHS}_{β}$ , and ${vHS}_{γ}$ , respectively. The azimuth angle toward the band minima (the Dirac cones) measured from the saddle points are indicated by the white lines. (c) DOS of graphene for the different shear-strain parameters, $ζ = 0$ (black dotted line), $ζ = 0.12$ (blue line), and $ζ = 0.2$ (green dashed line). The red lines indicate that $vHS$ shifts with increasing shear strain. (d) Absorption coefficients of graphene as a function of the shear-strain parameter $ζ$ . The red and blue lines indicate those for the incident-light polarization angles $θ = 120^{\circ}$ and $θ = 30^{\circ}$ . The insets show the resonant mechanisms corresponding to the double peaks of the red line (blue square and yellow triangles). (e) Schematic figure of photon absorption near ${vHS}_{α}$ for different incident-light polarization angles $θ = 30^{\circ}$ (upper figure) and $θ = 120^{\circ}$ (lower figure). (f) Energy differences at ${vHS}_{α}$ ( $E_{s}$ ) and the band-gap energy $E_{g}$ as a function of shear strain. The blue square and yellow triangle indicate the resonant points marked in Fig. 4.
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