High-order harmonic generation from zigzag graphene nanoribbons

Jiaqi Wu; Yinghui Zheng; Zhinan Zeng; Ruxin Li

doi:10.3788/COL202018.103201

Journals >Chinese Optics Letters >Volume 18 >Issue 10 >Page 103201 > Article

Chinese Optics Letters
Vol. 18, Issue 10, 103201 (2020)

High-order harmonic generation from zigzag graphene nanoribbons

Jiaqi Wu^1、2, Yinghui Zheng^2、*, Zhinan Zeng^2、**, and Ruxin Li^1、2

Author Affiliations

¹School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China

²State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

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DOI: 10.3788/COL202018.103201 Cite this Article Set citation alerts

Jiaqi Wu, Yinghui Zheng, Zhinan Zeng, Ruxin Li. High-order harmonic generation from zigzag graphene nanoribbons[J]. Chinese Optics Letters, 2020, 18(10): 103201 Copy Citation Text

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Abstract

High-order harmonic generation originated from zigzag graphene nanoribbons (ZGNRs) induced by intense laser pulses is investigated theoretically. During the interaction between the intense mid-infrared laser and the ZGNR, we find that localized edge states mainly contribute to the generation of the low-order harmonics, while cutoff harmonics result from the other confined states. Our result shows that the edge-state effect of ZGNR with narrow width can enhance the conversion efficiency of low-order harmonics, rather than the higher-order harmonics extended to the cutoff region.

Keywords

edge state graphene nanoribbons high-order harmonic generation

i ℏ \frac{\partial}{\partial t} | ψ_{k} (x, t) 〉 = [H_{0} + \frac{e}{m_{0}} A (t) p_{x}] | ψ_{k} (x, t) 〉,

(1)

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| ψ_{k} (x, t) 〉 = \sum_{n = 1}^{N_{\max}} α_{k}^{n} (t) | φ_{k}^{n} (x) 〉,

(2)

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i ℏ \frac{\partial α_{k}^{q} (t)}{\partial t} = E_{k}^{q} α_{k}^{q} (t) + \frac{e}{m_{0}} A (t) \sum_{l = 1}^{N_{\max}} p_{k}^{ql} α_{k}^{l} (t),

(3)

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j_{k} (t) = - \frac{e}{m_{0}} \frac{1}{Ω} \int_{Ω} d x {Re [ψ_{k}^{*} (x, t) p_{x} ψ_{k} (x, t)] + e A (t) {| ψ_{k} (x, t) |}^{2}},

(4)

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j_{k} (t) = - \frac{e}{m_{0}} {Re {\sum_{q, l} {[α_{k}^{q} (t)]}^{*} α_{k}^{l} (t) p_{k}^{ql}} + e A (t)},

(5)

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S (q ω) = {| J (q ω) |}^{2} .

(6)

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H_{0} | φ_{k}^{n} (x) 〉 = E_{k}^{n} | φ_{k}^{n} (x) 〉 .

(7)

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H_{0} = (\begin{matrix} 0 & 2 \cos (\frac{k a}{2}) & 0 & 0 & 0 & \dots \\ 2 \cos (\frac{k a}{2}) & 0 & 1 & 0 & 0 & \dots \\ 0 & 1 & 0 & 2 \cos (\frac{k a}{2}) & 0 & \dots \\ 0 & 0 & 2 \cos (\frac{k a}{2}) & 0 & 1 & \dots \\ 0 & 0 & 0 & 1 & 0 & \dots \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \end{matrix}) .

(8)

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Jiaqi Wu, Yinghui Zheng, Zhinan Zeng, Ruxin Li. High-order harmonic generation from zigzag graphene nanoribbons[J]. Chinese Optics Letters, 2020, 18(10): 103201

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