Abstract

We study the effect of strain on the band engineering in gapped graphene subject to external sources. By applying the Floquet theory, we determine the effective Hamiltonian of electron dressed by a linearly, circularly, and an elliptically polarized dressing field in the presence of strain along armchair and zigzag directions. Our results show that the energy spectrum exhibits different symmetries, and for the strainless case, it takes an isotropic and anisotropic forms whatever the values of irradiation intensity, whereas it is linear as in the case of pristine graphene. It increases slowly when strain is applied along the armchair direction but rapidly for the zigzag case. Moreover, it is found that the renormalized band gap changes along different strain magnitudes and does not change for the polarization phase \(\theta \) compared to linear and circular polarizations where its values change oppositely.

Graphic Abstract

(color online) The energy spectrum \(\varepsilon \) of electron dressed by the linearly polarized field versus the wave vector component \(k_x\) for \({\Delta _{g}}=2\) meV, \(\hbar \omega =10\) meV with three values of the irradiation intensities \(I=0.0\) (blue and magenta lines), \(I=13.3\) \(\hbox {kW/cm}^{2}\) (green and orange lines), \(I=26.7\) \(\hbox {kW/cm}^{2}\) (red and black lines). (a): Effect of armchair strain direction with \(S=0.7\). (b): Effect of zigzag strain direction with \(S=0.15\).

中文翻译：

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应变对带隙石墨烯中能带工程的影响

摘要

我们研究了应变对带隙石墨烯中能带工程的影响。通过应用Floquet理论，我们确定了在存在沿扶手椅和之字形方向的应变的情况下，通过线性，圆形和椭圆极化的修整场修整的电子的有效哈密顿量。我们的结果表明，能谱表现出不同的对称性，对于无应变的情况，无论辐射强度的值如何，它都具有各向同性和各向异性形式，而与原始石墨烯一样，它是线性的。沿扶手椅方向施加应力时，它缓慢增加，但之字形盒则迅速增加。而且，发现重新归一化的带隙沿着不同的应变幅度变化，并且对于极化相位不变化。\（\ theta \）与线性和圆极化的值相反地变化。

图形摘要

（在线彩色）由线性极化场修饰的电子的能谱\（\ varepsilon \）与波矢量分量\（k_x \）的\（{\ Delta _ {g}} = 2 \）  meV，\（ \ hbar \ omega = 10 \） meV，具有三个照射强度值\（I = 0.0 \）（蓝色和品红色线），\（I = 13.3 \） \（\ hbox {kW / cm} ^ {2} \）（绿色和橙色线），\（I = 26.7 \） \（\ hbox {kW / cm} ^ {2} \）（红色和黑色线）。（a）：扶手椅应变方向对\（S = 0.7 \）的影响。（b）：之字形应变方向对\（S = 0.15 \）的影响。