Photon-assisted Fano resonance tunneling periodic double-well potential characteristics
doi: 10.37188/CO.2020-0068
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摘要: 周期双阱势的光学性质是激光物理和量子光学的前沿研究领域之一。该文研究了具有时间周期双阱势的石墨烯系统中光子辅助狄拉克电子的Fano型共振隧穿。利用双量子阱结构，电子通过两量子阱之间的薄势垒的共振隧穿将导致束缚态能级的分裂，Fano型共振谱将分裂为两个不对称共振峰。通过改变相位、频率和振幅来调制Fano峰的形状，可以用来调制Dirac在石墨烯中的电子输运性质。数值分析表明，两个振荡场的相对相位可以调节非对称Fano型共振峰的形状。当相对相位从0增加到
${\text{π}}$ 时，共振峰谷从峰的一侧移到另一侧；在临界相位${{3{\text{π}} }/{11}}$ 处，不对称共振峰变得对称。此外，还可以通过改变振荡场的频率和振幅以及静态势阱的结构来调制Fano峰的分布。这些有趣的物理性质可以用来调节石墨烯中Dirac的电子输运性质。Abstract: Optical properties of periodic double-well potential are one of the frontier research fields in laser physics and quantum optics. In this work, we have employed time-periodic double-well potential for the investigation of Fano-type resonant tunneling of photon-assisted Dirac electrons in a graphene system. Using a double quantum well structure, it is found that the resonant tunneling of electrons in a thin barrier between the two quantum wells splits the bound state energy levels, and the Fano-type resonance spectrum splits into two asymmetric resonance peaks. The shape of Fano peak is regulated by changing the phase, frequency, and amplitude, that can directly modulate the electronic transport properties of Dirac in graphene. Our numerical analysis shows that the relative phase of two oscillating fields can adjust the shape of the asymmetric Fano type resonance peak. When the relative phase increases from 0 to${\text{π}}$ , the resonance peak valley moves from one side of the peak to the other. In addition, the asymmetric resonance peak becomes symmetric at critical phase${{3{\text{π}} }/{11}}$ . Furthermore, the distribution of Fano peaks can be modulated by varying the frequency and amplitude of oscillating field and the structure of the static potential well. Finally, we suggest that these interesting physical properties can be used for the modulation of Dirac electron transport properties in graphene.-
Key words:
- physical optics /
- resonant tunneling /
- photon-assisted tunneling /
- dirac electrons /
- quantum optics
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Figure 1. Sketch model of Dirac electron transport through a double-well potential and two applied oscillating fields.
${V_0}$ is the depth of the static well;$d$ is the width of wells,$a$ is the thickness of barrier. V1 cos (ωt + α) and V1 cos (ωt + β) are the applied oscillating fields
Figure 2. Fano-type resonance in conductance
$G$ for$\alpha = \beta = 0$ ,$a = 40\;{\rm{ nm}}$ ，${k_y} = 0.006\;{\rm{ n}}{{\rm{m}}^{ - 1}}$ . (a) ћ$\omega = 11\;{\rm{ meV}}$ ,${V_0} = - 50\;{\rm{ meV}}$ ，$d = 200\;{\rm{ nm}}$ ; (b)${V_1} = 1.0\;{\rm{ meV}}$ ,${V_0} = - 50\;{\rm{ meV}}$ ，$d = 200\;{\rm{ nm}}$ ; (c) ћ$ \omega = 11\;{\rm{ meV}}$ ，${V_1} = 1.0\;{\rm{ meV}}$ ,$d = 200\;{\rm{ nm}}$ ; (d)${V_1} = 1.0\;{\rm{ meV}}$ ，ћ$ \omega = 11\;{\rm{ meV}}$ ，${V_0} = - 50\;{\rm{ meV}}$ .
Figure 3. Conductance G as a function of E for different separation distance between two quantum wells at
$\alpha = \beta = 0$ ,${k_y} = 0.006\;{\rm{ n}}{{\rm{m}}^{ - 1}}$ , ћ$ \omega = 11\;{\rm{ meV}}$ ,${V_1} = 1.0\;{\rm{ meV}}$ ,${V_0} = - 50\;{\rm{ meV}}$ and$d = 200\;{\rm{ nm}}$ .
Figure 4. Variation of Fano-type resonance line-shape in conductance
$G$ with$\beta $ at$\alpha = 0$ ,$a = 40\;{\rm{ nm}}$ ,${k_y} = $ $ 0.006\;{\rm{ n}}{{\rm{m}}^{ - 1}}$ , ћ$ \omega = 11\;{\rm{ meV}}$ ,${V_1} = 1.0\;{\rm{ meV}}$ ,${V_0} = - 50\;{\rm{ meV}}$ and$d = 200\;{\rm{ nm}}$ . (a)$\,\beta$ =0; (b)$\,\beta=\dfrac{3\pi}{11}$ ; (c)$\,\beta= \dfrac{5\pi}{11}$ ; (d)$\,\beta=\pi $ . -
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