Doping and gap size dependence of high-harmonic generation in graphene: Importance of consistent formulation of light-matter coupling
Doping and gap size dependence of high-harmonic generation in graphene: Importance of consistent formulation of light-matter coupling
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DOI：
10.1103/physrevb.106.035204
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发表时间：
2022-05
影响因子：
3.7
通讯作者：
Y. Murakami;M. Schüler
中科院分区：
文献类型：
--
作者：
Y. Murakami;M. Schüler
固体中的高次谐波产生（HHG）是一种基本的非线性现象，它可以通过改变诸如掺杂水平和温度等系统参数来有效控制。为了正确预测HHG对这些参数的依赖性，对光与物质耦合进行一致的理论表述至关重要。最近，人们指出了在基于半导体布洛赫方程的HHG分析中经常缺失的对电流的贡献[J. 威廉，等人，《物理评论B》103卷，125419（2021）]。在本文中，通过系统地分析带隙石墨烯中HHG对掺杂和带隙大小的依赖性，我们讨论了这些项的实际影响。特别是，我们关注电流$J_{\rm ra}^{(2)}$的作用，它源于通过带间跃迁引起的带内偶极子的变化。当带隙较小且系统接近半填充时，带内和带间电流大多相互抵消，从而抑制了HHG信号——当忽略$J_{\rm ra}^{(2)}$时，这一重要特性就会被破坏。此外，如果没有$J_{\rm ra}^{(2)}$，HHG对掺杂和带隙大小的依赖性在性质上就会与完整评估结果不同。我们的结果表明，对于小带隙系统，电流的一致表达式对于研究HHG对参数的依赖性非常重要。
High-harmonic generation (HHG) in solids is a fundamental nonlinear phenomenon, which can be efficiently controlled by modifying system parameters such as doping-level and temperature. In order to correctly predict the dependence of HHG on these parameters, consistent theoretical formulation of the light-matter coupling is crucial. Recently, contributions to the current that are often missing in the HHG analysis based on the semiconductor Bloch equations have been pointed out [J. Wilhelm, et.al. PRB 103 125419 (2021)]. In this paper, by systematically analyzing the doping and gap-size dependence of HHG in gapped graphene, we discuss the practical impact of such terms. In particular, we focus on the role of the current $J_{\rm ra}^{(2)}$, which originates from the change of the intraband dipole via interband transition. When the gap is small and the system is close to half filling, intraband and interband currents mostly cancel, thus suppressing the HHG signal - an important property that is broken when neglecting $J_{\rm ra}^{(2)}$. Furthermore, without $J_{\rm ra}^{(2)}$, the doping and gap-size dependence of HHG becomes qualitatively different from the full evaluation. Our results demonstrate the importance of the consistent expression of the current to study the parameter dependence of HHG for the small gap systems.