标题： 基于第一性原理的锗掺杂石墨烯带隙工程、谷量子霍尔效应和非线性光学响应的量子见解，用于潜在的光电子应用 显示英文标题

标题： First-principles Quantum Insights into Bandgap Engineering, Valley Quantum Hall Effect, and Nonlinear Optical Response of Ge-Doped Graphene for Potential Optoelectronic Applications

摘要： 材料能带结构中的谷具有了越来越多的关注。 谷自由度的有前景应用包括下一代谷电子器件、量子信息处理、量子计算和光电器件。 由于石墨烯具有高载流子迁移率和方便的带隙工程特性，因此它是一种理想的高速谷电子应用量子材料。 本研究采用基于第一性原理的密度泛函理论方法，选择通过锗掺杂来打开带隙并增强单层石墨烯中的谷选择性作为带隙工程策略。 研究了2%、3.125%、5.5% 和 12.5% 的锗掺杂浓度对谷电子学的影响；谷霍尔效应、谷传输和光学性质。 报告的结果表明，通过改变锗的掺杂浓度可以有效地调节带隙、谷极化和倍频产生。 Berry曲率分布对于相应的K和K'谷是对称的，从而导致谷相关传输特性和潜在的谷霍尔效应。 最后，二阶极化率表现出对应的光学吸收峰，表明由于破缺的空间反演对称性而产生了有效的二倍频。 这些发现突显了锗掺杂石墨烯在非线性光学和谷电子学应用方面的潜力，同时提供了对其拓扑相和输运性质的新见解。 显示英文摘要

摘要： The valley in the band structure of materials has gained a lot of attention recently. The promising applications of the valley degree of freedom include the next-generation valleytronic devices, quantum information processing, quantum computing, and optoelectronic devices. Graphene is an ideal quantum material for high-speed valleytronic applications because of its high carrier mobility and convenience of bandgap engineering. Employing first-principles density functional theoretical approach, this study opted bandgap engineering strategy via Germanium doping to open bandgap and enhance valley selectivity in graphene monolayers. The impact of Ge dopant concentration of 2%, 3.125%, 5.5%, and 12.5% is explored on the valleytronic; valley Hall effect, valley transport, and optical properties. The reported results demonstrate that bandgap, valley polarization, and second harmonic generation can be tuned effectively by varying doping concentration of Germanium. The Berry curvature profile is antisymmetric for corresponding K and K' valleys, thus leading to valley-dependent transport properties and a potential valley Hall effect. Finally, the second-order susceptibilities exhibit corresponding optical absorption peaks, indicating efficient second-harmonic generation due to the broken inversion symmetry. These findings highlight the potential of Ge-doped graphene for nonlinear optics and valleytronics applications, while providing novel insights into its topological phase and transport properties.