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Gravitational Waves and Helicity in Undoped Graphene
Annalen Der Physik ( IF 2.2 ) Pub Date : 2020-06-04 , DOI: 10.1002/andp.202000122 Francesco Sorge 1
Annalen Der Physik ( IF 2.2 ) Pub Date : 2020-06-04 , DOI: 10.1002/andp.202000122 Francesco Sorge 1
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The behavior of a monolayer undoped graphene sheet in presence of a weak gravitational wave is discussed. In the low‐energy limit, the linear dispersion of the energy levels near the Dirac points can be ascribed to massless excitations obeying a Dirac equation in a 2+1D spacetime. Starting from a 2+1 dimensional (2+1D) Lagrangian, the equations of motion for the electron (hole) wavefunction in the graphene sheet are deduced and solved. The Bogolubov coefficients are then obtained and the gravitationally induced amplitude of the electron–hole pair excitations is evaluated. The typical quadrupolar distribution of the pair creation probability appears rotated by a angle in the plane of the graphene sheet, when compared to the case of a confined 2+1D massless scalar field in the same gravitational background. Such behavior can be understood taking into account the role of helicity in graphene during the interaction with the gravitational wave. Although very small, the effect offers an interesting example of interaction at nanoscale between a non‐trivial quantum system and a time‐dependent gravitational background. The strong analogy between the quantum theoretical description of the graphene physics and the standard quantum field theory can also suggest a similar analysis in different physical contexts.
中文翻译：
未掺杂石墨烯中的引力波和螺旋度
讨论了单层未掺杂石墨烯片在弱重力波存在下的行为。在低能量极限中，狄拉克点附近的能级线性分布可以归因于无质量激发，遵循2 + 1D时空中的狄拉克方程。从2 + 1维（2 + 1D）拉格朗日开始，推导并求解了石墨烯片中电子（空穴）波函数的运动方程。然后获得Bogolubov系数，并评估引力引起的电子-空穴对激发的振幅。对创建概率的典型四极分布似乎旋转了与相同引力背景下2 + 1D无质量标量有限磁场的情况相比，石墨烯片平面中的夹角较小。考虑到石墨烯中螺旋度在与重力波相互作用期间的作用，可以理解这种行为。尽管影响很小，但它提供了一个有趣的例子，说明了非平凡的量子系统与时间相关的引力背景之间的纳米级相互作用。石墨烯物理学的量子理论描述与标准量子场论之间的强烈类比也可以建议在不同的物理环境中进行类似的分析。
更新日期：2020-06-04
中文翻译：
未掺杂石墨烯中的引力波和螺旋度
讨论了单层未掺杂石墨烯片在弱重力波存在下的行为。在低能量极限中，狄拉克点附近的能级线性分布可以归因于无质量激发，遵循2 + 1D时空中的狄拉克方程。从2 + 1维（2 + 1D）拉格朗日开始，推导并求解了石墨烯片中电子（空穴）波函数的运动方程。然后获得Bogolubov系数，并评估引力引起的电子-空穴对激发的振幅。对创建概率的典型四极分布似乎旋转了与相同引力背景下2 + 1D无质量标量有限磁场的情况相比，石墨烯片平面中的夹角较小。考虑到石墨烯中螺旋度在与重力波相互作用期间的作用，可以理解这种行为。尽管影响很小，但它提供了一个有趣的例子，说明了非平凡的量子系统与时间相关的引力背景之间的纳米级相互作用。石墨烯物理学的量子理论描述与标准量子场论之间的强烈类比也可以建议在不同的物理环境中进行类似的分析。
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