固态波纹石墨烯的电子性质、海森堡原理和虫洞几何
Electronic properties of corrugated graphene, the Heisenberg principle and wormhole geometry in solid state
摘要：
对石墨烯的载流子采用纯二维相对论方程与海森堡不确定原理相矛盾，因为它需要将三维波函数的离面坐标设置为零。在这里，我们提出了一个理论框架，用于描述石墨烯的无质量相对论载流子根据这个最基本的所有量子原理。一个逐渐限制的过程是用来限制到一个表面上的动态和正常的表面部分，并在这个过程中嵌入到三维世界的表面占。结果，在表面部分中产生不变的几何势，其与平均曲率成线性比例，并使材料的费米能与弯曲成比例地移动。电子性质的应变诱导改性或“应变电子学”显然是石墨烯研究的一个重要领域。这为生产电子器件，MEMS和NEMS开辟了一个场所，其中电子特性通过几何方法控制，并且不需要石墨烯的额外改变。这种几何势的出现也为我们提供了一些线索，让我们知道在广义相对论的弯曲时空中，量子动力学是什么样子的。在这种情况下，我们探讨了一个二维截面的虫洞几何实现与石墨烯作为固态思想实验。
英文摘要：
Adopting a purely two dimensional relativistic equation for graphene's carriers contradicts the Heisenberg uncertainty principle since it requires setting off-the-surface coordinate of a three-dimensional wavefunction to zero. Here we present a theoretical framework for describing graphene's massless relativistic carriers in accordance with this most fundamental of all quantum principles. A gradual confining procedure is used to restrict the dynamics onto a surface and normal to the surface parts and in the process the embedding of this surface into the three dimensional world is accounted for. As a result an invariant geometric potential arises in the surface part which scales linearly with the Mean curvature and shifts the Fermi energy of the material proportional to bending. Strain induced modification of the electronic properties or "straintronics" is clearly an important field of study in graphene. This opens a venue to producing electronic devices, MEMS and NEMS where the electronic properties are controlled by geometric means and no additional alteration of graphene is necessary. The appearance of this geometric potential also provides us with clues as to how quantum dynamics looks like in the curved space-time of general relativity. In this context, we explore a two-dimensional cross-section of the wormhole geometry realized with graphene as a solid state thought experiment.
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