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arXiv 1607.02155cond-mat.mes-hallhep-th
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强电场下石墨烯及类似纳米结构的辐射过程

Radiative Processes in Graphene and Similar Nanostructures at Strong Electric Fields

S. P. Gavrilov, D. M. Gitman

摘要:

石墨烯单层和类似纳米结构中的低能单电子动力学由狄拉克模型描述,狄拉克模型是无质量QED的2+1维版本,其中光速被费米速度v_{F} =c/300代替。强场QFT的方法与狄拉克模型相关,因为任何低频电场都需要对无质量载流子进行非微扰处理,以防它在足够长的时间间隔内保持不变。在这种情况下,通过缓慢变化且小梯度的电场从真空产生的电子-空穴对的产生和湮灭的效应是相关的,从而基本上影响辐射图案。由于这个原因,标准的量子电动力学教科书中的光子发射理论是没有帮助的。我们构造了Dirac模型的Fock空间表示,它精确地考虑了由外部电场引起的真空不稳定性的影响,并在其中微扰地考虑了电子和光子之间的相互作用,遵循一般理论(广义Furry表示)。我们考虑光子发射的有效理论在一级近似下,并考虑到幺正关系,构建相应的总概率。

英文摘要:

Low-energy single-electron dynamics in graphene monolayers and similar nanostructures is described by the Dirac model, being a 2+1 dimensional version of massless QED with the speed of light replaced by the Fermi velocity v_{F}=c/300. Methods of strong-field QFT are relevant for the Dirac model, since any low-frequency electric field requires a nonperturbative treatment of massless carriers in case it remains unchanged for a sufficiently long time interval. In this case, the effects of creation and annihilation of electron-hole pairs produced from vacuum by a slowly varying and small-gradient electric field are relevant, thereby substantially affecting the radiation pattern. For this reason, the standard QED text-book theory of photon emission cannot be of help. We construct the Fock-space representation of the Dirac model, which takes exact accounts of the effects of vacuum instability caused by external electric fields, and in which the interaction between electrons and photons is taken into account perturbatively, following the general theory (the generalized Furry representation). We consider the effective theory of photon emission in the first-order approximation and construct the corresponding total probabilities, taking into account the unitarity relation.

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