Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance
Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance
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DOI：
10.1103/physrevb.90.165414
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发表时间：
2014-10-14
影响因子：
3.7
通讯作者：
Nishida, Yusuke
中科院分区：
文献类型：
--
作者：
Nishida, Yusuke
我们研究了超临界库仑势中的无质量狄拉克费米子，重点是它的低能物理是普适的，并且每个超临界角动量通道都可以用一个量来参数化。这个低能量参数的尺寸的长度被定义为只有乘法因子，因此每个超临界通道表现出离散的尺度不变性。特别是，我们表明，诱导真空极化有一个幂律尾，其系数是对数周期函数的总和相对于从潜在的中心的距离。这个系数也可以用所谓的原子坍缩共振的能量和宽度来表示。我们对真空极化及其与原子坍缩共振的关系的普遍预测揭示了量子电动力学长期存在的基本问题，原则上可以通过带电杂质的石墨烯实验进行测试。
We study massless Dirac fermions in a supercritical Coulomb potential with the emphasis on that its low-energy physics is universal and parametrized by a single quantity per supercritical angular momentum channel. This low-energy parameter with the dimension of length is defined only up to multiplicative factors and thus each supercritical channel exhibits the discrete scale invariance. In particular, we show that the induced vacuum polarization has a power-law tail whose coefficient is a sum of log-periodic functions with respect to the distance from the potential center. This coefficient can also be expressed in terms of the energy and width of so-called atomic collapse resonances. Our universal predictions on the vacuum polarization and its relationship to atomic collapse resonances shed light on the longstanding fundamental problem of quantum electrodynamics and can in principle be tested by graphene experiments with charged impurities.