There are few phenomena in condensed matter physics
that are defined only by the fundamental constants and do not depend on
material parameters. Examples are the resistivity quantum, h/e2(h is Planck's constant and e the electron charge), that appears
in a variety of transport experiments and the magnetic flux quantum, h/e,
playing an important role in the physics of superconductivity. By and large,
sophisticated facilities and special measurement conditions are required to
observe any of these phenomena. We show that the opacity of suspended graphene
is defined solely by the fine structure constant, α=e2/ℏc≈1/137
(where c is the speed of light), the parameter that describes coupling between
light and relativistic electrons and that is traditionally associated with
quantum electrodynamics rather than materials science. Despite being only one
atom thick, graphene is found to absorb a significant (πα = 2.3%) fraction of incident white light, a
consequence of graphene's unique electronic structure.凝聚态物理中很少有现象只由基本常数定义，不依赖于材料参数。例如电阻率量子h/e2（h是Planck常数，e是电子电荷），它出现在各种输运实验中，磁通量量子h/e在超导物理学中起着重要作用。总的来说，观察这些现象需要复杂的设备和特殊的测量条件。来自University of Manchester的A. K. Geim教授表明，悬浮石墨烯的不透明度仅由精细结构常数α=e2/ℏc≈1/137（其中c是光速）定义，该参数描述了光和相对论电子之间的耦合，传统上与量子电动力学而不是材料科学相关联。尽管只有一个原子厚，石墨烯被发现吸收入射白光的重要部分（πα = 2.3%），这是石墨烯独特电子结构的结果。相关内容于2008年以Fine Structure Constant Defines Visual Transparency of Graphene为题发表在Science (IF=56.9)上。最近（2008年）有人认为，石墨烯中Dirac费米子的高频（动态）电导率G应该是一个等于e2/4ħ的通用常数，并不同于其通用直流电导率4e2/πh （然而，实验并不符合直流电导率的预测）。通用G意味着石墨烯的透射率T和反射率R等可观测量也是通用的，对于法向光入射，由T ≡ (1 + 2πG/c)–2 =
(1 + ½πα)–2和R ≡ ¼π2α2T 给出。特别是，这产生了石墨烯的不透明度(1 – T) ≈ πα（这个表达式也可以通过用Fermi黄金法则计算二维Dirac费米子对光的吸收来导出）。由基本常数定义的光学性质的起源在于石墨烯的二维性质和无隙电子光谱，而不直接涉及其电荷载流子的手性。作者研究了特别制备的石墨烯晶体，使得它们覆盖了金属支架中的亚毫米孔（图1A插图）。这种适用于光学研究的单原子厚的大膜以前是无法获得的。图1A显示了他们的一个样品在透射白光下的图像。在这种情况下，他们选择显示一个仅被悬浮石墨烯部分覆盖的光圈，以便可以比较不同区域的不透明度。图像上的线扫描定性地说明了观察到的光强度的变化。进一步的测量产生石墨烯的不透明度为2.3 ± 0.1%，反射率可忽略不计（< 0.1%），而光谱学显示不透明度实际上与波长λ无关（图1B）。发现不透明度随着膜厚度的增加而增加，使得每个石墨烯层再增加2.3%（图1B插图）。他们的测量还产生了可见频率范围内的通用动态电导率G = (1.01 ± 0.04) e2/4ħ，即理想Dirac费米子的预期行为。![]()
Fig. 1. Looking through one-atom-thick crystals. (A)
Photograph of a 50-μm aperture partially covered by graphene and its bilayer.
The line scan profile shows the intensity of transmitted white light along the
yellow line. (Inset) Our sample design: A 20-μm-thick metal support structure
has several apertures of 20, 30, and 50 μm in diameter with graphene
crystallites placed over them. (B) Transmittance spectrum of
single-layer graphene (open circles). Slightly lower transmittance for λ <
500 nm is probably due to hydrocarbon contamination. The red line is the
transmittance T = (1 + 0.5πα)–2 expected for
two-dimensional Dirac fermions, whereas the green curve takes into account a
nonlinearity and triangular warping of graphene's electronic spectrum. The gray
area indicates the standard error for our measurements. (Inset) Transmittance
of white light as a function of the number of graphene layers (squares). The
dashed lines correspond to an intensity reduction by πα with each added layer.
图1. 透过一个原子厚的晶体观察。（A）部分被石墨烯及其双层覆盖的50 μm孔径的照片。线扫描轮廓显示了沿黄线透射白光的强度。（插图）他们的样品设计：一个20 μm厚的金属支撑结构有几个直径为20、30和50 μm的孔，上面放置有石墨烯微晶。（B）单层石墨烯的透射光谱（空心圆）。λ < 500 nm的透射率稍低可能是由于碳氢化合物污染。红线是二维双费米子预期的透射率T = (1 + 0.5πα)–2，而绿色曲线考虑了石墨烯电子光谱的非线性和三角形扭曲。灰色区域表示他们测量的标准误差。（插图）白光透射率与石墨烯层数（正方形）的关系。虚线对应于每增加一层强度降低πα。
实验和理论之间的一致性是惊人的，因为人们认为普遍性只适用于低能量（E < 1 eV），超过低能量，石墨烯的电子光谱变得强烈扭曲和非线性，Dirac费米子的近似被打破。然而，他们的计算表明，即使对于可见光，有限E校正也惊人地小（几%）。由于这些修正，α的计量精度将很难达到，但值得注意的是，精细结构常数可以直接用肉眼实际评估。单飞狮
feishishan2022@foxmail.com
