非门控石墨烯中电子空穴池的共形对称性
Conformal symmetry of electron-hole puddles in ungated graphene
摘要：
本文在E-F理论的基础上，考虑了电荷中性点处的单层石墨烯，将非均匀外电势和电子-电子相互作用同等对待。我们提出了关于基态电荷密度的概率测度的一些一般考虑。该系统显示出自相似性的程度。通过对基态载流子密度分布的分析，我们发现，虽然它不是高斯分布，但临界指数符合Kondev超标度关系。利用Schramm-Loewner（SLE）演化方法，我们证明了非门控石墨烯具有共形不变性，其随机零电荷密度轮廓为$_κ$与$κ=1.8\pm 0.2$ .
英文摘要：
In this paper the mono-layer graphene at the charge neutrality point is considered whithin Thomas-Fermi-Dirac theory, treating inhomogeneous external potentials and electron-electron interactions on equal footing. We present some general considerations concerning the probability measure of the ground state charge density. The system shows degrees of self-similarity. By analyzing the ground state carrier density profile, we show that although it is not Gaussian, the critical exponents are consistent with Kondev hyper-scaling relations. Using Schramm-Loewner (SLE) evolution we show that the ungated graphene has conformal invariance and the random zero-charge density contours are SLE$_κ$ with $κ=1.8\pm 0.2$.
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