论文标题
石墨烯平均场模型的狄拉克锥
Dirac cones for a mean-field model of graphene
论文作者
论文摘要
在本文中，我们表明，在解离状态和在非分离假设下，降低的哈特里 - 石墨烯理论在第一个布里群区域的顶点提出了迪拉克点，而费米水平正是圆锥的巧合。为此，我们首先考虑将军schrödinger运算符$ h =-Δ+v_l $在$ l^2（\ mathbb {r}^2）上作用，其潜在的$ v_l $，该$假定与某些带有长度尺度$ l $的lattice相对于某些lattice是周期性的。根据一些涵盖Hartree-fock理论的定期假设，我们表明，在限制$ l \ to \ infty $中，紧密结合模型为$ h_l $的低洼频谱频段赋予了领先订单。对于石墨烯的六边形晶格，后者在布里渊区的顶点呈现奇异性。另外，Bloch带的形状是使Fermi水平恰好在锥体上。
In this article, we show that, in the dissociation regime and under a non-degeneracy assumption, the reduced Hartree-Fock theory of graphene presents Dirac points at the vertices of the first Brillouin zone and that the Fermi level is exactly at the coincidence point of the cones. For this purpose, we first consider a general Schrödinger operator $H=-Δ+V_L$ acting on $L^2(\mathbb{R}^2)$ with a potential $V_L$ which is assumed to be periodic with respect to some lattice with length scale $L$. Under some assumptions which covers periodic reduced Hartree-Fock theory, we show that, in the limit $L\to\infty$, the low-lying spectral bands of $H_L$ are given to leading order by the tight-binding model. For the hexagonal lattice of graphene, the latter presents singularities at the vertices of the Brillouin zone. In addition, the shape of the Bloch bands is so that the Fermi level is exactly on the cones.
