平面波-光子福克腔QED-DFT：手性腔诱导石墨烯中的拓扑性质

中文摘要 AI 辅助

我们发展了一种显式的平面波（PW）×光子福克方法，用于处理周期体系第一性原理计算中的量子化速度规范Pauli-Fierz哈密顿量：由于量子化矢量势在空间上是均匀的，光-物质耦合简化为晶体动量K→K+Â/c的算符值平移，现有普通固态DFT的平面波机制几乎无需修改即可复用。这种PW×Fock构造使周期固体的第一性原理腔QED与已为分子发展的福克空间耦合簇和组态相互作用方法处于同等地位，从而将迄今难以触及的体系——特别是线性或手性腔中的材料——开放给第一性原理平面波计算。我们以单层石墨烯在线性和手性腔中的情况为例说明该方法，获得了偏振选择性的Haldane能隙以及相应的态密度、实空间和圆二色性光学特征。完整的布里渊区贝里曲率计算直接证实了手性腔能隙的拓扑性质：占据流形携带量子化的陈数，其通过非单调序列C=1→3→-1→1→2→-1→1步进，并带有两个狭窄的符号反转窗口——这是扩展的真空修饰物质的一种性质，在有限分子体系中没有对应物。

英文摘要

We develop an explicit plane-wave (PW) $\times$ photon-Fock approach to the quantized, velocity-gauge Pauli--Fierz Hamiltonian for periodic, first-principles calculations: because the quantized vector potential is spatially uniform, the light--matter coupling reduces to an operator-valued shift of the crystal momentum, $K\to K+\hat{\mathbf A}/c$, and the existing plane-wave machinery of ordinary solid-state DFT is reused essentially unchanged. This PW$\times$Fock construction puts first-principles cavity QED of periodic solids on the same footing as the Fock-space coupled-cluster and configuration-interaction methods already developed for molecules, opening hitherto inaccessible systems---materials in a linear or chiral cavity, in particular---to first-principles plane-wave calculations. We illustrate the method with monolayer graphene in linear and chiral cavities, obtaining a polarization-selective Haldane gap together with the corresponding density-of-states, real-space, and circular-dichroism optical signatures. A full Brillouin-zone Berry-curvature calculation confirms the topological character of the chiral-cavity gap directly: the occupied manifold carries a quantized Chern number that steps through a non-monotonic sequence, $C=1\to3\to{-1}\to1\to2\to{-1}\to1$, with two narrow, sign-reversed windows---a property of extended, vacuum-dressed matter with no counterpart in a finite molecular system.

发表机构

• Department of Physics and Astronomy, Vanderbilt University（范德堡大学物理与天文学系）

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