The surface of a Weyl semimetal famously hosts an exotic topological metal that contains open Fermi arcs rather than closed Fermi surfaces. In this work, we show that the surface is also endowed with a feature normally associated with strongly interacting systems, namely, Luttinger arcs, defined as zeros of the electron Green's function. The Luttinger arcs connect surface projections of Weyl nodes of opposite chirality and form closed loops with the Fermi arcs when the Weyl nodes are undoped. Upon doping, the ends of the Fermi and Luttinger arcs separate and the intervening regions get filled by surface projections of bulk Fermi surfaces. Remarkably, unlike Luttinger contours in strongly interacting systems, the precise shape of the Luttinger arcs can be determined experimentally by removing a surface layer. We use this principle to sketch the Luttinger arcs for Co and Sn terminations in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. The area enclosed by the Fermi and Luttinger arcs approximately equals the surface particle density in weakly coupled systems while the correction is governed by the interlayer couplings and the perimeter of the Fermi-Luttinger loop.

中文翻译：

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Weyl 半金属中的表面 Luttinger 弧

众所周知，外尔半金属的表面含有一种奇异的拓扑金属，它包含开放的费米弧而不是封闭的费米面。在这项工作中，我们表明表面还具有通常与强相互作用系统相关的特征，即 Luttinger 弧，定义为电子格林函数的零点。Luttinger弧连接相反手性的Weyl节点的表面投影，并在Weyl节点未掺杂时与Fermi弧形成闭环。掺杂后，费米弧和路廷格弧的末端分开，中间区域被体费米表面的表面投影填充。值得注意的是，与强相互作用系统中的 Luttinger 轮廓不同，Luttinger 弧的精确形状可以通过去除表面层通过实验确定。${\mathrm{公司}}_3{锡}_2{\mathrm{小号}}_2$. Fermi 和 Luttinger 弧所包围的面积大约等于弱耦合系统中的表面粒子密度，而校正由层间耦合和 Fermi-Luttinger 环的周长控制。