标题： 掺杂WTe$_2$单层中的激子和磁性相：Hartree-Fock方法 显示英文标题

标题： Excitonic and magnetic phases in doped WTe$_2$ monolayers: a Hartree-Fock approach

摘要： 输运和局域光谱测量表明，单层二碲化钨（$1T'$-WTe$_2$）在中性条件下除了表现出量子自旋霍尔效应和激子隙外，在低电子浓度下还成为超导体。 为了研究电子掺杂下不同破缺对称相之间的竞争，我们进行了广泛的Hartree-Fock计算，这些计算以电子密度和库仑相互作用强度为变量。 在电荷中性点处，我们在中间相互作用强度下重现了自旋密度波和围绕量子自旋霍尔绝缘体的自旋螺旋态的出现。 对于更强的相互作用，自旋螺旋态被一个破缺空间反演和时间反演对称性的状态所破坏（但它们的乘积不变），随后系统变成平凡带隙绝缘体。 通过电子掺杂，由于导带的Stoner型不稳定性，量子自旋霍尔绝缘体演化为易平面铁磁体。 这个相位在能量上与自旋螺旋态竞争。 我们讨论了我们的结果如何有助于解释过去的和未来的测量。 显示英文摘要

摘要： Transport and local spectroscopy measurements have revealed that monolayers of tungsten ditelluride ($1T'$-WTe$_2$) display a quantum spin Hall effect and an excitonic gap at neutrality, besides becoming superconducting at low electron concentrations. With the aim of studying the competition among different broken-symmetry phases upon electron doping, we have performed extensive Hartree-Fock calculations as a function of electron density and Coulomb interaction strength. At charge neutrality, we reproduce the emergence of a spin density wave and a spin spiral state surrounding a quantum spin Hall insulator at intermediate interaction strengths. For stronger interactions, the spin spiral is disrupted by a state breaking both inversion and time-reversal symmetries (but not their product) before the system becomes a trivial band insulator. With electron doping the quantum spin Hall insulator evolves into an easy-plane ferromagnet due to a Stoner-like instability of the conduction band. This phase competes energetically with the spin spiral state. We discuss how our results may help to interpret past and future measurements.