Erratum: Spin susceptibility of two-dimensional transition-metal dichalcogenides [Phys. Rev. B 90, 045412 (2014)]

Figure 1

Spin response of hole-doped monolayer ${\mathrm{MoS}}_2$. Panel (a) [(b)] shows ${\chi }_{zz}\left(q\right)$ [${\chi }_{xx}\left(q\right)$] obtained for a hole sheet density $n=1\times {10}^{12}\mathrm{cm}{}^{-2}$ (blue solid curve), $n=1\times {10}^{13}\mathrm{cm}{}^{-2}$ (red dashed curve), and $n=3\times {10}^{13}\mathrm{cm}{}^{-2}$ (black dot-dashed curve). Noteworthy features are the strong in-plane/out-of-plane anisotropy of the spin response, the deviations from ideal two-dimensional (2D) electron-gas behavior even for ${\chi }_{zz}\left(q\right)$, which are getting more pronounced as the density increases, and the nonanalyticity exhibited by ${\chi }_{zz}\left(q\right)$ [${\chi }_{xx}\left(q\right)$] for $q=2k_{\text{F}}\equiv 2k_{\text{F}}^{(+)}$ [$q=k_1>2k_{\text{F}}^{(+)}$].

Figure 2

Spin-response functions in real space. To highlight deviations from the ordinary 2D electron-gas behavior, we plot the quantities $A_j{\left(k_{\text{F}}R\right)}^2{\chi }_{jj}\left(R\right)$ in (a) [(b)] obtained for a hole density $n=1\times {10}^{12}\mathrm{cm}{}^{-2}$ ($n=3\times {10}^{13}\mathrm{cm}{}^{-2}$). The red dashed (blue solid) curve shows ${\chi }_{xx}$ (${\chi }_{zz}$). The decrease of the oscillation amplitude for ${\left(k_{\text{F}}R\right)}^2{\chi }_{xx}\left(R\right)$ shows that the in-plane spin response decays faster than the $R^{-2}$ power law expected for ordinary 2D electron systems. The scale factors are $A_x=50$ [5] and $A_z=1$ [1] in (a) [(b)], and ${\tilde{\chi }}_0={\chi }_0{k}_{\text{F}}^2/\left(2\pi \right)\equiv 2n{k}_0^2/\left(\pi E_0\right)$.