Comment on “Ideal strength and phonon instability in single-layer ${\mathbf{MoS}}_2$”

Li's paper [Phys. Rev. B 85, 235407 (2012)] presents density functional theory (DFT) results of stress as a function of different strain states. The work of Cooper et al. [Phys. Rev. B 87, 035423 (2013)] performs the same DFT calculations as part of an investigation into the nonlinear elastic properties of ${\mathrm{MoS}}_2$. Some of the DFT results of Li are substantially different from our recently published paper, Cooper et al. [Phys. Rev. B 87, 035423 (2013)]. Although both papers agree on states of equibiaxial stress, there is substantial disagreement on states of uniaxial tensile stress. In this Comment we show that our DFT computations are properly executed and consistent across three different DFT codes, including the one used by Li.

Figure 1

(a) is the biaxial stress state calculated with vasp, quantum espresso, and abinit. (b) and (c) are the uniaxial stress states in the $x_1$ and $x_2$ directions, respectively, calculated with the same three DFT codes. The results of Li's [1] uniaxial stress DFT calculations—indicated by red $\circ$'s—are shown for comparison. There is a qualitative and quantitative agreement between the calculations of Li [1] and the calculations of Cooper et al. [2] for a biaxial strain state in (a), but there is qualitative disagreement in the $x_1$ and $x_2$ directions as seen in (b) and (c). (d) shows the calculated sulfur height as a function of strain for the three DFT codes for the uniaxial stress in the $x_1$ and $x_2$ directions in the upper and lower axes, respectively.