In a recent article (Yaqoob et al., 2021), Yaqoob et al. studied the tunable electromagnetic surface wave propagation on the graphene-covered left-handed material (LHM) slab backed by the perfect electric conductor (PEC). They derived the dispersion relations for both transverse electric (TE) and transverse magnetic (TM)-polarized surface waves, and then used the relations for two types of LHMs according to the spectral range, i.e., GHz- and THz-LHM. The present Comment points out although the system under consideration (i.e., graphene-covered LHM) is itself physically challenging, the results for THz-LHM are also rather unreal because the frequency regime to accomplish the calculations falls within the high THz frequency band. In such a frequency band, the conductor substrate no longer behaves like a PEC and thus the results are rather unreal when considering THz-LHM. We note that the metal, for example, gold or silver may be modeled as a PEC, but only for a few THz. Moreover, when considering GHz-LHM, we obtain new forms of dispersion relations for both TE and TM surface waves. We find that our dispersion relations do not agree with the results obtained by Yaqoob et al.
