Recently, semimetallic tungsten ditelluride (WTe2) has been proposed as a natural material that supports hyperbolic plasmonic responses. In this paper, we have theoretically discovered that such hyperbolicity, which is due to strongly anisotropic in-plane interband transition of electrons, exists even in the monolayer and can become elliptic under proper doping. Using density functional theory, the permittivities include both the interband and intraband parts have been calculated, which are then used to derive the in-plane conductivities. Based on two-dimensional conductivity, the dispersion relations of the plasmonic modes in the extended monolayer have been analytically solved. It is surprising that monolayer WTe2 supports both elliptic as well as hyperbolic plasmonic responses in the infrared. Edge-confined modes in the extended monolayer in the elliptic regime and waveguiding modes in nanoribbons in the hyperbolic regime have been numerically investigated. After being doped with electrons, the Fermi level is shifted; it is found that moderate electron doping can change the topology of the plasmonic responses from a hyperbolic to an elliptic one within some frequency range. The effects of band broadening are also discussed and the permittivities are calculated using optimal basis functions to further verify our main conclusions. Then, the states corresponding to large interband transition peaks are marked and the wavefunctions are used to explain the strong in-plane dipole. In the end, the permittivities of bulk WTe2 have been investigated. Our investigations indicate that monolayer WTe2 is a promising platform for plasmonic applications.

In this paper, plasmonic responses of phosphorene in the presence of strain and doping have been systematically investigated. Based on density functional theory, permittivities include both the intraband and interband transitions of electrons have been calculated. Due to the modification of the band structure, significantly higher Drude plasma frequency has been observed along the zigzag direction, other than the armchair direction as in the usual case. The resulting unusual plasmonic responses change their anisotropy, both in the elliptic as well as the hyperbolic regimes. Based on our calculations, positive strain as large as 5% along the zigzag direction can even lead to so-called reversed hyperbolic plasmonic responses. The k-surfaces of the plasmonic modes in extended monolayer have been analytically solved, and it is found that actively switching the topology (between elliptic and hyperbolic regimes) of the plasmonic responses by changing the Fermi level is possible in phosphorene at certain frequencies. In the end, a simple model has been proposed to describe such plasmonic responses in the infrared and the parameters of the model have been listed in tables which can be used directly in calculating the permittivities. Our studies may extend the scope of existing investigations of phosphorene plasmons and lead to band engineering as a way to control plasmons in two-dimensional materials.

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