**Author details**

**7. Summary and remarks**

*correspond to the separation* <sup>a</sup> <sup>¼</sup> <sup>1</sup>*:*0k�<sup>1</sup>

**Figure 9.**

*Nanoplasmonics*

near-field opto-electronic devices.

**198**

In conclusion, we have developed a general theory for finite-temperature polarization function, plasmon dispersions and their damping for all known innovation 2D Dirac-cone materials with various types of symmetries and bandgaps. We have also derived a set of explicit transcendental equations determining the chemical potential as a function of temperature, which serves as a key part in calculating finite-temperature polarization function through the so-called thermal convolution path. The selection of a particular path with a specific *μ*ð Þ *T* could be employed for studying the temperature dependence of plasmon modes in each of the considered 2D materials. The fact that a chemical potential keeps its sign is true only for materials with symmetric energy bands of electrons and holes, but can cross the

*Nonlocal hybridized plasmon dispersions for α-*T <sup>3</sup> *layer coupled to a closely-located surface of a semi-infinite conductor. Panels (a)–(d) are for* T ¼ 0*, while plots (e) and (f) for* kBT ¼ E0*. All the upper-row plots*

<sup>F</sup> *, and the lower-row ones to* <sup>a</sup> <sup>¼</sup> <sup>0</sup>*:*5k�<sup>1</sup>

<sup>F</sup> *. Additionally, middle-column*

Using the calculated finite-temperature polarization function, we have further found the dispersions of hybrid plasmon-modes in various types of open systems including a 2D material coupled to a conducting substrate. The obtained plasmon dispersions in these 2D-layer systems are crucial for measuring spin-orbit interaction strength and dynamical screening to Coulomb interaction between electrons in 2D materials, as well as for designing novel surface-plasmon based multi-functional

We have generalized our developed theory for 2D materials further to most recently proposed *α*-T <sup>3</sup> lattices, in which the characteristic parameter *α* is the ratio of hub-rim to hub-hub hopping coefficients and can vary from 0 to 1 continuously

corresponding to different material properties. For *α*-T <sup>3</sup> materials, we have obtained the hybrid plasmon modes for different *α* values at both zero and finite temperatures and demonstrated that the resulting hybridized plasmon dispersions

zero line for TMDC's with asymmetric electron and hole bands.

*plots, (b) and (d), correspond to ϕ* ¼ *π=*7*, and all other columns to ϕ* ¼ *π=*10*.*

Andrii Iurov<sup>1</sup> \*, Godfrey Gumbs2,3 and Danhong Huang<sup>4</sup>

1 Department of Physics and Computer Science, Medgar Evers College of the City University of New York, Brooklyn, NY, USA

2 Department of Physics and Astronomy, Hunter College of the City University of New York, NY, USA

3 Donostia International Physics Center (DIPC), San Sebastian, Basque Country, Spain

4 Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, NM, USA

\*Address all correspondence to: aiurov@mec.cuny.edu; theorist.physics@gmail.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
