Acknowledgements

G.G. would like to acknowledge the support from the Air Force Research Laboratory (AFRL) through Grant #12530960.

Author details

, Thi Nga Do2

Polarizability and Impurity Screening for Phosphorene DOI: http://dx.doi.org/10.5772/intechopen.81814

provided the original work is properly cited.

New York, New York, NY, USA

2 Institute of Physics, Academia Sinica, Taipei, Taiwan

\*Address all correspondence to: ggumbs@hunter.cuny.edu

, Godfrey Gumbs3,4\* and Dipendra Dahal3

1 Department of Physics, National Cheng Kung University, Tainan, Taiwan

3 Department of Physics and Astronomy, Hunter College of the City University of

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

© 2018 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,

Po Hsin Shih1

Spain

59

## Conflict of interest

All the authors declare that they have no conflict of interest.

Polarizability and Impurity Screening for Phosphorene DOI: http://dx.doi.org/10.5772/intechopen.81814

EF = 1.0 eV. There exist Friedel oscillations for sufficiently small z0. Such oscillations might be smeared out for larger z0, e.g., the green and red curves. It is noticed that for EF = 1.0 eV, the room temperature of 300 K which is much smaller than the Fermi temperature (10,000 K) does not have significant effect on the

The energy band structure of BP, calculated using the tight-binding method, is anisotropic and so are its polarizability, dielectric function and screened potential. To illustrate these facts, we have presented numerical results for the polarizability in the x and y directions for a range of doping concentrations. The Re[ϵð Þ q;ω ¼ 0 ] of the static dielectric function for BP also reveals some interesting characteristics. At absolute zero temperature (T = 0) and with free carrier density corresponding to chosen Fermi energy EF, we have presented numerical results for Re[ϵð Þ q;ω ¼ 0 ] in different directions of the transferred momentum q. When q is larger than a critical value which is twice the Fermi momentum kF, our calculations show that Re [ϵð Þ q;ω ¼ 0 ] becomes substantially dependent on the direction of q. We also discuss the case at room temperature (T = 300 K). These results are in agreement with those reported by other authors. We employ our data to determine the static

G.G. would like to acknowledge the support from the Air Force Research Labo-

at T = 0 and 300 K (not shown) are

screened potential. Apparently, V r∥; z<sup>0</sup>

6. Concluding remarks and summary

shielding of an impurity in the vicinity of phosphorene.

All the authors declare that they have no conflict of interest.

ratory (AFRL) through Grant #12530960.

almost equivalent.

2D Materials

Acknowledgements

Conflict of interest

58
