Godfrey Gumbs

By Po Hsin Shih, Thi Nga Do, Godfrey Gumbs and Dipendra Dahal

Using a tight-binding Hamiltonian for phosphorene, we have calculated the real part of the polarizability and the corresponding dielectric function, Re[ ϵ q ω ], at absolute zero temperature (T = 0 K) with free carrier density 10 13 / cm 2 . We present results showing Re[ ϵ q ω ] in different directions of the transferred momentum q. When q is larger than a particular value which is twice the Fermi momentum kF, Re[ ϵ q ω ] becomes strongly dependent on the direction of q . We also discuss the case at room temperature (T = 300 K). These results which are similar to those previously reported by other authors are then employed to determine the static shielding of an impurity in the vicinity of phosphorene.

Part of the book: 2D Materials

By Andrii Iurov, Godfrey Gumbs and Danhong Huang

The purpose of this chapter is to review some important, recent theoretical discoveries regarding the effect of temperature on the property of plasmons. These include their dispersion relations and Landau damping rates, and the explicit dependence of plasmon frequency on chemical potential at finite temperatures for a diverse group of recently discovered Dirac-cone materials. These novel materials cover gapped graphene, buckled howycomb lattices (such as silicene and germanene), molybdenum disulfide and other transition-metal dichalcogenides, especially the newest dice and α-T3 materials. The most crucial part of this review is a set of implicit analytical expressions about the exact chemical potential for each of considered materials, which greatly affects the plasmon dispersions and a lot of many-body quantum-statistical properties. We have also obtained the nonlocal plasmon modes of graphene which are further Coulomb-coupled to the surface of a thick conducting substrate, while the whole system is kept at a finite temperature. An especially rich physics feature is found for α-T3 materials, where each of the above-mentioned properties depends on both the hopping parameter α and temperature as well.

Part of the book: Nanoplasmonics

By Sita Kandel, Godfrey Gumbs and Oleg L. Berman

We present a semi-analytical expression for both longitudinal and transverse optical conductivities of a model TNLSM employing the Kubo formula with emphasis on the optical spectral weight redistribution, deduced from appropriate Green’s functions. In this semimetal, the conduction and valence bands cross each other along a one- dimensional curve protected by certain symmetry group in the 3D Brillouin zone. Although the crossing cannot be removed by any perturbations, it can be adjusted by continuous tuning of the Hamiltonian with a parameter α. When α>0, the two bands cross each other near the Γ point in the (kx,ky) plane of the first Brillouin zone making a nodal circle of radius α. The circle shrinks to point when α=0 and for α<0, the nodal circle vanishes and a gap opens around Γ. Numerical results for the longitudinal optical response of such TNLSM are investigated by varying the gap due to modifying α, the chemical potential μ, temperature T and the dephasing parameter η. The longitudinal optical conductivity is anisotropic along the direction parallel or perpendicular to the nodal ring. However, the transverse optical conductivity vanishes due to rotational symmetry.

Part of the book: Advances in Nanosheets