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In this work we analyze the statistical thermodynamic functions and magnetic moment of a Dice lattice subject to a normal quantizing magnetic field. Our analysis addresses the Grand Potential and Helmholtz Free Energy, as well as the magnetic moment, entropy and specific heat at constant volume, explicitly determining their magnetic field dependencies in the degenerate statistical regime, replete with de Haas-van Alphen oscillatory phenomenology (and other magnetic field dependence); and also determining their temperature dependencies jointly with magnetic field features in the approach to the zero temperature limit. Furthermore, we evaluate the Grand Potential exactly, for arbitrary temperature and density. Our results are obtained with consideration of the presence of heat and particle baths with fixed chemical potential and they are discussed in relation to other pertinent work on the subject.

We examine the question “Can Dirac materials exist in a nondegenerate statistical state?,” deriving and employing an identity for the thermodynamic Grand Potential $\Omega$ (per unit volume/area) in the low density nondegenerate statistical regime, relating it to the density $n$ as $\Omega = -\beta ^{-1} n$ ($\beta ^{-1} = \kappa _{B} T$ is thermal energy, $\kappa _{B}$ is the Boltzmann constant, and $T$ is Kelvin temperature). The implications of this identity for Dirac materials are explored. The identity is universally valid for all thermodynamic systems in equilibrium in the nondegenerate, low density statistical regime, irrespective of size, dimensionality or applied static fields. Phenomena that may contribute to the realization of such a nondegenerate statistical equilibrium state in Dirac materials are discussed.

The dyadic Helmholtz Green’s function for electromagnetic (EM) wave transmission/ diffraction through a subwavelength nano-hole in a two-dimensional (2D) plasmonic layer is discussed here analytically and numerically, employing “contact potential”-like Dirac delta functions in 1 and 2 dimensions (δ(z) and δ(x)δ(y)≡δ(2)(r→)). This analysis is carried out employing a succession of two coupled integral equations. The first integral equation determines the dyadic electromagnetic Green’s function G^fs for the full non-perforated 2D quantum plasma layer in terms of the bulk 3D infinite-space dyadic electromagnetic Green’s function G^3D, with δ(z) representing the confinement of finite quantum plasma conductivity to the plane of the plasma layer at z=0. The second integral equation determines the dyadic electromagnetic “hole” Green’s function G^hole for the perforated 2D quantum plasma layer (containing the nano-hole) in terms of the dyadic electromagnetic Green’s function G^fs for the full non-perforated 2D plasma layer, with δ(2)(r→) describing the exclusion of the quantum plasma layer conductivity properties from the nano-hole region in the vicinity of r→=0 on the plane. Taking the radius of the subwavelength nano-hole to be the smallest length scale of the system in conjunction with the 2D Dirac delta function representation of the excluded nano-hole plasma conductivity, both of the successive coupled integral equations are solved exactly, and we present a thorough numerical analysis (based on the exact analytic solution) for the resulting dyadic “hole” Green’s function G^hole in full detail in both 3D and density plots. This result has been successfully applied to the determination of electromagnetic wave transmission/diffraction through the nano-hole of the perforated quantum plasmonic layer, jointly with the EM wave transmission through the rest of the plasma layer. This success necessarily involves spatial translational asymmetry induced by the use of spatial Dirac delta functions confining finite conductivity to the 2D quantum plasma sheet and the excision at a bit of it about the origin to represent the nano-hole perforation, thus breaking spatial translational invariance symmetry.

A detailed numerical study of the Helmholtz Green's function for the description of scalar wave propagation through a nano-hole on a plasmonic layer is presented in this chapter. In conjunction with this, we briefly review the analytic formulation taking the nano-hole radius as the smallest length parameter of the system. Figures exhibiting the numerical results for this Green's function in various ranges of the transmission region are presented. [ABSTRACT FROM AUTHOR]

This work is focused on the analysis of the quantum dynamics of a model one-dimensional lattice array of quantum dots on a two dimensional electron sheet/layer in a normal magnetic field. Our analysis is carried out with the derivation of the Green's function for the quantum dot lattice subject to Landau quantization using the corresponding "no-lattice" Green's function, for propagation along the axis of the 1D quantum dot lattice. The frequency/energy poles of this Green's function provide the dispersion relation for the Landau quantized energy spectrum, which exhibits Landau minibands, rather than discrete Landau levels. In the case of nonrelativistic carriers, the dispersion relation is explicitly exhibited in a closed form in terms of the Jacobi Theta Function of the third kind, and an approximate solution displaying the Landau miniband formation is obtained in terms of Laguerre polynomials. We also examine the case of "relativistic" graphene carriers, employing the appropriate Landau quantized graphene Green's function in a study of the associated wave packet dynamics in a graphene antidot lattice in a normal magnetic field. In this, we analyze the effects of pseudospin on the wave packet dynamics in Landau quantized graphene, including the role of Zitterbewegung in circular orbit motion. [ABSTRACT FROM AUTHOR]

We examine the role of the angle of incidence in the transmission of an electromagnetic wave through a subwavelength nano-hole in a thin semiconductor plasmonic layer, focusing on the near zone. In this, we treat both p- and s-polarizations of the incident wave for a variety of incident angles using a dyadic Green's function formulation that includes both (1) the electromagnetic field transmitted directly through the 2D plasmonic layer and (2) the radiation emanating from the nano-hole, explicitly exhibiting interference fringes. Employing an integral equation formulation, this dyadic Green's function approach incorporates the role of the 2D plasmon of the semiconductor layer, which is smeared due to its lateral wave number dependence. The interference fringes, clustered near the nano-hole, flatten to a uniform level of transmission directly through the semiconductor sheet alone at large distances from the nano-hole. As the incident angle increases, the axis of the relatively large central transmission maximum through the nano-hole follows it, accompanied by a spatial compression of interference fringe maxima forward of the large central transmission maximum, and a spatial thinning of the fringe maxima behind it. For p-polarization, the transmission results show a strong increase as the incident angle θ0 increases, mainly in the dominant Ez component (notwithstanding a concomitant decrease of the Ex component as θ0 increases). In the case of s-polarization of the incident EM wave, the transmission decreases as θ0 increases. [ABSTRACT FROM AUTHOR]

We address the magnetopolariton spectrum and magnetoconductivity tensor of a two dimensional plasma of nonrelativistic charge carriers subject to Landau quantization in a normal magnetic field. The analysis is carried out in the random phase approximation for linear electromagnetic response. Various regimes of magnetic field strength and wave number are considered. An exact integral representation of the magnetoconductivity tensor is derived and several expansions in terms of modified Bessel functions and Laguerre polynomials are obtained, as well as a low wave number power expansion. These results encompass the nondegenerate and degenerate statistical regimes as well as intermediate field and quantum strong field strengths. The two-dimensional magnetopolariton dispersion relation is formulated and solved for the electromagnetic normalmodes, and local and nonlocal magnetopolaritons/ plasmons are discussed, including nonlocal Bernstein modes, all subject to Landau quantization. The leading nonlocal corrections to the local modes are shown to exhibit de Haas-van Alphen oscillatory quantum structure in the degenerate statistical regime. [ABSTRACT FROM AUTHOR]

In this work we analyze the exact temperature and density dependencies of the thermodynamic properties of the two dimensional pseudospin-1 T-3 Diced Lattice. Starting from the Gibbs canonical partition function, we determine the exact grand canonical ensemble thermodynamic potential, entropy and specific heat at arbitrary temperature and density, and confirm results in the degenerate and nondegenerate statistical regimes. [ABSTRACT FROM AUTHOR]

This chapter addresses the pseudospin-1 T-3 "Diced" Lattice in regards to its quantum dynamics, spectrum and statistical thermodynamics, both with and without an impressed normal magnetic field. As in the preceding chapter, it is based on lecture notes composed of slides that have been carefully prepared to provide clear explanations of the material to audience members whose native language may not have been English, using the standard terms and mathematical symbols of theoretical physics. Considerable detail is presented to enhance understanding of the derivations and results described on the slides and pertinent references are provided. [ABSTRACT FROM AUTHOR]

This chapter is focused on the Landau-quantized dynamics and statistical thermodynamics of nanostructured Dirac-like materials in a normal magnetic field, as exemplified by Graphene and the Group VI Dichalcogenides. The chapter is based on notes on lectures presented at the UNESCO International Center for Theoretical Physics in Trieste, Italy in May 2019. They are composed of slides presented at the lectures, which were carefully prepared to provide clear explanation of the material to audience members whose native language may not have been English, using the standard terms and mathematical symbols of theoretical physics. Sufficient detail is provided to facilitate understanding the derivations and results presented and relevant references are listed. [ABSTRACT FROM AUTHOR]