Characteristics of plasmon transmittivity over potential barriers

Abstract

In this paper we use the Schrödinger-Poisson model to obtain a linear coupled pseudoforce system from which the wave function and the electrostatic potential of the free electron gas plasmon is deduced. It is shown that unlike for single particle wave function the plasmon wave function and corresponding electrostatic potential are characterized with two different wave numbers associated with two distinct characteristic length scales, namely, that of the single electron oscillation and of the collective Langmuir excitations. Interaction of plasmon with a rectangular potential step/well indicates features common with that of the ordinary single quantum particle. However, the twotone oscillation character of the wave function and potential appear on the transmitted amplitude over the potential barrier/well. The plasmon propagation is found to have a distinct energy gap corresponding to the plasmon energy value of ǫ g = µ 0 + 2ǫ p below which no plasmon excitations occur. For instance, the zero-point plasmon excitation energy for Aluminium, is around ǫ 0 ≃ 41.7eV at room temperature, with the Fermi energy of ǫ F ≃ 11.7eV and plasmon energy of ǫ p ≃ 15eV. It is seen that for plasmon energies very close to the energy gap, i.e. where the two characteristic scales match (k 1 ≃ k 2 ), the quantum beating effect takes place. The study of plasmon tunneling through the potential barrier indicates that the transmittivity has oscillatory behavior similar to that of a quantum particle tunneling through the potentials, but, with a characteristic two-tone oscillatory profiles. Current development can have a broad range of applications in plasmon transport through diverse free electron environments with arbitrary degeneracy and electron temperature. It also makes progress in rapidly growing nanotechnology and plasmonic fields.

Effect of Dynamic Ions on Band Structure of Plasmon Excitations

“…Application of quantum plasma theories have revealed a large number of interesting new linear and nonlinear aspects of collective interactions among different plasma species [52][53][54][55][56][57][58][59][60][61][62][63][64][65] and has led do discovery of many new phenomena such as resonant shift and electron spill-out [66], novel quantum screening [67][68][69][70] and plasmon-soliton [71], to name a few. Application of linearized Schrödinger-Poisson system for eigenvalue problem has shown many interesting new aspects of quantum plasmas due to the unique dual lengthscale character of plasmon excitations [72][73][74][75][76][77][78][79]. In current research we would like to extend our previous results of pseudoforce approach to the plasmon energy band structure in complex plasma environments.…”

“…For k ≫ 1 it has particle-like character and reduces to conventional parabolic form E ≃ γk 2 while for k ≪ 1 it has wave-like character and it turns into E ≃ Z 2 /k 2 . The duallength scale character of plasmon excitations, which is evidently due to both single-particle and collective behavior, has shown to produce many fundamental properties in an unmagnetized electron gas [73][74][75][76][77][78][79]. The dispersion curve has a minimum value at k m = γ 1/4 √ Z and E m = 2Z √ γ…”

Quantum Level Instability of Transverse Excitation in Electron Flow

“…Recent investigation [80][81][82][83][84] of plasmon excitations in arbitrary degenerate electron gas trapped in an infinite wall one dimensional box within the frameworks of the Schrödinger-Poisson model reveals energy quantization of collective modes with statefunctions characterized by features present in single-electron wavefucntion modulated by fine-structured density oscillations due to electrostatic interaction modeled via Poisson's relation coupled to the Schrödinger equation.…”

Resonant Electron-Plasmon Interactions in Drifting Electron Gas

“…Application of these theories predicts a very insightful future for the science of quantum plasmas and have helped to discover a broad range of new interesting collective phenomena of quantum electron gas unknown up until the recent decade [55-61, 63-66, 86]. Application of Schrödinger-Poisson system [67] and coupled pseudoforce method has shown a double-tone wave-particle dynamics of the quantum electron gas in a unique picture [68][69][70][71][72][73][74]. We strongly believe that this dual-lengthscale theory of quantum plasmas provides a better picture for wave-particle phenomena in collective environments such as plasmas and fluids.…”