Electric-field effect on the transmittivity of aperiodic Kronig-Penney crystals

Abstract

We describe the effect of a static and uniform electric field on the electronic transport properties of one-dimensional periodic and deterministic aperiodic systems described by the Kronig-Penney model. We study the crystal transmittivity as a function of the length of the sample and of the field strength. In the periodic case we interpret the results exploiting the tilted band scheme and point out regions with a more than exponential decreasing rate of transmittivity. In the case of an incommensurate slowly varying potential we interpret the fine structure of the transmittivity by means of a continuous approximation. In the pseudorandom case we confirm the delocalization effect of the field and we compare the results with the purely random case

Nonclassical properties of electronic states of aperiodic chains in a homogeneous electric field

“…One of the simplest but nontrivial examples of the interactions is the effect of the homogeneous electric field on electronic states in crystals where the Wannier-Stark quantization was predicted [13][14][15][16] and confirmed experimentally in artificial semiconductor and optical superlattices. [17][18][19] Discussion of the effect in one-dimensional periodic systems has been carried out for many years [20][21][22][23][24][25][26][27][28] and is still the subject of current experimental as well as theoretical research. [29][30][31][32] In this paper, we apply the phase-space approach based on the nonclassical distribution functions [33][34][35][36] to the problem of electronic states in isolated and finite one-dimensional aperiodic systems generated by the Fibonacci and Thue-Morse sequences [37][38][39] in the presence of an external homogeneous electric field.…”

“…One of the simplest but nontrivial examples of the interactions is the effect of the homogeneous electric field on electronic states in crystals where the Wannier-Stark quantisation was predicted [13][14][15][16] , and confirmed experimentally in artificial semiconductor and optical superlattices [17][18][19] . Discussion of the effect in one-dimensional periodic systems has been carried out for many years [20][21][22][23][24][25][26][27][28] and is still the subject of current experimental as well as theoretical research [29][30][31][32] .…”

Electrical resistance of ballistic-electron transport through a finite disordered Fibonacci chain

“…The discovery of quasicrystals 3 has stimulated interest in exploring the physical nature of quasiperiodic (e.g., Fibonacci and Thue-Morse) sequences 4 as well as commensurateincommensurate systems. 5 Previous work on quasiperiodic sequences included, for example, plasmon excitation, 6 localization, 7 neutron polarization, 8 density-of-states, 9 optical-phonon tunneling, 10 nonlinear optical filters, 11 optical absorption in a random superlattice, 12 electric-field-induced localization, 13 and defect-assisted tunneling. 14 The quasiperiodicity in an infinite chain leads to a self-similar structure in the transmission of electrons as a function of their incident energy.…”