Surface states of a semi-infinite superlattice

Abstract

The surface states of a semi-infinite superlattice with a step discontinuity in the potential at the interface has been calculated within the framework of the Kronig-Penney model. An explicit solution is obtained for the eigenenergy of the surface state. Surface states are shown to exist only for certain values of the barrier widths and/or heights of the semi-infinite superlattice and of the potential step discontinuity at the interface. Approximate, but very accurate, formulas are derived for the surface-state energy and its respective characteristic decay length, allowing one to readily determine the conditions for the existence of surface states.

Electromagnetic surface modes of a dielectric superlattice: the supercell method

“…On the theoretical side, an analytic expression for the dispersion relation (␤) was obtained by use of the Bloch theorem with a complex Bloch wave vector in the semi-infinite superlattice and by matching this solution with an exponentially decaying wave in the air. 6 Most of the theoretical studies for acoustic surface modes, 1 surface plasmon polaritons, 16 and surface electronic states 17 in superlattices were based on the application of similar ideas. However, only a few years ago, 18 complete dispersion curves for surface electromagnetic modes in dielectric superlattices were published.…”

Electronic band structure of GaAs/AlxGa1−xAs superlattice in an intense laser field

“…edge which leads to the barrier height at 228 meV. The relation between the effective masses and the Al content is given as m n w ¼ 0:0665m 0 and m n b ¼ ð0:0665 þ0:083xÞm 0 where m 0 is the bare electron mass [40,41].…”

Symmetry of Surface States in Graphene Superlattices Terminated With Magnetic Cap Layers

“…The complex-basis SLs normally consist of three or four different layers instead of two, such as a stepwell basis and a δ-doped SLs, and the basis of biperiodic SLs consist of two-wells and two-barriers. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] In practical applications, SLs are normally finite in length and terminated on one end or both ends, the termination interrupts the periodicity of infinite SL and introduces an asymmetric perturbation potential to the SL, which leads to the appearance of surface states within the energy band gap. The surface states are important for optoelectronic characteristics of SLs.…”