Таммовские Связанные Состояния Электронов На Поверхности Кристалла И Поверхностные Колебания Атомов Решётки

Abstract

Т. LVI, вып. 4 УСПЕХИ ФИЗИЧЕСКИХ НАУКВ первой части статьи даётся обзор последовательных этапов развития теории таммовских поверхностных состояний электронов. Во второй части рассматриваются явления, в которых поверхност-ные состояния электронов играют существенную роль, и приводятся экспериментальные доказательства действительного существования этих состоякиЯ в реальных кристаллах. В третьей части статьи излагается теория поверхностных колебаний кристаллической ре-шётки, которая математически близка и генетически связана с тео-рией поверхностных состояний электронов *).

Magnetic-field-driven surface electromagnetic states in the graphene-antiferromagnetic photonic crystal system

“…(1) and (2), where vector H substitutes for vector B, permittiv ity ε 2 substitutes for ε 1 , and field equations have the form (15) Using the approach developed in [46] to describe the coupled Tamm states on a crystal surface, we rep resent the fields in the region y > Nd as the superposi tion of incident and reflected waves, (20) where k is the Bloch wavenumber [47], the first terms in Eqs. (19) and (20) correspond to the fields of the wave incident on the interface y = Nd, and the second terms correspond to the fields of the wave reflected from the interface y = Nd.…”

Effect of the δ-shaped quantum well at the one-dimensional lattice boundary on properties of Tamm-type surface electronic states

“…Let us write such a dependence of the electron potential energy on the coordinate y as follows: (1) where d is the structure period and δ(y) is the Dirac delta function. The electron wave function ψ in the problem under consideration satisfies the time inde pendent Schrödinger equation (2) where ប is Planck's constant, m is the electron mass, and E is the total electron energy. In the region y < 0, the solution to wave equation (2) is given by (3) where κ = /ប.…”

“…In [1], within the Kronig-Penney approximation, it was shown that bound electronic states can exist at the one dimensional lattice boundary, if the electron energy falls within the band gap of an infinite one dimensional lattice and is lower than its potential energy in the external space. From the time of the the oretical prediction of SESs, a large number of works were devoted to the study of their properties (see, e.g., [2][3][4][5][6][7] and references therein). Interest in SESs is caused by their ability to affect physical properties of crystalline solids.…”

Electronic states on the rough surface of a solid

“…2 These results are summarized by I. M. Lifshitz and S. I. Pekar (1955) for nonpolar lattice vibrations. 3 A review 3 shows that the theory of surface electronic states is deeply analogous with the theory of surface vibrations of crystal lattice atoms. In the one-dimensional case one of the branches of the energy spectrum transitions into Rayleigh branches, while others form surface optical branches.…”