Dynamics of soliton in semiconductor with a superlattice

Interaction of kink-lattice solitons with small-amplitude waves in finite-size superlattices

“…The most popular version is the 1D sG equation whose single-and double-soliton solutions, i.e. kink and breather, deeply influenced our understanding of various condensed matter phenomena among which are charge transfers in quasi-1D conductors [17,18], flow of flux quanta in Josephson Junctions [19] and also in superlattices [14][15][16]. The single-kink solution of the 1D sG equation is usually obtained in the form:…”

“…The key physical parameter describing the electron distribution in the bands is the dispersion relation, for superlattices the following dispersion law is most often considered [14][15][16]:…”

“…In the second, it is suspected that a strong electromagnetic (EM) wave could make its propagation medium essentially nonlinear due to the self-action effect, in virtue of which it is modulated into a soliton EM field. Tetervov [14] remarked that if the superlattice is acted upon by a weak probing EM wave simultaneously with the soliton EM field, the scattering coefficients of the probing wave will depend on the soliton parameters. However, in our opinion, the conjectured soliton collapse after some characteristic collision time is rather speculative by the very intrinsic stability properties of topological solitons [1,2].…”

Excitation of Breather (Bion) in Superlattice

“…Then the electron current density can be written as canonical momentum p; u p is the electron velocity, e the electron charge and Ar; t the vector potential. The key physical parameter describing the electron distribution in the bands is the dispersion relation, for superlattices the following dispersion law is most often considered [16,17]:…”

“…The sG equation has not only a soliton solution but also a solution in the form of a breather which can be interpreted as bound states of solitons and antisolitons. The solution of the sG equation has deeply in£uenced our understanding of various condensed matter phenomena, notable among which are charge transfers in quasi 1-D conductors [13,14], £ow of £ux quanta in Josephson junctions [15] and in superlattices [16,17].…”