Abstract
A “one-point” approximation is proposed to investigate the transmission of electrons through the extra thin heterostructures composed of two parallel plane layers. The typical example is the bilayer for which the squeezed potential profile is the derivative of Dirac’s delta function. The Schr¨odinger equation with this singular one-dimensional profile produces a family of contact (point) interactions each of which (called a “distributional” б′-potential) depends on the way of regularization. The discrepancies widely discussed so far in the literature regarding the family of delta derivative potentials are eliminated using a two-scale power-connecting parametrization of the bilayer potential that enables one to extend the family of distributional б′-potentials to a whole class of “generalized” б′-potentials. In a squeezed limit of the bilayer structure to zero thickness, the resonant tunneling through this structure is shown to occur in the form of sharp peaks located on the sets of Lebesgue’s measure zero (called resonance sets). A four-dimensional parameter space is introduced for the representation of these sets. The transmission on the complement sets in the parameter space is shown to be completely opaque.
Publisher
National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka)
Subject
General Physics and Astronomy
Reference41 articles.
1. F.A. Berezin, L.D. Faddeev. Remark on the Schr?odinger equation with singular potential. Dokl. AN SSSR, 137, 1011 (1961).
2. Y.N. Demkov, V.N. Ostrovskii. Zero-Range Potentials and Their Applications in Atomic Physics (Plenum Press, 1988).
3. S. Albeverio, F. Gesztesy, R. Hoegh-Krohn et al. Solvable Models in Quantum Mechanics, with appendix by P. Exner (Amer. Math. Soc., 2005).
4. S. Albeverio, P. Kurasov. Singular Perturbations of Differential Operators: Solvable Schr?odinger-Type Operators (Cambridge Univ. Press, 1999).
5. D.J. Griffiths. Boundary conditions at the derivative of a delta function. J. Phys. A: Math. Gen. 26, 2265 (1993).
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献