In the framework of the two-band (Dirac) model, we analyze the electronic structure of nanoscale systems, based on narrow-gap semiconductors of Pb,_xSnx (Se, S) type. Themain attention is paid to the influence of properties of the surface, encoded in appropriate boundary conditions, on the size-quantized spectrum. From this point of view we consider two types of systems: spherical (quantum dots) and quasi one-dimensional (films).It is shown that the spectrum of the spherical quantum dot consists not only of usual size-quantized states, located above the gap edge, but also surface modes residing inside the gap. Such states manifest themselves in the far infrared part of the absorption spectrum, the measurement of which allows one to extract information about the dot surface.Next, we consider a film with the energy gap modulated in the <111> (growth) direction. It is shown that the spectrum of the infinite crystal possesses a supersymmetrical structure. The film boundaries, generally speaking, destroy the supersymmetry, i.e. size-quantized subbands turn out to be spin-split. However, there exists a class of boundary conditions that do not lift spin degeneracy. Physically, in this case there is no band mismatch at interfaces. Our central statement, therefore, consists of the following: even when the inversion symmetry is destroyed by the bulk inhomogeneity, the spin-splitting of the spectrum is a purely surface effect. This is illustrated on a simple example, when the energy gap varies linearly over the film width.Finally, we investigate the role of boundary conditions in the problem of scattering of spinor waves by a quantum dot. It is shown that the existence of surface states greatly modifies the scattering data; in particular, outgoing waves may turn out to be fully polarized. / Department of Physics and Astronomy
| Identifer | oai:union.ndltd.org:BSU/oai:cardinalscholar.bsu.edu:handle/187963 |
| Date | January 2005 |
| Creators | Isaev, Leonid |
| Contributors | Joe, Yong S. |
| Source Sets | Ball State University |
| Detected Language | English |
| Format | vii, 100 leaves : ill. ; 28 cm. |
| Source | Virtual Press |
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