CONFINAMIENTO NANOSC´OPICO EN ESTRUCTURAS ... - It works!

Confinamiento dieléctrico 285Dielectric confinement in quantum dots 17spatial confinement is in general the main constraint determining the physical propertiesof nano-crystallites, such as e.g. the discrete energy spectrum (this is particularly true forsmall QDs), other sources of confinement can exceed it, under specific circumstances,to yield a completely different physics. This competition between dielectric and spatialconfinement parallels the probably better known competition between magnetic and spatialconfinements. In the latter case, as the QD is pierced by a magnetic field that is strongenough to yield a magnetic confinement length Ð ÑÕ smaller than the effectiveBohr radius £ ¼ , then, the system undergoes a gradual transition from a non-degenerateground state (of pure spatial confinement) toward a limit case of infinite-fold degeneration(the so-called Landau states), corresponding to a pure magnetic confinement. [61] In thissection we will pay some attention to the electron dynamics in the presence of a dielectricmismatch producing surface states. At first sight one may guess that Coulomb interactionshould increase heavily as we go from volume to surface states, as we reduce the systemdimensionality from 3D to nearly 2D. However, it is not that simple. The dielectric mismatchnot only induces the appearance of surface states. In addition, and depending uponthe environment permittivity, it modulates the system dynamics from almost independentparticles to strongly interacting particles yielding a Wigner-like localization [9].Figure 3 includes the self-polarization potential (lower panel) for an Ê ¿ ÒÑ, ÓØ spherical quantum dot surrounded by (a) an ÓÙØ ¼dielectric medium and (b)an ÓÙØ ½ dielectric medium. The vertical dotted line indicates the quantum dot edge.We can see that the self-polarization potential well always arises by the QD border, eitherinside/outside the QD if the QD dielectric constant ÓØ is smaller/larger than that of thesurrounding medium ÓÙØ . The corresponding radial density of the one-electron ½× statefor Ñ £ ÓØ ¼, Ñ£ ÓÙØ ½, Î ¼ ¼ eV is also shown in the upper panel for each case.We can see that in both situations a strong radial localization occurs. It should be stressedthat in addition to the monoelectronic ground state (Ò ½, ¼), several energeticallylow-lying excited states (Ò ½, ¼) also undergo a self-energy-induced localization.The self-polarization potential well can also induce surface localization ofthe Ê electronic density when a second excess electron is added to the QD. Thisis shown in Fig. 4(a) and 4(c), where the radial pair density Ê´Ö ½ Ö ¾ µ ¾ ©´Ö ½ Ö ¾ µ ¾ Ö½ ¾Ö¾ ¾ ×Ò ½ ×Ò ¾ ½ ¾ ½ ¾ is represented for the two differentdielectric environments displayed in Fig. 3, namely ÓÙØ ¼and ÓÙØ ½, respectively.For the sake of comparison, the case of an unpolarized dot ( ÓÙØ ÓØ ) has also beenincluded. When ÓÙØ ÓØ (case (a) in Fig. 4) it is found that the bare Coulombrepulsion is almost totally screened by the polarization effects. As a consequence, thekinetic energy dominates, the correlation effects become negligible and both electronsbehave almost as independent particles. This is shown in Fig. 5, where the angularcorrelation density ´µ Æ ©´´Ö ÑÜ ¼ ¼µ ´Ö ÑÜ ¼µµ ¾ (with Ö ÑÜ correspondingto the coordinates Ö ½ Ö ¾ of the maximum Ê´Ö ½ Ö ¾ µ and Æ representing the appropriatenormalization factor) is represented. In the second case, ÓÙØ ÓØ (case (c) in Fig.