Browsing by Subject "Gaussian confinement"

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Open Access
Polaronic effects in a gaussian quantum dot
(Elsevier, 2008) Yanar, S.; Sevim, A.; Boyacioglu, B.; Saglam, M.; Mukhopadhyaya, S.; Chatterjee, A.
The problem of an electron interacting with longitudinal-optical (LO) phonons is investigated in an N-dimensional quantum dot with symmetric Gaussian confinement in all directions using the Rayleigh-Schrödinger perturbation theory, a variant of the canonical transformation method of Lee-Low-Pines, and the sophisticated apparatus of the Feynman-Haken path-integral technique for the entire range of the coupling parameters and the results for N = 2 and N = 3 are obtained as special cases. It is shown that the polaronic effects are quite significant for small dots with deep confining potential well and the parabolic potential is only a poor approximation of the Gaussian confinement. The Feynman-Haken path-integral technique in general gives a good upper bound to the ground state energy for all values of the system parameters and therefore is used as a benchmark for comparison between different methods. It is shown that the perturbation theory yields for the ground state polaron self-energy a simple closed-form analytic expression containing only Gamma functions and in the weak-coupling regime it provides the lowest energy because of an efficient partitioning of the Gaussian potential and the subsequent use of a mean-field kind of treatment. The polarization potential, the polaron radius and the number of virtual phonons in the polaron cloud are obtained using the Lee-Low-Pines-Huybrechts method and their variations with respect to different parameters of the system are discussed.
Open Access
Two-electron singlet states in semiconductor quantum dots with Gaussian confinement: a single-parameter variational calculation
(IOP, 2007) Boyacıoğlu, B.; Sağlam, M.; Chatterjee, Ashok
The problem of two electrons in a three-dimensional quantum dot with Gaussian confinement is investigated for the singlet pairing by a variational method with a very simple wavefunction containing only a single parameter and a Jastrow-like factor, which is shown to yield fairly good results for deep confining potentials. The calculation is also performed for a few realistic semiconductor quantum dots and the phase diagrams for the two-electron singlet states are obtained for these materials. The pair density function is calculated for several parameter values and its peak positions are obtained as a function of the confinement length and the depth of the potential to study the behaviour of the electron-pair size. The size of the bound pair of electrons is also obtained by directly calculating the average distance between the two electrons in three different ways and compared with the pair correlation results. It is furthermore shown that, other properties remaining the same, the two-electron energy and the electron-pair size depend crucially on the effective electronic mass and the dielectric constant of the material. Finally, the ways of improving the wavefunction are also indicated.