Physica E 8 (2000) 230–238 www.elsevier.nl/locate/physe Parabolic dot in tilted magnetic eld T. Pyragien˙ e * , A. Matulis Institute of Semiconductor Physics, Go stauto 11, 2600 Vilnius, Lithuania Received 8 March 2000; received in revised form 3 April 2000; accepted 10 April 2000 Abstract The electron motion, the power absorption spectrum and the oscillator strengths are considered in the case of the parabolic dot in a tilted magnetic eld by means of solving the equations of motion. It is shown that for a linear system the classical dynamic matrix diagonalization leads to the second quantization representation in quantum mechanical description. It enables to generalize the Fock single-electron wave function set for the case with the tilted magnetic eld. ? 2000 Elsevier Science B.V. All rights reserved. PACS: 73.20.Dx; 03.65.-w Keywords: Electron density; Excitation spectrum; Oscillator strengths 1. Introduction Quantum dots, or articial atoms, have been a sub- ject of intense theoretical and experimental research over the last few years [1]. The useful instrument in spectroscopy experiments is the magnetic eld applied in perpendicular to the quantum dot plane direction which enables to trace easily the quantum dot proper- ties dependence on various parameters. Recently the experiments with the magnetic eld in quantum dot plane (Voight conguration) gained interest [2– 4], and even the magneto-photoluminescence dependence on the tilted magnetic eld direction was investigated [5]. The tilted magnetic eld couples the in-plane elec- tron motion to the vertical one, and thus, enables to re- cover the quantum dot excitations which are forbidden * Corresponding author. in the case of more symmetric perpendicular magnetic eld. To our knowledge the tilted magnetic eld has been used for the theoretical polaron spectrum studies in the parabolic quantum wells [6]. The theoretical description of electron system in a quantum dot is mainly based on the wave function expansion into the series of non-interacting elec- tron wave functions. In the most popular case of the parabolic dots the energy spectrum and the single-electron wave functions were calculated by Fock [7]. The analytical solution was obtained due to the circular symmetry of the quantum dot which leads to the separation of the variables. The tilted magnetic eld breaks the symmetry, and conse- quently, makes the problem more dicult. In the case of quantum well the remaining translation symme- try in the well plane along the perpendicular to the magnetic eld direction is sucient for the separa- 1386-9477/00/$ - see front matter ? 2000 Elsevier Science B.V. All rights reserved. PII:S1386-9477(00)00150-8