2-d finite barrier rectangular quantum dots II: Dirac description

• Inseparable piecewise potential is used as the relativistic confinement potential of the quantum dot.
• Theoretical approach is based on elimination of the inexactness of the wave vector components employing the transfer matrices, and the reflection and the rotation symmetries of the dot.
• The transcendental energy relations of the dot are obtained as 2fold degenerate and quantized by half of the rotation angles, similar to nonrelativistic case.
• Considerable energy differences between these descriptions are observed due to spin effect.

The Schrödinger description of 2-d finite barrier rectangular quantum dots [1] is expanded to Dirac description through transfer matrices and reflection and rotation symmetries of the dot system. Inexactness of wave vector components of spinors is then reduced to two relations which lead to two different bispinors and four quantized transcendental energy relations corresponding to even–even, odd–odd and even–odd, odd–even factorizing functions of each bispinor. In order to show the spin effect on the dot energy levels, the solutions of the transcendental relations of the Schrödinger and Dirac descriptions are plotted.

Comparison of the finite-barrier rectangular quantum dot energy solutions for Schrödinger and Dirac descriptions, where gray geometric objects are for energy solutions of inside wave vector component κxκx defined quantized transcendental energy relations of Schrödinger and Dirac descriptions, while black ones for those of the inside wave vector component κyκy defined relations, for n=0,1 values. Schrödinger description results of inseparable finite barrier rectangular quantum dots are expanded to relativistic Dirac description.Figure optionsDownload as PowerPoint slide