Charged coplanar semiconductor quantum rings: Magnetization and inter-ring electron-electron correlation

Abstract

We study a coplanar system of electrostatically coupled semiconductor quantum rings each charged by a single electron using a configuration-interaction approach. We find that the electron densities confined in separate rings are significantly deformed by the inter-ring coupling which results in reduction of the persistent currents and the magnetic dipole moments that they generate, particularly at half flux quanta for which the persistent current loops are broken by appearance of zeros of angular single-ring wave functions. For three and more rings, the magnetic properties of the system strongly depend on the geometry of the ring configuration. We demonstrate a frustration mechanism which prevents the charge density deformation and reduction of the magnetization that occurs for rings near symmetry centers of the system. Due to this mechanism, the average magnetization produced by a linear array of rings exceeds several times the one generated by a square array. We discuss the nature of the electron-electron spatial inter-ring correlation. In the ground state, the correlation is semiclassical and can be reproduced by a separable wave function. Quantum correlation is weak and short range in the ground state. Excited states with longer range zigzag correlated structures formed in the internal degrees of freedom are also discussed.