Thermodynamics of coupled nanorings under external fields: Electron localization and inter-ring coupling

We investigate the thermodynamic response of a single electron confined in a pair of laterally coupled volcano-shaped InAs/GaAs quantum rings under external electric and magnetic fields. The electronic structure is described within an effective single-band Hamiltonian derived from the Kane model, with energy-, position-, and temperature-dependent material parameters. The strongly confined axial motion is treated within an adiabatic approximation, and the axial problem is solved with Ben Daniel–Duke boundary conditions, so that its lowest eigenvalue defines the effective in-plane confinement. The resulting temperature-dependent spectra are used to evaluate the entropy and heat capacity in a canonical framework. The Kane/parabolic comparison is restricted to the isolated-ring spectral benchmark, whereas the thermodynamic response of the coupled-ring molecule is evaluated exclusively from the Kane-derived spectrum to examine the effects of inter-ring coupling and external fields.