Confinement Effects on the Weak-Field Magnetic Susceptibility of a Two-Dimensional Electron Gas

Abstract We study the weak-field magnetic susceptibility of a two-dimensional electron gas for different types of confinement potentials. The susceptibility is strongly dependent on the boundary confinement, and removal of the boundary results in a singularity. The cases of spatially isotropic parabolic, anisotropic, and Gaussian confinement potential are discussed in detail. The effect of spin–orbit interaction via Rashba type of coupling is analyzed in detail for all the potentials mentioned above. We show that a field-dependent susceptibility emerges when the confinement is Gaussian, in contrast to the canonical case of a field-independent susceptibility. The field-dependent weak-field susceptibility arises, even without Rashba spin–orbit coupling or many-body interactions. This distinguishes our result from conventional systems where such behavior typically relies on disorder, spin–orbit effects, or strong correlations. The combination of smooth confinement and magnetic field effects in our model leads to field-dependent behavior in a simple single-particle Hamiltonian, making it potentially amenable to experimental realization in semiconductor quantum wells and nanostructures. Our findings challenge the conventional understanding of susceptibility in weak-field regimes and open new avenues for exploration in quantum and nanoscale systems. We also show that the weak-field susceptibility is independent of the anisotropy parameter as well as the spin–orbit coupling for the anisotropic confinement model. For all the other models, the susceptibility vanishes for large spin–orbit coupling.