Quantum confinement in mesoscopic annular regions withC1υandC∞υsymmetries

Abstract

The single-electron energy spectrum is studied, highlighting axial-symmetry-breaking ${(C}_{\ensuremath{\infty}\ensuremath{\upsilon}}\ensuremath{\rightarrow}{C}_{1\ensuremath{\upsilon}})$ aspects, in annular two-dimensional and three-dimensional mesoscopic finite-potential wells. The closed analytical forms for the elements of the matrix utilized in calculations are those obtained after satisfying the effective-mass boundary conditions exactly at both the interfaces. The limiting cases when the barrier heights or the effective-mass discontinuities become infinite are analyzed and it is observed that they produce just opposite effects on the finite-well eigenvalues. Also, these cases require the well region wave function to satisfy respectively the Dirichlet and Neumann boundary conditions analogous to the longitudinal fields of the transverse magnetic and transverse electric modes in electromagnetic waveguides with perfect metallic boundaries. The consideration of a ``massive wall'' thus unveils interesting physics and establishes one-to-one correspondence between electron and electromagnetic waveguides. Moreover, the general trend for doublet splittings when ${C}_{\ensuremath{\infty}\ensuremath{\upsilon}}\ensuremath{\rightarrow}{C}_{1\ensuremath{\upsilon}}$ in our study under the Dirichlet condition is in conformity with recent experimental observations [Dembowski et al., Phys. Rev. Lett 84, 867 (2000)].