Abstract
<title>Abstract</title> <p>We investigate whether an artificial annular pinning landscape can control the transition from a single-vortex state to an L = 2 giant vortex in a mesoscopic type-II superconducting cylinder. The problem is formulated within the axisymmetric Ginzburg–Landau framework, with the strength, radius, and width of a Gaussian suppression of the linear Ginzburg–Landau coefficient treated as inverse-design variables. Candidate profiles are screened variationally and then validated by solving the full radial boundary-value problem and comparing Gibbs-energy branches. For a homogeneous cylinder, the L = 1 to L = 2 transition occurs at H1→2 = 0.485411 Hc2. The optimized annular profile, defined by V0 = 1.20, rp = 1.90 ξT, and σ = 0.36 ξT, shifts the transition to H1→2 = 0.383876 Hc2, a reduction of 20.92%, while retaining a comparable L = 2 stability interval. At He/Hc2 = 0.434644, the homogeneous cylinder remains in the L = 1 state, whereas the annularly pinned cylinder is stable in the L = 2 state. A fixed-field two-dimensional pseudo-time-dependent Ginzburg–Landau relaxation benchmark further shows that the optimized annulus produces the smallest L = 2 energy penalty among the tested homogeneous, central-defect, uniform-suppression, and off-axis-defect controls. These results identify annular suppression as a symmetry-preserving route for tuning discrete vortex-state transitions in confined superconductors.</p>