Quantization and confinement effects in superconducting nanostructures

The confinement of the flux lines by a lattice of submicron holes (‘antidots’) has been studied in nanostructured superconducting Pb/Ge multilayers. By introducing regular arrays of sufficiently large antidots, multi-quanta vortex lattices have been stabilized. Sharp cusp-like magnetization (M) anomalies, appearing at matching fieldsH_m=mφ₀/Sin superconducting films with the antidot lattices having a unit cell areaS, are successfully explained. These anomalies are, analogues of the well-knownM(H) cusp atH_c1, but for the onset of multi-quanta (m+1)φ₀-vortices penetration at each subsequent matching fieldH_m. It is shown that theM(H) curve between the matching fieldsH_m<H<H_m+1follows a simpleM∝ln(H−H_m) dependence. These experimental observations have revealed an unusual expansion of validity of the London limit in superconductors with lattices of relatively large antidots. The successful high quality fit of theM(H,T) curves convincingly demonstrates that a new type of the critical stateB=const (‘single-terrace critical state’) can be realized in superconductors with the antidot lattices.