Hysteresis in mesoscopic superconducting disks: the Bean-Livingston barrier

The magnetization behavior of mesoscopic superconducting disks can show hysteretic behavior which we explain by using the Ginzburg-Landau (GL) theory and properly taking into account the de-magnetization effects due to geometrical form factors. In large disks the Bean-Livingston surface barrier is responsible for the hysteresis. While in small disks a volume barrier is responsible for this hysteresis. It is shown that although the sample magnetization is diamagnetic (negative), the measured magnetization can be positive at certain fields as observed experimentally, which is a consequence of the de-magnetization effects and the experimental set up.