R/ξ 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 D/ξ 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8 State µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ µ/µ$_{0}$ Meissner 0-36 < 100 < 100 < 100 0-18 0-76 < 100 < 100 0-14 0-46 < 100 < 100 0-14 0-20 0-22 0-22 1 GVS - - - - 20-30 78-100 - - 16-24 48-76 - - 16-22 22-100 - - 2 GVS - - - - 32 - - - 26-30 78-100 - - 24-30 - - - 3 GVS - - - - - - - - 32-38 - - - 32-36 - - - 4 GVS - - - - - - - - 40-50 - - - 38-44 - - - 5 GVS - - - - - - - - - - - - 46-50 - - - 3-fold - - - - - - - - - - - - - 34-38 24-34 24-32 4-fold - - - - - - - - - - - - - 40-44 36-42 34-40 5-fold - - - - - - - - - - - - - 46-52 44-48 42-48 6-fold - - - - - - - - - - - - - 54-56 50-54 50-58 7-fold - - - - - - - - - - - - - - 56-62 - Meissner - - - - - - - - - - - - - - 64-74 60-100 1 GVS - - - - - - - - - - - - - - 76-100 - Normal > 36 ? ? ? > 32 ? ? ? > 50 ? ? ? ? ? ? ? Table 1: The sequence of ground states for the of rods considered here. The magnetic dot is positioned 2 ξ away from the rod’s top surface and oriented along the z -axis. The question mark means the normal state was not reach. [11] A. R. de C. Romaguera, M. M. Doria, F. M. Peeters, [10] M. M. Doria, A. R. de C. Romaguera, F. M. Peeters, Unpublished. [9] A. Y. Aladyshkin, D. A. Ryzhov, A. V. Samokhvalov, D. A. Savinov, A. S. Mel’nikov, V. V. Moshchalkov, Phys. Rev. B 75 (18) (2007) 184519. [8] D. G. Gheorghe, R. J. Wijngaarden, W. Gillijns, A. V. Silhanek, V. V. Moshchalkov, Phys. Rev. B 77 (5) (2008) 054502. [7] M. J. Van Bael, K. Temst, V. V. Moshchalkov, Y. Bruynseraede, Phys. Rev. B 59 (22) (1999) 14674. [6] Z. Yang, M. Lange, A. Volodin, R. Szymczak, V. V. Moshchalkov1, Nature Material 3 (2004) 793. [5] M. V. Miloˇsevi´c, G. R. Berdiyorov, F. M. Peeters, Phys. Rev. B 75 (5) (2007) 052502. [4] A. R. de C. Romaguera, M. M. Doria, F. M. Peeters, Phys. Rev. B 76 (2) (2007) 020505. [1] B. J. Baelus, F. M. Peeters, V. A. Schweigert, Phys. Rev. B 63 (14) (2001) 144517. [2] I. V. Grigorieva, W. Escoffier, J. Richardson, L. Y. Vinnikov, S. Dubonos, V. Oboznov, Phys. Rev. Lett. 96 (7) (2006) 077005. [3] A. Kanda, B. J. Baelus, F. M. Peeters, K. Kadowaki, Y. Ootuka, Phys. Rev. Lett. 93 (25) (2004) 257002. 4 4. Conclusions 5. Acknowledgment Figure 4: (Color online) Isosurfaces of the Cooper pair density for a mesoscopic rod with R = 4 ξ and D = 6 ξ . Ev- ery image corresponds to one of the states N-folder states listed in Table 1. A. R. de C. Romaguera acknowledges the brazilian agency FACEPE for financial support. M. M. Doria acknowledges CNPq and FAPERJ. F. M. Peeters acknowledges Flemish Science Foundation (FWO-Vl), the Belgian Science Pol- icy (IUAP) and the ESF-AQDJJ network. Using Simulated Annealing, a truly three- dimensional approach, we obtain the vortex pat- terns of mesoscopic rods with a point-like mag- netic moment on top. We conclude that rods with thickness smaller than 4 ξ can be considered as thin disks since only top to bottom giant vortex states are obtained. For rods with thickness big- ger than 4 ξ , we observed the appearance of N-fold vortex states, namely N top-to-side vortices. The onset and disappearance of these states is from a single GVS or Meissner state line, as contin- uous transitions from it. Consequently, for suffi- cient large magnetic moments one can retrieve the Meissner state before reaching the normal state, and this, leads to a reentrant behavior. References