A nano size pyramidal superconducting tip is characterized theoretically. Vortex states are achieved in the framework of three-dimensional (3D) numerical discretization of Ginzburg-Landau (GL) formalism. Systematic investigation is performed according to the geometric parameters of the tip and different GL parameter κ. Meissner state and critical field of the tip are obtained in the presence of external magnetic field which is perpendicular to the square base of the tip. It is found that upper critical field H_c2 comes to lower with increasing κ but superconductivity persists up to higher filed in case of a much sharp tip. The results are important to comprehend the properties of superconducting tips, which are presently employed in scanning tunneling microscopy (STM), in the presence of an external magnetic field.

在理论上表征了纳米尺寸的金字塔形超导尖端。涡态是在Ginzburg-Landau（GL）形式主义的三维（3D）数值离散化框架中实现的。根据尖端的几何参数和不同的GL参数κ进行系统的研究。尖端的迈斯纳状态和临界场是在存在垂直于尖端方形底部的外部磁场的情况下获得的。发现上临界场H _{c 2}随着κ的增加而降低但是在出现非常尖锐的尖端时，超导电性会持续到更高的场。该结果对于理解在存在外部磁场的情况下目前用于扫描隧道显微镜（STM）的超导尖端的特性很重要。