Static properties of STM tip in response to magnetic field
Introduction
The significance of the study of superconducting tips is raising remarkably because of the advancement of modern fabrication technique. There are growing interests to explore the properties of superconducting tips of scanning tunneling microscope [1] for their unique performance such as; superconducting tips have been used to increase the resolution of the spectroscopy [2], [3], [4], [5], [6], [7]. In general, it is observed that the pyramidal shape of the tip offers to increase the critical field several times than the bulk critical field of the tip’s material [8]. In a sharp pyramidal tip, superconductivity remains at the tip’s apex within large stability of the Meissner state [9]. Micropatterned diamond pyramidal tips have been characterized by Kang et al. [10]. Pan et al. observed atomic image of a NbSe2 surface and the tunneling current by STM with Niobium tip which was fabricated following a mechanical polishing method [11]. Uehara et al. studied the capability of Niobium tip to produce STM images of highly oriented pyrolytic graphite and Au surfaces with atomic spatial resolution [12]. The magnetic field dependence properties of the superconducting tip has been examined by Rodrigo et al. [13]. By using a superconducting tip, Kohen et al. investigated the superfluid velocity on the surface of a superconductor [14]. Martin-Rodero et al. theoretically studied the dc Josephson effect in a STM configurations and evoked that the Josephson current could be applied as a further probe for surface investigations [15].
Several theoretical works have been conducted on superconducting tips within three dimensional Ginzburg-Landaue formalism. When the scanning tunneling spectroscopy investigated the specimen surfaces through a superconducting tip in the presence of an applied field, superconductor condensate of the tip could be interrupted by the possible presence of vortices. Vortex phenomenology of mesoscopic superconductors (the dimension of the sample is comparable to the coherence length ξ or to the magnetic penetration depth λ) has been observed in a well accepted way and explained in various perspectives [16], [17], [18], [19]. Misko et al. studied theoretically a superconducting bridge following the Ginzburg-Landau theory and explained giant vortex states [20]. Vortex configurations of a pyramidal STM tip in the presence of 3D tilted applied magnetic field have been reported in Ref. [21]. Vortices in a superconducting cone shaped tip of STM in the presence of an applied field are analyzed by Chen et al., they found giant vortex states, curved multivortex states and a combination of both of them [22].
In this work, we would like to study the entry/exit point of the vortex in the superconducting pyramidal tip with their stability in the presence of magnetic field with the dimensions of the sample by applying Ginzburg-Landau theory which has the importance for experiment as well. The amount of flux penetrating the superconducting pyramidal tip as a function of the height of the sample to be investigated. Here, the tip in magnetic field is fully characterized in three dimensions and the magnetic moment of the whole sample has been considered as well as vortex configurations are studied in detail.
Section snippets
Methods and theoretical formalism
STM pyramidal tip made with type II (i.e. for characteristic length λ > ξ) superconducting materials is considered immersed in an insulating medium (e.g. air) and exposed to uniform magnetic field (super conducting region as well as in non-superconducting region; in whole 3D space of simulations) along with z-axis. Using the dimensionless variables and the London gauge div for vector potential we write the system of two coupled Ginzburg-Landau (GL) equations [23], [24], [25] in the
Results
The free energy of PR tip sample as a function of the applied magnetic field and various superconducting static properties such as; ISO-surface plots from 3D data of Cooper pair density (|ψ|2), contour plots of phase of the order parameter (φ) and |ψ|2, and quiver plots of super current (J3D) at corresponding vortex (L) states are shown in Fig. 2 at T=0.70Tc and Ginzburg-Landau parameter κ=3. Phase change from zero to 2π are shown by white to Magenta. The total number of vortex nucleation
Conclusion
In this work, superconducting critical properties and magnetic behavior of mesoscopic superconducting pyramidal tip are investigated. The vortex states of a mesoscopic superconducting pyramidal sample were achieved by solving two coupled nonlinear static Ginzburg-Landau equations self consistently. The magnetic field is applied perpendicular to the base of the tip with demagnetization effects are fully taken into account. We reported different vortex configurations by changing the size of the
Declaration of Competing Interest
None.
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