As the fundamental solution of the Laplace equation, the logarithm function is the gravitational potential in R 2 . We prove that the logarithm central force problem is block regularizable, that is, the (incomplete) flow may be continuously extended over the singularity at the origin after a re-parametrization. Further, we prove that as the particle approaches the origin, the scattering angle admits a continuous extension at collision, with the particle experiencing a fictitious transmission.

The potential utility of two-dimensional transition-metal dichalcogenides (TMDs) in electronics, thermoelectrics, and spintronics have sparked an increase in scientific interest in the same. In accordance with this, we have done a study on VS2 based device, using first principle Density Functional Theory (DFT) calculations combined with Non-equilibrium Green’s Function (NEGF) formalism to investigate spin transport properties. We constructed a toy-model of a 2-terminal VS2 based device using MATLAB, and further applied a tunneling potential barrier across the channel and measured current through the same, on applying voltage across the terminals. Using the data obtained, we analyzed the spin filtering effect in the device by considering spin splitting in presence of magnetic field, and plotting the spin polarization (SP) and the magnetoresistance (MR) against bias voltage, respectively. The SP is observed to be 36% for a ballistic device between a bias range of 0.3 and 0.5V, which increases to 63% on applying a potential barrier of height twice the Fermi level of VS2. For a ballistic device, we observed an increase in MR from 60% to 76% for large barrier height, within the same bias range as earlier. In each case, the peak value of current per unit cross sectional area of the device was found to be of the order of 10A/μm2. Using these findings, we can conclude that our modeled VS2 device exhibits properties to be used as a promising candidate for spintronic applications.

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