Temperature dependence of Vortex Charges in High Temperature Superconductors

Using a model Hamiltonian with d-wave superconductivity and competing antiferromagnetic (AF) interactions, the temperature (T) dependence of the vortex charge in high T_c superconductors is investigated by numerically solving the Bogoliubov-de Gennes equations. The strength of the induced AF order inside the vortex core is T dependent. The vortex charge could be negative when the AF order with sufficient strength is present at low temperatures. At higher temperatures, the AF order may be completely suppressed and the vortex charge becomes positive. A first order like transition in the T dependent vortex charge is seen near the critical temperature T_{AF}. For underdoped sample, the spatial profiles of the induced spin-density wave and charge-density wave orders could have stripe like structures at T < T_s, and change to two-dimensional isotropic ones at T > T_s. As a result, a vortex charge discontinuity occurs at T_s.Comment: 5 pages, 5 figure

Existence Of Best Proximity Points Satisfying Two Constraint Inequalities

In this paper, we prove the existence of best proximity point and coupled best proximity point on metric spaces with partial order for weak proximal contraction mappings such that these critical points satisfy some constraint inequalities © 2020. American Institute of Mathematical SciencesWe Would Like To Express Our Gratitude To The Anonymous Referees For Their Helpful Suggestions And Corrections