In this work, we have studied the spin-dependent quantum transport of charged fermion on ( 2 + 1 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2+1)$$\end{document} -dimensional spacetime, whose spatial part is described by a wormhole-type geometry in the presence of constant axial magnetic flux. Choosing the solutions of the Dirac equation associated with real energy and momentum, we explored the spin-dependent transmission probabilities and giant magnetoresistance (GMR) through a single layer of wormhole graphene with an external magnetic field, using the transition matrix (T-Matrix) approach. The spin-up and spin-down components within the A and B sublattices of graphene in the matrix of 4 x 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\times 1$$\end{document} wave function are coupled to each other due to the wormhole structure and the magnetic field. We have found that transport properties strongly depend on the magnetic field, incident energy, and geometric parameters of the system. We observed that the transmission probability increases as the radius of the wormhole increases, and the length of the wormhole decreases. The higher energies lead to a decrease in the transmission probabilities of particles. Furthermore, we observed that the probability of the spin-flip effect is almost larger than that of the non-spin-flip effect, illustrating that electrons lose their spins during transmission. These findings highlight the complex and interesting behavior of wormhole graphene in the presence of external magnetic fields and suggest that these nano structures can have potential applications in electronic and spintronic devices.
