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In the framework of the Dirac-Bogoliubov-de Gennes formalism, we investigatethe transport properties in the surface of a 3-dimensional topologicalinsulator-based hybrid structure, where the ferromagnetic and superconductingorders are simultaneously induced to the surface states via the proximityeffect. The superconductor gap is taken to be spin-singlet $d$-wave symmetry.The asymmetric role of this gap respect to the electron-hole exchange, in onehand, affects the topological insulator superconducting binding excitationsand, on the other hand, gives rise to forming distinct Majorana bound states atthe ferromagnet/superconductor interface. We propose a topological insulatorN/F/FS junction and proceed to clarify the role of $d$-wave asymmetry pairingin the resulting subgap and overgap tunneling conductance. The perpendicularcomponent of magnetizations in F and FS regions can be at the parallel andantiparallel configurations leading to capture the experimentally importantmagnetoresistance (MR) of junction. It is found that the zero-bias conductanceis strongly sensitive to the magnitude of magnetization in FS region $m_{zfs}$and orbital rotated angle $\alpha$ of superconductor gap. The negative MR onlyoccurs in zero orbital rotated angle. This result can pave the way todistinguish the unconventional superconducting state in the relatingtopological insulator hybrid structures.

Asymmetric $d$-wave superconducting topological insulator in proximity with a magnetic order