Quantum information aspects on bulk and nano interacting Fermi system: A spin-space density matrix approach

•In contrast to a s-wave superconductor, the quantum correlation of the d-wave superconductor is sensitive to the change of the gap magnitude.•Quantum discord of the d-wave superconductor oscillates.•Quantum discord becomes zero at a characteristic length of the d-wave superconductor.•Quantum correlation strongly depends on the length of grain. Length of the superconductor lower, the quantum correlation length higher.•Quantum tripartite entanglement for a nano-scale d-wave superconductor is better than for a bulk d-wave superconductor.

By approximating the energy gap, entering nano-size effect via gap fluctuation and calculating the Green's functions and the space-spin density matrix, the dependence of quantum correlation (entanglement, discord and tripartite entanglement) on the relative distance of two electron spins forming Cooper pairs, the energy gap and the length of bulk and nano interacting Fermi system (a nodal d-wave superconductor) is determined. In contrast to a s-wave superconductor, quantum correlation of the system is sensitive to the change of the gap magnitude and strongly depends on the length of the grain. Also, quantum discord oscillates. Furthermore, the entanglement length and the correlation length are investigated. Discord becomes zero at a characteristic length of the d-wave superconductor.