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We consider a ring geometry with a quantum dot (QD) embedded in one of its arms, which is coupled symmetrically to two normal leads and threaded by Aharonov-Bohm (AB) flux φ. The QD is coupled to a topological nanowire. Using scattering matrix method, the differential conductance and current cross correlation are investigated. By varying the external magnetic field strength and the coupling strength between the QD and Majorana bound state (MBS), the zero-bias conductance peak (ZBCP) will split and oscillate due to the overlapping of the two MBSs. Due to the sum rule in a pair of well-separated MBSs, the total differential conductance at zero bias voltage is quantized to 2 e 2/ h. The total differential conductance and the current cross correlation show the periodicity of π with zero QD energy level and 2 π with nonzero QD energy level. • The differential conductance and the current cross correlation in an AB ring with QD embedded in one of its arms are investigated. • The zero-bias conductance peak split and oscillate due to the overlapping of the two MBSs. • The total differential conductance and the current cross correlation show the periodicity of π with zero QD energy level. [ABSTRACT FROM AUTHOR]

Performing the scattering matrix approach, we calculate the current noise cross correlation and the differential conductance in the Majorana bound states (MBSs) comb. The teeth on the comb consist of topological super-conducting nanowire sandwiched between two quantum dots (QDs). We find that the nonlocal property of MBSs comb can be effectively modulated by the quantum dots. For only one "QD-MBSs-QD" building block, N = 1, the current noise cross correlation is negative at small bias and becomes positive at lager bias. A zero bias conductance peak of 2 e 2/ h can be found, and it splits with ϵ u increasing, where ϵ u is the energy level of up-part QD. For N ≥ 2, the current noise cross correlation is zero at small bias and becomes positive at larger bias. Different from the case of N = 1, the zero bias conductance peak is 4 e 2/ h due to the local Andreev reflection. Besides, we find that the differential conductance is robust against the influence of N. • The current noise cross correlation and the differential conductance in the Majorana bound states (MBSs) comb are investigated. • The MBSs comb can be effectively modulated by the up-part quantum dots due to the effective resonance between the Majorana bound state and the dot. • For only one "QD-MBSs-QD" building block, N = 1, a zero bias conductance peak of 2 e 2/ h can be found. For N = 2, the zero bias conductance peak is 4 e 2/ h. [ABSTRACT FROM AUTHOR]