Impact of Majorana fermions on the Kondo state in the carbon nanotube quantum dot
We have studied the quantum conductance of the Kondo state in the carbon nanotube quantum dot (CNTQD) with side-attached multi-Majorana fermion states in topological superconductors (TSCs). The zero-energy Majorana fermions interfere with the fourfold degenerate states of the CNTQD in the spin-orbital Kondo regime. Using the extended Kotliar-Ruckenstein slave-boson mean-field approach, we have analyzed the symmetry reduction of the SU(4) Kondo effect to the SU$^{\star}$(3) Kondo state with a fractional charge in the system by increasing the tunneling strength to a single Majorana fermion (TSC). We observed the fractional quantum conductance, the residual impurity entropy, the enhancement of the thermoelectric power with two compensation points, the fractional linear and nonlinear Fano factor ($F_{K}$) and the spin polarization of the conductance. Two Majoranas (2TSC) in conjunction with the CNTQD have reduced the spin-orbital Kondo effect to the SU$^{\star}$(2) Kondo state with 2e in the system. $F_{K}$ contains information about the effective charge and the interaction between the quasiparticles, two- and three-body correlators and identifies the broken symmetry of the Kondo state. We discussed the local quadratic Casimir operator separately for the states associated with the Kondo effect and the Majorana fermion state to show the difference between the fluctuations of the pseudospin in both quantum channels. We have shown that the device coupled with three Majorana fermions (3TSC) achieves a quantized conductance $5/2(e^{2}/h)$, conserves the U$^{\star}$(1) charge symmetry at the electron-hole symmetry point and manifests the increase in nonlinear current and shot noise due to the entanglement in octuplets with opposite charge-leaking states. Furthermore, we have investigated the influence of the spin-orbit interaction in the CNTQD-TSC device on the quantum transport properties.