The Effect Of Spin Flip Scattering On Thermal Transport Properties In Majorana Fermions Structure

Majorana fermions has been widely explored because of its special properties and wide application prospects.In this paper,we add spin flip scattering to the structure that Majorana fermions side coupled to the quantum dot,and study the thermoelectric transport properties of this structure from two aspects: the electron with Coulomb interaction and the electron without Coulomb interaction.In this paper,firstly,we use the method of motion equation,and use some approximate methods to calculate the Green functions we studied in the structure.And the expressions of the state density,conductance,thermal conductance,thermopower and figure of merit are also expressed.Secondly,we consider that there is a quantum dot in the middle of the left and right ferromagnetic electrodes,then add Majorana fermions to the quantum dot,and separate the electrons from the up spin and down spin.With the increase of the coupling coefficient between the quantum dot and the first Majorana fermion,the state density and conductance of the spin up and spin down are calculated.Then we find that the state density and conductance of spin up are unaffected,while the state density and conductance of spin down have been divided into three peaks,it is because the coupling coefficient is only coupled with the electron of spin down.Based on this result,we add spin flip scattering to this structure.It is found that the state density and conductance of spin up are affected by the coupling coefficient,the energy level splits and the maximum value no longer appears at the quantum dot energy level.Moreover,the spin flip scattering mainly affects the spin up electrons,which suppresses the conductance at the Fermi level of the spin up electrons,resulting in the energy level splitting.And for the density of states and conductance of spin down electronic,it has little effect on the side peaks due to the addition of the Majorana fermion.Lastly,the influence of thermoelectric effect on coupling coefficient of the electron with the Majorana fermion,the spin flip coefficient and the polarization constant is calculated when there is Coulomb interaction and no Coulomb interaction in the quantum dot.And the comparison between the two electrodes is made.In a words,the coupling of electron with the Majorana fermion will split the energy levels,so the conductance in the energy levels of quantum dots are split into three peaks.When the Coulomb interaction intensity is added(U = 5),a peak will appear at the energy level position opposite(? = 2.5)to the quantum dot energy level.However,this peak is not only related to the intensity of Coulomb interaction,but also related to the number of the Majorana fermions.It is clear that the coupling between the first and the second Majorana fermion is competitive with the coupling of electrons in the quantum dot and the first Majorana fermion,which leads to the appearance or disappearance of this peak.We further add spin filp scattering,and find that spin flip scattering also plays an important role in tuning this peak: When the spin flip coefficient is small,the range is 0 to 0.4,the conductance at ? = 2.5 is zero,it is suppressed,but when the spin flip coefficient R = 0 or R ? 0.4,a peak conductance will appear at ? = 2.5.When the spin flip coefficient is equal to 0.1,the thermal efficiency of the structure is the highest,so our research work will be helpful to the improvement of thermal efficiency.In addition,when the ferromagnetic electrodes are parallel,the change of the polarization constant will change the values,but when the ferromagnetic electrodes are antiparallel,the change of the polarization constant has no effect on the thermoelectric effect.