Theoretical Study Of Anderson Impurities In Two-dimensional Materials

With the development of experimental technology,Kondo effect has been observed in mesoscopic quantum system,and controlled by gate voltage,bias voltage,external magnetic field,temperature and other means.Kondo effect involves the antiferromagnetic exchange coupling between local spin and conduction electrons.Kondo screen of magnetic impurities in metals can be studied directly by measuring the variation of local density spectrum with external parameters.The magnetic impurities in the superconductor will scatter cooper pairs and induce the Yu-ShibaRusinov bound state in the gap.At this time,the Kondo screen effect needs to overcome the energy scale of the superconducting pairing,and the quantum phase transition process can be controlled by adjusting the experimental parameters.Recently,it was found that a single layer molybdenum disulfide material with graphene-like structure,it was direct energy-gap semiconductor,and it was also proved to have strong spin-orbit coupling effect with spin-energy valley locking property,namely Ising spin-orbit coupling.The superconducting transformation can be realized by gate voltage doping with monolayer molybdenum disulfide,and the critical magnetic field intensity parallel to the two-dimensional interface direction is far greater than the Pauli limit,so it has attracted the attention of experiment and theory.In this paper,we will study the Kondo effect of magnetic impurities in molybdenum disulfide materials,and discuss the dominant quantum phase transformation problem caused by the competition between Kondo effect and Ising superconductivity.Based on the single Anderson impurity model,we calculated Ising spin-orbit coupling effect in the material,and superconducting pairing interaction in the conduction band electrons near the K and-K point.Then the local electronic Green's function is obtained by processing the Hamiltonian of the system with the equation of motion of the Green's function.According to the numerical results,it was found that Ising spin-orbit coupling effect had the opposite effect on the Kondo screen effect of impurities in the different cases of electron doping and hole doping,and the Kondo effect strength of the system could be further adjusted by regulating the chemical potential of the system.In the case of electron doping,Ising spin-orbit coupling was able to protect the cooper pairs,and Kondo effect was inhibited within Ising spin-orbit coupling effect when the chemical potential intersected both spinsplitting bands.With the enhancement of Ising spin-orbit coupling effect,the ground state of system was gradually transformed from Kondo singlet to magnetic doublet.When the chemical potential only intersects one of the spin-splitting bands,Ising spin-orbit coupling effect can enhance Kondo effect.In the case of hole doping,the Fermi surface passed through two spin-splitting bands between the valleys,and the Yu-Shiba-Rusonov bound state was very close to the energy gap.Due to the broadening of the impurity level,Ising spin-orbit coupling effect was enhanced on Kondo effect.Kondo effect was inhibited by Ising orbital coupling effect when the sum of chemical potentials was intersected within one of the two spin-splitting bands.This work studied the effect of Ising spin-orbit coupling on Kondo effect through theoretical calculation,providing theoretical support for the design of new spintronics device based on transition metal disulfide material.