Study On Bogoliubov Quasi-particle Interference Spectrum In Multi-band Superconductor CeCu₂Si₂

As the first unconventional superconductor discovered,the heavy fermion compound CeCu₂Si₂ has been widely concerned by people.The emergence of CeCu₂Si₂has broken the public's understanding of the microscopic mechanism of traditional superconductivity,and CeCu₂Si₂ has been the top priority in the research of heavy fermion superconductors since its emergence for more than 40 years.The study of heavy fermion superconductors is very important to explore the micro mechanism of unconventional superconductors,and can promote the development of other novel superconductors.In recent years,a large number of low-temperature experiments have revealed that CeCu₂Si₂ is a multi-band superconductor.Through calculation,it is found that its Fermi surface is mainly composed of a light hole band and a heavy electron band.In addition,a large number of studies have proposed that there is nodeless gap in CeCu₂Si₂,and the pairing symmetry of CeCu₂Si₂ supports the s-wave of the node with no gap,such as the pairing of s^+--wave with sign inversion and s⁺⁺-wave without sign inversion.Due to the special topological structure of the Fermi surface of CeCu₂Si₂,the traditional phase-sensitive measurement method cannot detect and distinguish the pairing symmetry well.As this time,the high-resolution scanning tunneling microscope(STM)experiment can be used as a new spectral measurement technology to directly detect the band structure;the heavy fermion quasi-particle interference spectrum(QPI)can be used to determine the quasi-particle pairing relationship at lower temperature,and measure the detailed momentum space gap function in the range of microelectronic volt energy.This paper theoretically applies this calculation method to CeCu₂Si₂ to distinguish its superconducting energy gap structure.Firstly,we apply the LDA+U method to calculate the dual band model of CeCu₂Si₂hybrid.In this paper,the influence of a single nonmagnetic impurity on the local electronic density of states in momentum space,namely the Bogoliubov quasi-particle interference spectrum,is calculated by using T-matrix approximation combined with the Green's function method in the double band model.We find that under the limit of Born scattering,only the quasi-particle coherent peaks of d²²_x-y-wave and d_xy-wave pair change with the change of energy,while the QPI images of s^+--wave and s⁺⁺-wave pair do not change with the change of energy.Then,in order to distinguish the nodeless s^+--wave and s⁺⁺-wave pairs,the impurity scattering intensity was increased to the strong scattering limit.It is found that only after the introduction of inter-band impurity scattering,the symmetry of s^+--wave and s⁺⁺-wave pairs would be affected with the change of energy.At this time,we can make a clear distinction between nodeless s^+--wave and s⁺⁺-wave.These calculation results can provide a theoretical basis for the experimental observation of scanning tunneling spectrum,thereby help to clarify the superconducting gap symmetry of CeCu₂Si₂.