Unconventional Charge Density Wave And Superconductivity In Kagome Superconductors

Charge density wave is the modulation of charge density in real space.It was first proposed in one-dimensional metals,and then extended to two-dimensional sys-tems.It has been widely studied in two-dimensional transition metal sulfide and some high-temperature superconductors.At the beginning of 2021,in a newly discovered kagome superconductors(1₃(7₅(=,（7,）,the 2×2 charge density wave which breaks time-reversal symmetry was observed,the discovery of this charge density wave has aroused great concern and extensive research interest in condensed matter physics.With the deepening of the research,more novel phenomena have been discovered in the kagome superconductors,such as:electronic nematic phase,pair density wave and so on.This paper focuses on introducing the chiral flux phase we proposed to describe the time-reversal-symmetry-breaking（TRSB）charge density wave,and properties of the su-perconductivity in Kagome superconductors when considering the presence of the chiral flux phase.The chiral flux phase breaks both time-reversal symmetry and spatial trans-lational symmetry,and its model describes a Chern insulator,by using this property,we can explain the time reversal symmetry breaking and intrinsic anomalous Hall ef-fect observed in experiments.Moreover,by calculating the local density of states,we find the distribution of the charge density on Kagome lattice is 2×2,which is consistent with the experimental observation.From the point of view of the low energy effective model,the chiral flux phase can be regared as the scattering between three van Hove singularities with pure imaginary coefficient.The property that the coefficient must be pure imaginary is derived from the form of the structure factor and the commensurable condition.Thus the chiral flux phase can be regarded as the extension of the d-density wave on Kagome lattice.In addition,we find out all flux phase within 2×2 unit cell,and classify them by symmetry.As for the superconductivity,the decreasing of the knight shift at superconduc-tivity transition temperature and the Hebel-Slichter peak show that the superconduc-tivity in Kagome superconductor belongs to the s-wave spin singlet superconductivity.However,the nonzero residual thermal conductivity shows that the superconductivity in Kagome superconductor is nodal superconductivity.The local density of states of the quasiparticle in different areas show different node properties measured by scanning tunneling microscope（STM）.By analysing the results of the first principle calculation,we construct a four band model by using the local(92-2orbital of the V atoms and theorbital of the Sb atoms.In this model,the boundary state in the chiral flux phase which is not affected by the s-wave superconductivity is used to explain the seemingly contradictory phenomena about the node properties observed in the experiments.Then we considered the coupling of the chiral flux phase and the s-wave superconductivity,and proposed that the time-reversal-symmetry-breaking-pair superconductivity can be induced in Kagome superconductors.The model of-pair superconductivity has been established.With this model,we conclude that the magnetic moment increases with the increasing of the strength of-pair superconductivity.We believe that the newly discovered TRSB superconductivity under pressure is-pair superconductivity,which can be used to explain the further raising of the muon-spin relaxation rate below the new superconductivity transition temperature under pressure.Finally,we discussed some other theories about the intertwined orders in Kagome superconductors.We also prospected the detecting of the chiral flux phase in exper-iments and further studying in theories.In short,as a material with rich phases,the Kagome superconductor is useful for studying the competition or coexistence of vari-ous phases.To reveal the origin of the TRSB charge density wave orders,pair density wave and electron nematic orders in Kagome superconductors,all of us need to think and explore more deeply in both theory and experiment.The exploration of these novel physical effects raises the possibility of the born of new physical mechanisms.