RKKY Interaction In Three-dimensional Tilted Dirac And Weyl Semimetals

The study of topological semimetals is the most advanced direction in condensed matter physics in recent years,in which Dirac and Weyl semimetals plays an important role in topological semimetals.There is zero energy gap and limited contact point be-tween the conduction band and the valence band of Dirac and Weyl semimetals in the three-dimensional Brillouin zone,which is similar to graphene.Currently,a plenty of Dirac and Weyl semimetals materials have been predicted based on the first-principles calculation according to it's band structure,which also have been verified in experiment.The Ruderman-Kittel-Kasuya-Yosida(RKKY)interaction studies the coupling inter-action conducted by free electron in conduction band between two local spins,which is meaningful for understanding the properties of magnetically doped Dirac and Weyl semimetals.In our work,we introduce the tilted Dirac cones and explore the influences of the tilt to the RKKY interaction.We consider the exchange coupling interaction be-tween the impurity spin and the conducted electron as a perturbation,and utilize the Green's function to obtain the analytical expression of the RKKY interaction.Our re-sults show several distinctive features.Firstly,the main influences of the tilted Dirac cones on the RKKY interaction of Dirac and Weyl semimetals is modulation to oscil-lation frequency.For the s-d interaction in the intranode process,we found that the oscillation frequency is highly enhanced by the tilt.For the s-d interaction in the in-ternode process,the range functions of RKKY interaction have two oscillation patterns and the oscillation frequency for one pattern is increased by tilt while the other is sup-pressed.Besides,our results show a non-zero Ising term for homogeneous coupling case in the tilted Dirac SMs.At last,for intrinsically doped case,we find that the tilt could change the ratio of Heisenberg term and Ising term,which may change the type of RKKY interaction in the tilted Weyl SMs with inversion symmetry.Our results enrich the knowledge of magnetic properties of materials with tilted Dirac cones and may see an important application in spintronics.