Research On Transport Characteristics In Skyrmion Crystal And Lieb Lattice System

Skyrmions with the topological number Nsk equal to an integer larger than 1 are called high-topological-number skyrmions or high-Nsk skyrmions.In this work,we theoretically study the topological Hall effect in square-lattice high-Nsk skyrmion crystals(SkXs)with Nsk=2 and Nsk=3.As a result of the emergent magnetic field,the Landau-level-like electronic band structure gives rise to quantized Hall conductivity when the Fermi energy is within the gaps between the adjacent single band and intertwined multiple bands.We found that different from the conventional(Nsk=1)SkX,the Hall quantization number increases by 1/Nsk on average when the elevating Fermi energy crosses each band.We attribute the result to the fact that the Berry phase e is measured in the momentum space and the topological number of a single skyrmion Nsk is measured in the real space.The reciprocality does not affect the conventional SkX because Nsk=1=1/Nsk.In general,the Dirac-Weyl Fermi system with pseudospin-1 can make incident electrons exhibit complete transmission of the barrier in addition to the normal incidence of the barrier,and within a larger range of incident angles,it can also show complete transmission of the barrier.This paper presents a transport theory that connects the Lieb lattice tight-binding model and the pseudospin-1 Dirac equation.Taking Lieb lattice as the research object,we studied the influence of incident electron energy,Lieb lattice barrier height,and barrier width on the transmission probability of incident electrons based on Green's function theory.We found that when the incident electron energy Ef is exactly 0.5 times the height of the barrier V0,the incident electron exhibits complete transmission of the barrier in all incident angle ranges,which is a manifestation of the super Klein tunneling.In addition,when the wave vector qx of the incident electron meets certain conditions,the transmission probability curve will show several maximum peaks with a transmission probability of 1,which is a manifestation of the resonance transmission effect.Combining these transport characteristics,this article believes that Lieb lattice has a higher average transmission probability than graphene.