The gapless edge states with a certain spin and valley index can be realized in topological domain walls. In this work, we study various domain walls thoroughly and demonstrate that multiple kinds of edge states with a perfect spin and valley polarization can be realized, leading to the possibility of establishing spin filters and spin-valley filters. Moreover, the spin and valley index of the edge states can be tuned by an external electric field. We also investigate the finite size effect on the edge states when two domain walls approach each other. Generally, the finite size effect can cause the hybridization of edge states and open a gap. We find that the evolutions of the bandgap as a function of the finite size effect for different topological edge states are distinguished from each other.

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We theoretically study the Landau levels and the magneto-optical conductivity of eight-Pmmn borophene in the presence of a perpendicular magnetic field and an inplane electric field. We find that in the absence of the inplane electric field, the magneto-optical conductivity of eight-Pmmn borophene presents a series of striking single resonance peaks as functions of the frequency ω, and the longitudinal conductivities are found to be anisotropic due to its anisotropic tilted Dirac cones. In the presence of the inplane electric field, some novel effects are predicted on the Landau levels and the magneto-optical conductivity. The Landau level spacings in the two tilted Dirac cones are different, which lifts the degeneracy of the twofold valley, and the magneto-optical conductivity appears a double peak structure. We also discuss the influence of the chemical potential between different Landau levels on the double peak of the magneto-optical response. The valley related magneto-optical properties in the anisotropic structure may make eight-Pmmn borophene a candidate for the new optical devices.

We investigate the magneto-optical transport properties and Landau levels of type-II nodal line semimetals. The tilted liner dispersion in type-II nodal line semimetals makes the conduction band and valence band asymmetric, and Landau levels are coupling in the presence of a magnetic field. We find the background of absorption peaks is curved. The oscillation peaks are tailless with the change of magnetic field. Through tuning tilt term, we find the absorption peaks of optical conductivity change from incomplete degenerate structure to splitting double peaks structure. We also find interband absorption peaks is no longer zero in the imaginary part of Hall conductivity. With the change of the tilt term, the contribution of the absorption peak has two forms, one is that the negative peak only appears at high frequencies, and the other is two adjacent peaks with opposite signs. In addition, the resistivity, circularly polarized light and magnetic oscillation of Hall conductivity are studied.