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We study the effect of linearly polarized light on the band structure and longitudinal conductivity in ABC-stacked trilayer graphene. The linearly polarized light can induce a pair of additional points in ABC-stacked trilayer graphene, where conduct and valence bands touch. The locations of these points are determined by the amplitude of the light. Furthermore, the layer pseudospin polarization can be controlled by the light. When the Fermi energy locates at Dirac points, i.e., E f = 0, the longitudinal conductivity shows resonance phenomena when the light is present. Away from the Dirac points, the longitudinal conductivity is unchanged as varying E f for weak light field at larger Fermi energy, and the amplitude of longitudinal conductivity can be controlled by tuning the light field amplitude. Moreover, the effect of linearly polarized light on resonance phenomena in k-cubic Rashba–Dresselhaus system under the irradiating of linearly polarized light is discussed.

We investigate the Hall effects of quadratic band crossing (QBC) fermions in a square optical lattice with spin–orbit coupling and orbital Zeeman term. We find that the orbital Zeeman term and shaking play critical roles in the systems, which can drive a topological transition from spin Hall phases to anomalous Hall phase with nonvanishing (spin) Chern numbers. Due to the interplay among the orbital Zeeman term, spin–orbit coupling, and the shaking, the phase diagram of the system exhibits rich phases, which are characterized by Chern number.

We investigate the photoconductivities of injection current and the shift current in transition metal dichalcogenide with warping term in the presence of sublattice potential and spin orbit coupling. The system shows the valley photoconductivities of injection current and the photoconductivities of shift current. It is found that the warping term and the geometric tensor play a critical role in the system, which are responsible for the photoconductivities. Due to the interplay between the sublattice potential and the spin orbit coupling, the photoconductivities can be tuned. Furthermore, the effect of warping term on geometric tensor and the amplitude of the photoconductivities are also discussed.

In this paper, we study transport properties of the X point in the Brillouin zone of the topological Kondo insulator SmB6 under the application of a circularly polarized light. The transport properties at high-frequency regime and low-frequency regime as a function of the ratio (κ) of the Dresselhaus-like and Rashba-like spin–orbit parameter are studied based on the Floquet theory and Boltzmann equation respectively. The sign of Hall conductivity at high-frequency regime can be reversed by the ratio κ and the amplitude of the light. The amplitude of the current can be enhanced by the ratio κ. Our findings provide a way to control the transport properties of the Dirac materials at low-frequency regime.

Based on the Keldysh Green's functions theory, we present a general formula of the thermal and thermoelectric transport. In the clean limit, our formula recovers the previous results obtained from the semiclassical transport theory. In our approach, we propose an appropriate energy current operator and electric current operator, and the unphysical divergence from the direct application of the Kubo formula is eliminated. As an application, we study the thermal and the thermoelectric Hall conductivities of a gapped Dirac fermion model in the presence of impurity scattering.