Topological insulators (TIs) have attracted great attention in recent years. These systems have an insulating bulk but gapless edge/surface state protected by time reversal symmetry. There are also rapid developments in finding new phenomena in TIs through interactions with light. The well-known three-dimensional (3D) TI Bi_{2}Se_{3} has only one spin-momentum-locked Dirac cone and a relatively large bulk gap of about 0.3eV, which makes it suitable for terahertz (THz) and mid-infrared applications. In *J. Phys.: Condens. Matter* **25** 425603, we theoretically studied the influence of a continuous linearly polarized THz field on the longitudinal dc conductivity of the Dirac electron formed at the surface of a 3D TI.

We first demonstrated the quasi-energy spectrum of a 3D TI under normal-incidence linearly polarized THz light by means of the Floquet theory. It is found that the photon dressed spectrum is clearly anisotropic and no gap opens at the Dirac point. When the momentum is parallel to the polarized direction of the THz field, the quasi-energy spectrum is the same as the original Dirac energy spectrum. However, when the momentum is perpendicular to the polarized direction, the quasienergy spectrum has a pronounced gap around *k* = 0.5*Ω*/*ν*_{F}, where *Ω* is the THz field frequency. We then derived the time average longitudinal dc conductivity of the irradiated surface electron of a 3D TI using Green’s function and the Kubo formula. Due to the anisotropy of the quasi-energy, the perpendicularly polarized conductivity is generally greater than the parallel. When the chemical potential is zero, the conductivities in both directions undergo an oscillation against the electron-field interaction parameter or THz field strength (figure 1 (top)). We ascribe the increase mainly to the photon-modulated sideband transport around zero energy, and the decrease to the difficult contribution of sidebands far away from zero energy or zero momentum.

When the chemical potential is not zero, the conductivity oscillation behaviour is dramatically suppressed. The conductivity decreases as the field strength increases from zero. In addition, there is a pronounced dip in the dc conductivity at a specific field frequency (figure 1 (bottom)), where the chemical potential is half the THz field energy and lies inside the quasi-energy spectrum gap at *k* = 0.5*Ω*/*ν*_{F} along most directions. The maximum decrease in conductivity can also be modulated by the THz field strength. Therefore, 3D TI samples with different chemical potentials can be used to detect specific THz field frequencies and other devices.