All-optical band engineering of gapped Dirac materials

We demonstrate theoretically that the interaction of electrons in gapped Dirac materials (gapped graphene and transition-metal dichalchogenide monolayers) with a strong off-resonant electromagnetic field (dressing field) substantially renormalizes the band gaps and the spin-orbit splitting. Moreover, the renormalized electronic parameters drastically depend on the field polarization. Namely, a linearly polarized dressing field always decreases the band gap (and, particularly, can turn the gap into zero), whereas a circularly polarized field breaks the equivalence of valleys in different points of the Brillouin zone and can both increase and decrease corresponding band gaps. As a consequence, the dressing field can serve as an effective tool to control spin and valley properties of the materials and be potentially exploited in optoelectronic applications.

Figure 1

Sketch of the considered gapped Dirac materials subject to an electromagnetic wave (dressing field): (a) Graphene grown on the substrate of hexagonal boron nitride; (b) transition-metal dichalcogenide monolayer ${\mathrm{MoS}}_2$.

Figure 2

The energy spectrum of dressed electron, $\tilde{\varepsilon }\left(\mathbf{k}\right)$, near the band edge of gapped graphene (${\mathrm{\Delta }}_g=2$ meV, $\gamma /\hslash ={10}^6$ m/s) irradiated by a dressing field with the photon energy $\hslash \omega =10$ meV and the different intensities, $I$. In parts (a) and (b) the dressing field is linearly polarized along the $x$ axis; the irradiation intensities are $I=0$ (solid lines), $I=7.5\mathrm{kW}/{\mathrm{cm}}^2$ (dashed lines), and $I=15\mathrm{kW}/{\mathrm{cm}}^2$ (dotted lines). In part (c) the dressing field is circularly polarized; the solid line describes the energy spectrum of “bare” electron ($I=0$), whereas the dotted and dashed lines correspond to the different circular polarizations ($\tau \xi =-1$ and $\tau \xi =1$, respectively) with the same irradiation intensity $I=300\mathrm{W}/{\mathrm{cm}}^2$.

Figure 3

Dependence of the band gap in irradiated gapped graphene (${\mathrm{\Delta }}_g=2$ meV, $\gamma /\hslash ={10}^6$ m/s) on the irradiation intensity, $I$, and the polarization, $\theta$, for the photon energy $\hslash \omega =10$ meV. In part (a) the dotted line corresponds to the linearly polarized dressing field, whereas the dashed and solid lines correspond to the different circular polarizations $(\tau \xi =-1$ and $\tau \xi =1$, respectively). In part (b) the dashed lines correspond to the polarizations, $\theta$, which do not change the band gap.

Figure 4

Dependence of the band gap, ${\tilde{\mathrm{\Delta }}}_g$, and the spin splitting of conduction and valence bands, ${\tilde{\mathrm{\Delta }}}_{so}^{c,v}$, on the irradiation intensity for ${\mathrm{MoS}}_2$ monolayer (${\mathrm{\Delta }}_g=1.58$ eV, ${\mathrm{\Delta }}_{so}^c=3$ meV, ${\mathrm{\Delta }}_{so}^v=147$ meV, $\gamma /\hslash =7.7\times {10}^5$ m/s) irradiated by a circularly polarized field with the photon energy $\hslash \omega =10$ meV: (a) The field-induced changing of the band gap and the spin splitting for the circularly polarized field with $\tau \xi =-1$; (b) The renormalized spin-slitting of conduction band for different field polarizations (the solid and dashed lines correspond to $\tau \xi =-1$ and $\tau \xi =1$, respectively).