Floquet-engineered half-valley-metal state in two-dimensional gapped Dirac materials

The half-valley-metal (HVM) states where the gap of one valley is closed while the other valley remains semiconducting are quite crucial for achieving 100% valley polarization and valley-Hall-effect. However, the symmetry of materials makes the HVM states scarce. In this work, using Floquet theory, we demonstrate the laser-dressed HVM states in two-dimensional (2D) gapped-Dirac materials. We show that as a circularly polarized laser is applied to a 2D gapped-Dirac material, the gaps of the two valleys (K and K’) can be regulated by varying the photon energy, amplitude and chirality of the laser. At specific photon energies and laser amplitudes, the linear energy-momentum dispersion of Dirac materials is restituted in one valley while the gap in the other valley is preserved. On the basis of first-principles calculations, we also propose a promising candidate material, boron antimonide (BSb) monolayer to achieve the laser-dressed HVM states. More interestingly, the Berry curvature in the two valleys can be tuned by changing the laser parameters.

Figure 1

Variation of the band gaps at the $K$ and $K^{\prime }$ points under circularly polarized laser as a function of amplitude and photon energy of the laser obtained from the effective Hamiltonian of Eq. (5). (a) The photon energy is set to $\hslash \omega =0.5eV$. The half-valley-metal (HVM) state emerges as the band gap at the $K$ point is closed. (b) The dependence of the band gaps on the photon energy varying from 0.1 to 0.9 eV and the amplitude. The parameters are set to $m_1=-m_2=0.155$, ${\lambda }_v=0.0065$ and ${\lambda }_c=0.005$.

Figure 2

(a) Electronic band structures of BSb monolayer without SOC. The Fermi level is set to zero. The orange and pale blue in band structure represent the contribution of $\mathrm{B}-p_z$ orbitals and $\mathrm{Sb}-p_z$ orbitals. (b) Electronic band structure of BSb monolayer with SOC. The black solid line and red dotted line represent the results from DFT calculation and Wannier fitting, respectively. (c) and (d) The electron wave functions of conduction band maximum and valence band maximum of BSb monolayer.

Figure 3

(a)–(c) Band structures of BSb monolayer around $K$ and $K^{\prime }$ valley near Fermi level under the left-handed CPL with amplitudes of 320 V/c, 514 V/c and 600 V/c and phonon energy of 6 eV, respectively. (d) The variation of bandgap at the $K$ and $K^{\prime }$ valley as a function of amplitude. The solid lines represent the result from the model. The dots represent the result from BSb monolayer. (e) Three-dimensional band structure near the $K$ point with $A=514\mathrm{V}/\mathrm{c}$. (f) The renormalized Berry curvature around $K$ and $K^{\prime }$ with different amplitudes.

Figure 4

Dependence of the band gap of BSb monolayer in the $K$ valley on the photon energy E, and amplitude A. The half-valley-metal state is marked by red dashed lines.