Revealing Berry curvature of the unoccupied band in high harmonic generation

Abstract

Experimental determinations of the net Berry curvature have been made for the occupied band because they are basically available on the basis of electronic and magnetic responses of carriers occupying the band, for instance, through the measurement of the anomalous Hall effect or the magneto-optical Kerr effect. Here, we investigate the circular dichroism of the high-order harmonic generation (HHG) in undoped monolayer ${\mathrm{MoS}}_{2}$. Breaking the threefold rotational symmetry of the pristine monolayer ${\mathrm{MoS}}_{2}$ by applying uniaxial strain and an external bias field, we find that the third-order HHG signals deliver nonvanishing dichroic signatures. These signatures are essentially identical as the net Berry curvatures obtained from the electron-doped monolayer ${\mathrm{MoS}}_{2}$ with the aforementioned symmetry broken. This finding implies an experimental challenge to observe the net Berry curvature of the unoccupied empty band, which should open another stage toward the advancement of valleytronics.