Diverging shift current responses in the gapless limit of two-dimensional systems

The shift current responses of two-dimensional systems in the gapless limit are investigated. As the energy gap becomes smaller, the interband transition probability becomes larger at the band edges. We find the divergence of the shift current response in a manner proportional to the inverse of the gap size when the system becomes a two-dimensional Weyl semimetal in the gapless limit. This behavior is different from that for electric polarization, which remains finite and has a jump across the gapless limit. It means that the quantitative relationship between electric polarizations and shift currents is broken in this gapless limit.