Zero-Magnetic-Field Hall Effect in Broken-Mirror-Symmetry Conductors under Illumination

A novel effect is predicted for conductors with a broken mirror symmetry [e.g., polar metals and asymmetrical quantum well (QW) structures]: if such a conductor is under the direct current $\mathbf{J}\sim {\mathbf{E}}^{(d)}$, the circular polarized infrared radiation should induce an additional transverse current ${\mathbf{J}}_H\sim {\mathbf{E}}^{(d)}\times \mathbf{c}$, where ${\mathbf{E}}^{(d)}$ is the driving electric field and $\mathbf{c}$ is a vector directed either along the polar axis or perpendicular to a QW. The sign of the current ${\mathbf{J}}_H$ can be reversed by switching the helicity of the light from right to left-handed. Thus the phenomenon is, in fact, something like the Hall effect in which light acts as an external magnetic field.

Figure 1

The diagrams for the changes of the conductivity tensor due to the illumination. The dotted areas denote the impurity-ladder insertions. Note that any of the light vertices of diagrams (b) and (c) can be anomalous.

Figure 2

The diagrams for the impurity-dressed velocity vertex.

Figure 3

The relation showing the cancellation of the antisymmetric parts of the diagrams of Fig. 1c at ${\omega }_0\to 0$.