Interactions Remove the Quantization of the Chiral Photocurrent at Weyl Points

The chiral photocurrent or circular photogalvanic effect (CPGE) is a photocurrent that depends on the sense of circular polarization. In a disorder-free, noninteracting chiral Weyl semimetal, the magnitude of the effect is approximately quantized with a material-independent quantum $e^3/h^2$ for reasons of band topology. We study the first-order corrections due to the Coulomb and Hubbatrd interactions in a continuum model of a Weyl semimetal in which known corrections from other bands are absent. We find that the inclusion of interactions generically breaks the quantization. The corrections are similar but larger in magnitude than previously studied interaction corrections to the (nontopological) linear optical conductivity of graphene, and have a potentially observable frequency dependence. We conclude that, unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in Weyl semimetals is not protected but has perturbative corrections in interaction strength.

Figure 1

Schematic picture of two Weyl nodes of opposite chirality separated by energy $|{\mu }_1|+|{\mu }_2|$. The quantization of the circular photogalvanic effect in the noninteracting material occurs provided $2|{\mu }_1|<\omega <2|{\mu }_2|$.

Figure 2

First-order self-energy [(a)–(d)] and vertex [(e)–(f)] corrections. Solid and dashed lines correspond to the Green’s function of the first and second node, respectively. Diagrams (a), (c), and (e) describe the intranodal processes, while (b), (d), and (f) stand for the internodal scattering (important only for the Hubbard interaction).

Figure 3

The dependence of function $F$, Eq. (14), on $q_0$ at $|\mu |/\omega =0.00$, 0.40, and 0.43 for the cases of the soft-cutoff and the dimensional regularizations. At $v_F{q}_0\gg \omega$, all curves approach $F=0$.