Optical conductivity of unconventional charge-density-wave systems: Role of vertex corrections

The optical conductivity of a $d$-CDW conductor is calculated for electrons on a square lattice and a nearest-neighbor charge-charge interaction using the lowest-order conserving approximation. The spectral properties of the Drude-like peak at low frequencies and the broad hump due to transitions across the gap at large frequencies are discussed, also as a function of temperature and of the second-nearest neighbor hopping term $t^{\prime }$. We find that vertex corrections enhance the dc conductivity, make the Drude peak narrower and provide a smooth transition from a renormalized regime at low to the bare theory at high frequencies. It is also shown that vertex corrections enhance the temperature dependence of the restricted optical sum leading to a non-negligible violation of the sum rule in the $d$-CDW state.

Figure 1

Diagrammatic representation of the integral equation for the current vertex.

Figure 2

(Color online) Spectral gap ${\Delta }_0$ and the parameter $b$ as a function of temperature $T$, using $2J$ as the energy unit.

Figure 3

Optical conductivity $\sigma \left(\omega \right)$ with (solid line) and without (dashed line) vertex corrections.

Figure 4

(Color online) Low-frequency behavior of $\sigma \left(\omega \right)$ with (solid curve) and without (dotted curve) vertex corrections. The dashed curve is a Lorentzian with the same value $\sigma \left(0\right)$ as the solid curve.

Figure 5

Restricted optical sums with (solid line) and without (dot-dashed line) vertex corrections, and Drude weights with (dashed line) and without (dotted line) vertex corrections.

Figure 6

(Color online) Optical conductivity $\sigma \left(\omega \right)$ for $T=0$, $\Delta =0.197$ (solid line), $T=0.06$, $\Delta =0.158$ (dashed line), and $T=0.08$, $\Delta =0.041$ (dot-dashed line).