Berry Curvature Effects on Quasiparticle Dynamics in Superconductors

We construct a theory for the semiclassical dynamics of superconducting quasiparticles by following their wave packet motion and reveal rich contents of Berry curvature effects in the phase space spanned by position and momentum. These Berry curvatures are traced back to the characteristics of superconductivity, including the nontrivial momentum-space geometry of superconducting pairing, the real-space supercurrent, and the charge dipole of quasiparticles. The Berry-curvature effects strongly influence the spectroscopic and transport properties of superconductors, such as the local density of states and the thermal Hall conductivity. As a model illustration, we apply the theory to study the twisted bilayer graphene with a $d_{x^2+y^2}+i{d}_{xy}$ superconducting gap function and demonstrate Berry-curvature induced effects.

Figure 1

(a) Berry curvatures of the tight-binding model for twisted-bilayer graphene with $d_{x^2-y^2}$ and $i{d}_{xy}$ superconducting gaps. (b) The quasiparticle thermal Hall conductivity as a function of temperature. Berry-curvature modifications to the momentum space (c) and local (d) density of states with a constant supercurrent ${\nabla }_{\mathit{r}}\theta =(\sqrt{2}\pi /10)\widehat{x}$. In (d) only the result for one of the two bands at the Fermi surface is plotted (solid line). The conventional density of states $n_0(\omega )$ is demonstrated for comparison. Model parameters are taken as $t_2/t_1=0.05$, $t_3/t_1=0.2$, $\mu =-0.9t_1$, and $\mathrm{\Delta }/t_1=0.1$.