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 Berry curvature effects in phase space spanned position momentum. These curvatures are traced back to characteristics superconductivity, including nontrivial momentum-space geometry pairing, real-space supercurrent, charge dipole quasiparticles. The Berry-curvature strongly influence spectroscopic transport properties superconductors, such as local density states thermal Hall conductivity. As model illustration, we apply study twisted bilayer graphene with ${d}_{{x}^{2}+{y}^{2}}+i{d}_{xy}$ gap function demonstrate induced effects.