Inertial Mass of a Vortex in Cuprate Superconductors

We present here a calculation of the inertial mass of a moving vortex in cuprate superconductors. This is a poorly known basic quantity of obvious interest in vortex dynamics. The motion of a vortex causes a dipolar density distortion and an associated electric field which is screened. The energy cost of the density distortion as well as the related screened electric field contribute to the vortex mass, which is small because of efficient screening. As a preliminary, we present a discussion and calculation of the vortex mass using a microscopically derivable phase-only action functional for the far region which shows that the contribution from the far region is negligible, and that most of it arises from the (small) core region of the vortex. A calculation based on a phenomenological Ginzburg-Landau functional is performed in the core region. Unfortunately such a calculation is unreliable, the reasons for it are discussed. A credible calculation of the vortex mass thus requires a fully microscopic, non-coarse grained theory. This is developed, and results are presented for a s-wave BCS like gap, with parameters appropriate to the cuprates. The mass, about 0.5 $m_e$ per layer, for magnetic field along the $c$ axis, arises from deformation of quasiparticle states bound in the core, and screening effects mentioned above. We discuss earlier results, possible extensions to d-wave symmetry, and observability of effects dependent on the inertial mass.