Effective Vortex Mass from Microscopic Theory

1. Effective Vortex Mass from Microscopic Theory 한 정훈, 김 준서 (성균관대)

2. Mass without Mass “PHASING-OUT” of (BARE) MASS FROM PHYSICAL EQUATIONSNewton’s 2nd law: F=maNewton’s gravity: F = GMm/r2 Einstein’s law: E=mc2Quantum field theory: Lagrangians with zero mass, but calculated mass is finite!Interaction generates massSuperconductivity: Meissner effect due tophotons acquiring finite mass Electrons in periodic potential: Effective mass can be vastly different from bare mass of 0.5 MeVPhonon renormalization of mass, etc. mass is given mass is generated/destroyed dynamic mass generation In solid state physics

3. Calculating the Effective Mass – Diagrammatic Approach A bare propagator for a quasiparticle is characterized by bare mass: Interaction gives rise to self-energy. Real part of self-energy is the mass renormalization.

4. RENORMALIZATION CLOUD Calculating the Effective Mass - Caldeira-Leggett Approach A foreign object moving through a medium experiences friction and mass renormalization due to interaction with the mediumWrite down the Lagrangian for the (object)+(medium) Integrate out the degrees of freedom of the (medium) Effective action for the (object) contains interaction effects

5. S e 2e N Vortex Motion through a Type-II Superconductor Imagine a small magnet with its north/south poles on either side of a thin slab of type-II superconductor. On dragging the magnet the vortex moves too. Force needed to execute the motion is (m+M) am=mass of magnetM=effective mass of vortex M can be calculated within Caldeira-Leggett theory

6. Vortex Structure from BdG equation self-consistent solution of BdG equation for a single vortex Gap profile

7. extended-to-extended Energy core-to-core core-to-extended Mass Equation and Transition Matrix Elements Transition matrix element between localized and extended states arenon-zero due to vortex motionSecond-order perturbation theory gives mass correction

8. Effective Mass for Pure Superconductor Vortex Mass ~ Mass of electrons occupying a cylinder of radius at T=0 Rises to a maximum at T ~ 0.5 Tc Falls to zero at T= Tc

9. Effective Mass for Impure Superconductor Impurities can wash out localized core levels.Core-to-core contribution to mass vanishes,and effective mass is greatly reduced.