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This study explores the concept of effective mass within microscopic frameworks, addressing the generation and renormalization of mass in quantum field theories. Key physical principles, including Newton's laws and Einstein's concepts of mass-energy equivalence, serve as foundations for understanding mass behavior. We investigate vortex motion in Type-II superconductors, detailing how interactions with a medium impact effective mass. Using the Caldeira-Leggett framework, we analyze the mass corrections and behaviors under varying conditions, paving the way for deeper insights into superconductivity and quasiparticle dynamics.
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Effective Vortex Mass from Microscopic Theory 한 정훈, 김 준서 (성균관대)
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
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.
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
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
Vortex Structure from BdG equation self-consistent solution of BdG equation for a single vortex Gap profile
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
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
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.
