Effective Vortex Mass from

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Effective Vortex Mass from Microscopic Theory
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Mass without Mass
PHASING-OUT of (BARE) MASS FROM PHYSICAL
EQUATIONSNewtons 2nd law FmaNewtons
gravity F GMm/r2 Einsteins law Emc2
Quantum 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
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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.
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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
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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
(mM) ammass of magnetMeffective mass of
vortex M can be calculated within
Caldeira-Leggett theory
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Vortex Structure from BdG equation
self-consistent solution of BdG equation for a
single vortex
Gap profile
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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
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Effective Mass for Pure Superconductor
Vortex Mass Mass of electrons occupying a
cylinder of radius at T0 Rises to
a maximum at T 0.5 Tc Falls to zero
at T Tc
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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.