The feature of pinning on vortex–antivortex generation in the type-II superconducting film

The quasiorder-disorder phase transition and peak effect in MgB2 type-II superconducting materials and thin films

“…The full Hamiltonian of the fluctuation for the flux line lattice in the z-direction for magnesium diboride, MgB 2 , anisotropicsave type-II superconductor is given by [15][16][17][18][23][24][25] …”

“…where H f represents the Hamiltonian for the free modes of the vortex lattice [15][16][17][18][23][24][25], H R describes the random Hamiltonian [15][16][17][18][23][24][25], (μ, ν) = (x, y), ρ stands for the effective mass density of the flux line [26],…”

The quasiorder‐disorder phase transition and peak effect in MgB2 type‐II superconducting materials and thin films

“…where H f represents the Hamiltonian for the free modes of the vortex lattice [15][16][17][18][23][24][25], H R describes the random Hamiltonian [15][16][17][18][23][24][25], (µ, ν)=(x, y), ρ stands for the effective mass density of the flux line [26], K 2 ⊥ = K 2 x + K 2 y , P µ ( K),S µ ( K) are the Fourier transformations of the momentum and displacement operators, f R ( K) is the Fourier transformation of the random potential energy of the collective pinning force f R ( r)=− − → ∇V R ( r), with V R ( r) the random potential energy of the collective pinning [25], which is the sum of the contributions of defects within a distance ξ of the vortex core position r,whereξ is the temperature-dependent coherent length, C L , C 11 , C 44 and C 66 are temperature-and K-dependent bulk modulus, compression modulus, tilt modulus and shear modulus [27], respectively.…”

“…It is understood that the free Hamiltonian of Eq. ( 2) can be diagonalized with the eigenmodes spectrum [15][16][17][18][23][24][25],…”

Developing a Tool for a Qualitative Measurement of Pinning Forces Using Rotational Magnetization Experiments

“…The vortex-pair production was also calculated in terms of temperature, magnetic field and current. [12][13][14] The role of randomly distributed strong pinning sites and collective pinning on vortex-antivortex production was also investigated. 15 In Ref.…”