Vortex nucleation barrier in superconductors beyond the Bean-Livingston approximation: A numerical approach for the sphaleron problem in a gauge theory

Supercurrent Induced by Chiral Coupling in Multiferroic/Superconductor Nanostructures

“…In the simulation we tune the SOC-parameter such that |α| = 0.1h/ξ GL , whereas the values of the external magnetic field and of the current remain the same. A change in the winding number leads to a spatial variation of the magnetic field in the SC with the strength and distribution being determined by Equation (10). The gate voltage applied to the magnetically active elements is symmetric with respect to the central axis e y of the SC with a constant local magnetic moment and exchange field h = −e z along the y-axis.…”

“…Microsized SCs of non-elipsoidal shape are known to display large energy barriers for flux penetration and expulsion. In general, these surface barriers depend in a complicated way on the material properties as well as on the geometry of the specimen, which makes their systematic investigation challenging [ 8 , 9 , 10 ]. Nonetheless, the understanding of them is of great importance for applications.…”

Numerical Approach in Superconductivity: An Advanced Study

“…Various numerical approaches have been used to describe superconductivity. For example, numerical approach in description of vortex nucleation in the Ginzburg-Landau model of superconductivity [3] and a numerical method of solving the mean-field self-consistent Bogoliubov de Gennes equations by expanding the Nambu Greens functions in terms of Chebyshev polynomials [4] which both require phenomenological assumptions or complex calculations on grid. All of them do not give a clear dependence of the observed parameters of a superconductor on its material composition and lattice structure.…”

Vortex nucleation barriers and stable fractional vortices near boundaries in multicomponent superconductors

“…That is defined as a path in the configuration space such that it crosses the minimum in the cotangent space of the path point by point. Until the recent publication [17], there were no controllable analytical or numerical methods to find saddle points in nonlinear gauge theories.…”

“…In Ref. [17] it has been proposed a generalization of the string method for classical gauge theories that allows calculating, in a numerically controllable way, vortex nucleation processes in a single-component Ginzburg-Landau model.…”