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We discuss the derivation of the electrodynamics of superconductors coupled to the electromagnetic field from a Lorentz-invariant bosonic model of Cooper pairs. Our results are obtained at zero temperature where, according to the third law…
Making use of the extended Ginzburg Landau theory, which includes the fourth order derivative term, we study the vortex state in a magnetic field parallel to the $ c$ axis. The vortex core structure is distorted due to this higher order…
We investigate the three-dimensional, time-reversal invariant topological superconductors with generic interaction by their response to external fields. The first description is a gravitational topological field theory, which gives a $Z_2$…
The Boltzmann equation for excess Cooper pairs above T_c is derived in the framework of the time-dependent Ginzburg-Landau (TDGL) theory using Langevin's approach of the stochastic differential equation. The Newton dynamic equation for the…
We derive the Ginzburg-Landau-Wilson theory for the superconducting phase transition in two dimensions and in the magnetic field. Without disorder the theory describes a fluctuation induced first-order quantum phase transition into the…
It is generally accepted that vortex core is charged, what illustrates that even in stationary superconductors electric field may be present. Vortex structure and other properties of superconductors are usually calculated in the framework…
Abrikosov vortices play a central role in the disruption of superconductivity in type-II superconductors. It is commonly accepted that as one moves away from the vortex's axis of an $s$-wave superconductor, the density of superconductive…
A detailed theoretical analysis of the Gaussian fluctuations of the order parameter in layered superconductors is performed within the Ginzburg-Landau (GL) theory. The available results for the Gaussian fluctuations are systematized and a…
We have calculated the Bardeen-Stephen contribution to the vortex viscosity for uniaxial anisotropic superconductors within the time-dependent Ginzburg-Landau (TDGL) theory. We focus our attention on superconductors with a mismatch of…
The dual approach to the Ginzburg-Landau theory of a Bardeen-Cooper-Schrieffer superconductor is reviewed. The dual theory describes a grand canonical ensemble of fluctuating closed magnetic vortices, of arbitrary length and shape, which…
There has been intense recent interest in the two-dimensional electron gases (2DEGs) that form at the surfaces and interfaces of KTaO$_3$ (KTO), with the discovery of superconductivity at temperatures significantly higher than those of…
We study the effect of critical fluctuations on the $(B,T)$ phase diagram in extreme type-II superconductors in zero and finite magnetic field using large-scale Monte Carlo simulations on the Ginzburg-Landau model in a frozen gauge…
The Ginzburg-Landau functional for a two-gap superconductor is derived within the weak-coupling BCS model. The two-gap Ginzburg-Landau theory is, then, applied to investigate various magnetic properties of MgB2 including an upturn…
The criticism of Babaev and Silaev notwithstanding, we conclude that our analysis is correct. We have found in our papers on two-band superconductors close to Tc, where the Ginzburg-Landau (GL) theory applies, that these materials are…
We develop a theory for the electrical and thermal transverse linear response functions such as the Hall, Nernst and thermal Hall effects in magnetic materials that harbor topological spin textures like skyrmions. In addition to the…
We have numerically investigated the dynamics of vortices in a clean layered superconductor placed in a perpendicular magnetic field. We describe the energetics using a Ginzburg-Landau free energy functional in the lowest Landau level…
We study the interaction-induced quantum correction \delta\sigma_{\alpha\beta} to the conductivity tensor of electrons in two dimensions for arbitrary T\tau (where T is the temperature and \tau the transport scattering time), magnetic…
In an influential paper of 2002, Babaev, Faddeev and Niemi conjectured that two-component Ginzburg-Landau (TCGL) theory in three dimensions should support knot solitons, where the projective equivalence class of the pair of complex…
We propose a mechanism which can generate supercurrents in spin-orbit coupled superconductors with charged magnetic inclusions. The basic idea is that through spin-orbit interaction, the in-plane electric field near the edge of each…
A model to describe Cooper pairs near the transition point (on temperature and magnetic field), when the distance between them is big compared to their sizes, is proposed. A superconducting plate whose thickness is less than the pair size…