Research
Microscopic theory of superconductivity, topological solitons in finite-size physical systems, and application of methods of modern quantum field theory to problems of condensed-matter physics
S. V. Kuplevakhsky (Group Leader), S. V. Bengus
Within the framework of microscopic theory of superconductivity, a rigorous mathematical method of derivation of Ginzburg-Landau-type free-energy functionals for superconducting structures with Josephson links (single junctions and multilayers) was developed: see [1] and references therein.
The classical problem of the Josephson tunnel junction of arbitrary (but finite) barrier length in the presence of external parallel magnetic fields and transport currents was solved analytically [2, 3, 4]. Exact analytical expressions for the complete set of Josephson vortices (topological solitons of the static sine-Gordon equation) were obtained.
Exact analytical expressions for the complete set of static topological solitons in mesoscopic two-band-superconducting cylinders were derived. Their physical properties were thoroughly discussed [5].
Based on mathematical methods and concepts of modern quantum field theory, we proposed a new and rigorous approach to the theory of superconductivity of structurally-inhomogeneous systems [6].
Literature:
1. S. V. Kuplevakhsky
Exact solutions of the Lawrence-Doniach model for layered superconductors.
2. S. V. Kuplevakhsky and A. M. Glukhov
Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions.
3. S. V. Kuplevakhsky and A. M. Glukhov
Exact analytical solution of the problem of current-carrying states of the Josephson junction in external magnetic fields.
Phys. Rev. B 76, 174515 (2007) 
4. S. V. Kuplevakhsky and A. M. Glukhov
Exact analytical solution of a classical problem of the Josephson tunnel junction .
Low Temp. Phys. 36, 1012 (2010) 
5. S. V. Kuplevakhsky, A.N. Omelyanchouk, and Y.S. Yerin
Soliton states in mesoscopic two-band-superconducting cylinders.
6. S. V. Kuplevakhsky
Higgs mechanism in superconducting structures.
Low Temp. Phys. 43, 329 (2017)