This book presents modern theory of nonstationary and nonequilibrium superconductivity. It deals with superconductors in external fields varying in time and studies transport phenomena in superconductors. The book provides the microscopic theory based on the Green function formalism within the Bardeen, Cooper, and Schrieffer (BCS) theory. The method of quasiclassical Green functions is formulated for both stationary and nonequilibrium problems in the theory of superconductivity. Chapters 1 to 4 give an introduction to the Green function formalism in the BCS theory for clean materials and alloys. In next two chapters, the quasiclassical approximation is introduced and applied to some generic stationary problems such as the Ginzburg–Landau (GL) equations, critical magnetic fields, gapless superconductivity, d-wave superconductivity, bound states in the vortex core. Chapter 7 describes the quasiclassical method for layered superconductors. In Chapter 8 the nonstationary theory is formulated using both the method of analytical continuation and the Keldysh diagram technique. Next two chapters are devoted to the quasiclassical approximation and to generalized kinetic equations in nonstationary situations. Chapter 11 demonstrates how the GL model can be extended to nonstationary problems. A considerable part of the book is devoted to the vortex dynamics, which treats behaviour of type II superconductors when they carry electric currents in presence of a magnetic field. Chapters 12 to 15 deal with the dynamics of vortices. In Chapter 12, the time-dependent GL model is used to calculate the resistivity in the flux flow regime. Chapter 13 derives the forces acting on a moving vortex using the Green function formalism and applies the microscopic theory to the vortex dynamics in superconducting alloys. In Chapters 14 and 15 the vortex dynamics in clean superconductors is considered and the flux-flow conductivity, the vortex Hall effect, and the vortex mass are calculated.

We show that the topologically protected flat band emerging on a surface of a nodal fermionic system promotes the surface superconductivity due to an infinitely large density of states associated with the flat band. The critical temperature depends linearly on the pairing interaction and can be thus considerably higher than the exponentially small bulk critical temperature. We discuss an example of surface superconductivity in multilayered graphene with rhombohedral stacking.

No abstract

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. Here we show that in gapless topological media, the bulk-surface and bulk-vortex correspondence is more effective: it produces topologically protected gapless fermions without dispersion -- the flat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines and in the vortex core in systems with topologically protected Fermi points (Weyl points). Flat band has an extremely singular density of states, and we show that this property may give rise in particular to surface superconductivity which could exist even at room temperature.Comment: 9 pages, 5 figures, version to appear in JETP Letter

No abstract

Hydrodynamic flow in classical and quantum fluids can be either laminar or turbulent. Vorticity in turbulent flow is often modelled with vortex filaments. While this represents an idealization in classical fluids, vortices are topologically stable quantized objects in superfluids. Superfluid turbulence is therefore thought to be important for the understanding of turbulence more generally. The fermionic 3He superfluids are attractive systems to study because their characteristics vary widely over the experimentally accessible temperature regime. Here we report nuclear magnetic resonance measurements and numerical simulations indicating the existence of sharp transition to turbulence in the B phase of superfluid 3He. Above 0.60T(c) (where T(c) is the transition temperature for superfluidity) the hydrodynamics are regular, while below this temperature we see turbulent behaviour. The transition is insensitive to the fluid velocity, in striking contrast to current textbook knowledge of turbulence. Rather, it is controlled by an intrinsic parameter of the superfluid: the mutual friction between the normal and superfluid components of the flow, which causes damping of the vortex motion.

No abstract

Excitations in vortex cores in superconductors and other Fermi superfluids are single-particle excitations with a peculiar energy spectrum. These excitations are responsible for many important thermodynamic properties such as specific heat, London penetration length, etc. They also determine the dynamic characteristics of superconductors and superfluids through their interaction with vortices. Flux flow resistance, the Hall effect in type II superconductors and the mutual friction in superfluids are the most important phenomena which strongly depend on vortex core excitations. These phenomena determine the electromagnetic responses of type II superconductors and the hydrodynamic behaviour of superfluids and are of great significance for practical applications of superconducting devices and for understanding the most fundamental properties of correlated electrons and other Fermi particles. In this review we consider the dynamic properties of superconductors and superfluids and outline the basic ideas and results on the vortex dynamics in clean superfluid Fermi systems. The forces acting on moving vortices are discussed including the problem of the transverse force which was a matter of confusion for quite some time. We formulate the equations of the vortex dynamics, which include all the forces and the inertial term associated with excitations bound to the moving vortex.