Phenomenological theory of unconventional superconductivity

Abstract

This article is a review of recent developments in the phenomenological description of unconventional superconductivity.Starting with the BCS theory of superconductivity with anisotropic Cooper pairing, the authors explain the group-theoretical derivation of the generalized Ginzburg-Landau theory for unconventional superconductivity. This is used to classify the possible superconducting states in a system with given crystal symmetry, including strong-coupling effects and spin-orbit interaction. On the basis of the BCS theory the unusual low-temperature properties and the (resonant) impurity scattering effects are discussed for superconductors with anisotropic pairing. Using the Ginzburg-Landau theory, the authors study several bulk properties of such superconductors: spontaneous lattice distortion, upper critical magnetic field, splitting of a phase transition due to uniaxial stress. Two possible mechanisms for ultrasound absorption are discussed: collective modes and damping by domain-wall motion. The boundary conditions for the Ginzburg-Landau theory are derived from a correlation function formulation and by grouptheoretical methods. They are applied to a study of the Josephson and proximity effects if unconventional superconductors are involved there. The magnetic properties of superconductors that break time-reversal symmetry are analyzed. Examples of current and magnetic-field distributions close to inhomogeneities of the superconducting order parameter are given and their physical origin is discussed. Vortices in a superconductor with a multicomponent order parameter can exhibit various topo1ogical structures. As examples the authors show fractional vortices on domain walls and nonaxial vortices in the bulk. Furthermore, the problem of the possible coexistence of a superconducting and a magnetically ordered phase in an unconventional superconductor is analyzed. The combination of two order parameters that are almost degenerate in their critical temperature is considered with respect to the phase-transition behavior and effects on the lower and upper critical fields. Because heavy-fermion superconductors -which are possible realizations of unconventional superconductivity -have been the main motivation for the phenomenological studies presented here, the authors compare the theoretical results with the experimental facts and data. In particular, they emphasize the intriguing features of the compound UPt3 and consider in detail the alloy U& Th Be/3.

Chirald-wave superconductivity in doped graphene

“…For a superconducting transition at T c we need α, β 1 > 0. If further β 2 < 0 then a d x 2 −y 2 -or a d xy -wave state would arise, whereas for β 2 > 0 the complex combinations d x 2 −y 2 ± id xy is energetically favored [35]. For both graphene around the van Hove singularity [43] and for generic circular Fermi surfaces on the hexagonal lattice [86], it has been shown that β 2 > 0, and thus the chiral d x 2 −y 2 ± id xy -wave combination is the widely favored solution.…”

“…It preserves full SU(2) spin-rotation symmetry, as long as the normal state is spindegenerate. However, it breaks time-reversal symmetry since the time-reversal operator K acts as K∆(k) = ∆ * (−k) on a spin-singlet order parameter [35]. It thus belongs to class C in the Altland-Zirnbauer classification of Bogoliubov-de Gennes systems [112,113].…”

“…The preference for the d x 2 −y 2 ± id xy -wave solutions can also very generally be obtained using a GinzburgLandau expansion of the free energy. Calling the (possibly complex) coefficients in front the two different d-wave basis functions ∆ 1 and ∆ 2 , the fourth-order expansion of the free energy on the hexagonal lattice has the form [35]:…”

“…Quite generally (see e.g. [35]) we can start in momentum space by writing an effective Hamiltonian with attractive interaction between pairs of electrons with zero total momentum as ‡:…”

A General Model of N/S Conductance Spectroscopy in Non-Unitary Superconductors Applied to PrOs4Sb12

“…where Q( k) = 1/ √ 4| q|(| q| + q z ) and σ are the Pauli matrices [11]. In the particle-hole basis, the eigenstates ofˆ ( k) are…”