Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, unlike the usual BCS state, for the Cooper pair to have a nonzero total momentum. For this reason, in this state the gap varies in space, the ground state is inhomogeneous, and a crystalline structure might be formed. This situation was considered for the first time by Fulde and Ferrell (1964) and Larkin and Ovchinnikov (1964), after whom the corresponding state is called the LOFF state. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated with the presence of long-wavelength excitations of zero mass. The situation described here is of interest both in solid-state and in elementary-particle physics, in particular in quantum chromodynamics at high density and low temperature. This review presents the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories.

/pdf/inhomogeneous-superconductivity-in-condensed-matter-and-qcd-2ydtjowk3x.pdf

Inhomogeneous superconductivity in condensed matter and QCD

Bonds, bands, charge transfer excitations and superconductivity of YBa2Cu3O7-δ

First-principles full potential linear muffin-tin orbital--generalized gradient approximation electronic structure calculations of the new medium-${T}_{C}$ superconductor (MTSC) ${\mathrm{MgB}}_{2}$ and related diborides indicate that superconductivity in these compounds is related to the existence of ${p}_{x,y}$-band holes at the $\ensuremath{\Gamma}$ point. Based on these calculations, we explain the absence of medium-${T}_{C}$ superconductivity for ${\mathrm{BeB}}_{2},$ ${\mathrm{AlB}}_{2},$ ${\mathrm{ScB}}_{2}$, and ${\mathrm{YB}}_{2}.$ The simulation of a number of ${\mathrm{MgB}}_{2}$-based ternary systems using a supercell approach demonstrates that (i) the electron doping of ${\mathrm{MgB}}_{2}$ (i.e., ${\mathrm{MgB}}_{2\ensuremath{-}y}{X}_{y}$ with $X=\mathrm{Be},$ C, N, O) and the creation of defects in the boron sublattice (nonstoichiometric ${\mathrm{MgB}}_{2\ensuremath{-}y})$ are not favorable for superconductivity, and (ii) a possible way of searching for similar or higher MTSC should be via hole doping of ${\mathrm{MgB}}_{2}$ $({\mathrm{CaB}}_{2})$ or isoelectronic substitution of Mg (i.e., ${\mathrm{Mg}}_{1\ensuremath{-}x}{M}_{x}{\mathrm{B}}_{2}$ with $M=\mathrm{Be},$ Ca, Li, Na, Cu, Zn) or creating layered superstructures of the ${\mathrm{MgB}}_{2}/{\mathrm{CaB}}_{2}$ type.

/pdf/electronic-structure-of-superconducting-mgb-2-and-related-2k3eh5so0c.pdf

Electronic structure of superconducting MgB 2 and related binary and ternary borides

During the last three decades a large interest has developed in the field of rare-earth borides. Six different families have been discovered: REB2, REB4, RE2B5, REB6, REB12 and REB∼66. Their extension is discussed, and it is shown on the base of both geometrical and electronic considerations how the RE atoms contribute to the stabilization of the electron-deficient boron framework. Attention has been devoted to the ability of metal or non-metal impurities either to stabilize a particular structure or to modify drastically the electrical and magnetic properties of the borides. A wide range of the fascinating physical properties of the rare-earth borides is considered, including insulator–metal transitions, superconductivity, mixed-valence behaviour, magnetic phase transitions and thermoelectronic properties.

Structure and physical features of the rare-earth borides

We report upper critical field Bc2(T) data for LaO0.9F0.1FeAs1- δ in a wide temperature and field range up to 60 T. The large slope of Bc2≈- 5.4 to -6.6 T K-1 near an improved Tc≈28.5 K of the in-plane Bc2(T) contrasts with a flattening starting near 23 K above 30 T we regard as the onset of Pauli-limited behaviour (PLB) with Bc2(0)≈63–68 T. We interpret a similar hitherto unexplained flattening of the Bc2(T) curves reported for at least three other disordered closely related systems, Co-doped BaFe2As2, (Ba,K) Fe2As2 and NdO0.7F0.3FeAs (all single crystals), for applied fields H∥(a,b), also as a manifestation of PLB. Their Maki parameters have been estimated by analysing their Bc2(T) data within the Werthamer–Helfand–Hohenberg approach. The pronounced PLB of (Ba, K)Fe2As2 single crystals obtained from an Sn flux is attributed also to a significant As deficiency detected by wavelength dispersive x-ray spectroscopy as reported by Ni et al (2008 Phys. Rev. B 78 014507). Consequences of our results are discussed in terms of disorder effects within conventional superconductivity (CSC) and unconventional superconductivity (USC). USC scenarios with nodes on individual Fermi surface sheets (FSS), e.g. p- and d-wave SC, can be discarded for our samples. The increase of dBc2/dT|Tc by sizeable disorder provides evidence for an important intraband (intra-FSS) contribution to the orbital upper critical field. We suggest that it can be ascribed either to an impurity-driven transition from s± USC to CSC of an extended s++-wave state or to a stabilized s±-state provided As-vacancies cause predominantly strong intraband scattering in the unitary limit. We compare our results with Bc2 data from the literature, which often show no PLB for fields below 60–70 T probed so far. A novel disorder-related scenario of a complex interplay of SC with two different competing magnetic instabilities is suggested.

/pdf/orbital-and-spin-effects-for-the-upper-critical-field-in-as-4ftq7gbe29.pdf

Orbital and spin effects for the upper critical field in As-deficient disordered Fe pnictide superconductors

Within the past decade an enormous increase of interest has occurred in the field of ternary superconductors, the number of which is growing rapidly due to the extraordinary flexibility Nature offers in combining three elements. A summary of the recent superconducting systems is presented followed by a more extensive discussion on the relationships between structural parameters and superconducting properties of the two largest families,i.e. the ternary molybdenum chalcogenides (Chevrel phases) and the ternary rhodium borides.

C. Rossel

Papers

Superconductivity in ternary compounds