Superconductors can usefully be divided into two classes, those that are well described by the classic Bardeen–Cooper–Schrieffer (BCS) theory and its extensions and those which require a different microscopic description.

The BCS theory of superconductivity solved the long standing mystery of this spectacular phenomenon and described all superconductors that were known when it was formulated in the 1950s. The key ingredient is an attractive interaction generated by the exchange of phonons between electrons which overcomes a Coulomb repulsion weakened by screening, to give a net attractive force on the low energy scale. In this case the simplest s-wave pairing always maximises the energy gain. There were speculations a little later that other types of electron pairing could be possible, but it took a quarter of a century until the first signs of superconductors with different and exotic pairing appeared. In the intervening thirty years many superconductors with exotic pairing have been and continue to be discovered and the study of their superconductivity has grown into a major subfield of condensed matter physics today.

The importance of these exotic superconductors with unconventional symmetry is that their pairing is of electronic origin. As a result they are freed from the restrictions of low transition temperatures that go along with the phonon driven conventional superconductors. However in two of the main classes of the exotic superconductors, namely heavy fermion and organic superconductors, the intrinsic energy scales are very small leading to low temperature scales. The third class contains the small number of superconducting transition metal compounds with exotic pairing symmetry. The most studied of these are the high-T_c cuprates, the newly discovered iron pnictides and strontium ruthenate which is closely related to superfluid ³He. Although the basic electronic structure of these materials is well understood, the origin of the pairing is more complex here and a consistent theoretical description of all aspects of their superconductivity remains a formidable challenge. While the discovery of the BCS theory led, in only a few years, to the complete and consistent theoretical description of all aspects of conventional superconductivity, we are far from this goal for the exotic superconductors. Hence these superconductors continue to be the focus of most research activity in the field of superconductivity today.

The papers in this special issue represent a cross section of current activity in both experiment and theory on these fascinating materials.

Focus on Superconductors with Exotic Symmetries Contents

Phase-sensitive-measurement determination of odd-parity, spin-triplet superconductivity in Sr₂RuO₄
Ying Liu

Striped superconductors: how spin, charge and superconducting orders intertwine in the cuprates
Erez Berg, Eduardo Fradkin, Steven A Kivelson and John M Tranquada

A twisted ladder: relating the Fe superconductors to the high-T_c cuprates
E Berg, S A Kivelson and D J Scalapino

Fractional vortex lattice structures in spin-triplet superconductors
Suk Bum Chung, Daniel F Agterberg and Eun-A Kim

Momentum dependence of pseudo-gap and superconducting gap in variation theory
T Watanabe, H Yokoyama, K Shigeta and M Ogata

Variational ground states of the two-dimensional Hubbard model
D Baeriswyl, D Eichenberger and M Menteshashvili

Charge dynamics of vortex cores in layered chiral triplet superconductors
M Eschrig and J A Sauls

Vortices in chiral, spin-triplet superconductors and superfluids
J A Sauls and M Eschrig

Flux periodicities in loops of nodal superconductors
Florian Loder, Arno P Kampf, Thilo Kopp and Jochen Mannhart

Evidence of magnetic mechanism for cuprate superconductivity
Amit Keren

Wave function for odd-frequency superconductors
Hari P Dahal, E Abrahams, D Mozyrsky, Y Tanaka and A V Balatsky

Nernst effect as a probe of superconducting fluctuations in disordered thin films
A Pourret, P Spathis, H Aubin and K Behnia

Pairing state at an interface of Sr₂RuO₄: parity-mixing, restored time-reversal symmetry and topological superconductivity
Y Tada, N Kawakami and S Fujimoto

Momentum-resolved superconducting gap in the bulk of Ba_1-xK_xFe₂As₂ from combined ARPES and μSR measurements
D V Evtushinsky, D S Inosov, V B Zabolotnyy, M S Viazovska, R Khasanov, A Amato, H-H Klauss, H Luetkens, Ch Niedermayer, G L Sun, V Hinkov, C T Lin, A Varykhalov, A Koitzsch, M Knupfer, B Büchner, A A Kordyuk and S V Borisenko

Cooper-pair formation by anharmonic rattling modes in the β-pyrochlore superconductor KOs₂O₆
Jun Chang, Ilya Eremin and Peter Thalmeier

Doping-dependent optical properties of Bi2201
E van Heumen, W Meevasana, A B Kuzmenko, H Eisaki and D van der Marel

Phase diagram and single-particle spectrum of CuO₂ high-T_c layers: variational cluster approach to the three-band Hubbard model
E Arrigoni, M Aichhorn, M Daghofer and W Hanke

Heat transport as a probe of superconducting gap structure
H Shakeripour, C Petrovic and Louis Taillefer

Pressure-induced magnetic transition and volume collapse in FeAs superconductors: an orbital-selective Mott scenario
Andreas Hackl and Matthias Vojta

Orbital magnetic moment of a chiral p-wave superconductor
James F Annett, B L Györffy and K I Wysokiński

Magnetism and superconductivity in strongly correlated CeRhIn₅
Tuson Park and J D Thompson

Superconducting gap structure of heavy-Fermion compound URu₂Si₂ determined by angle-resolved thermal conductivity
Y Kasahara, H Shishido, T Shibauchi, Y Haga, T D Matsuda, Y Onuki and Y Matsuda

Polar Kerr effect as probe for time-reversal symmetry breaking in unconventional superconductors
Aharon Kapitulnik, Jing Xia, Elizabeth Schemm and Alexander Palevski

Influence of non-magnetic impurities on hole-doped two-leg Cu–O Hubbard ladders
P Chudzinski, M Gabay and T Giamarchi

Pairing in the iron arsenides: a functional RG treatment
Christian Platt, Carsten Honerkamp and Werner Hanke

Tracking anisotropic scattering in overdoped Tl₂Ba₂CuO_6+δ above 100 K
M M J French, J G Analytis, A Carrington, L Balicas and N E Hussey

The disordered Fulde–Ferrel–Larkin–Ovchinnikov state in d-wave superconductors
Youichi Yanase

The chiral superconductor–ferromagnet–chiral superconductor Josephson junction
P M R Brydon, C Iniotakis and Dirk Manske

Unusual behaviours and impurity effects in the noncentrosymmetric superconductor CePt₃Si
I Bonalde, R L Ribeiro, W Brämer-Escamilla, C Rojas, E Bauer, A Prokofiev, Y Haga, T Yasuda and Y Onuki

Nature of stripes in the generalized t–J model applied to the cuprate superconductors
Kai-Yu Yang, Wei Qiang Chen, T M Rice, M Sigrist and Fu-Chun Zhang