IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

This review presents a summary and evaluation of the experimental properties of unconventional superconductivity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ as they were known in the spring of 2002. At the same time, the paper is intended to be useful as an introduction to the physics of spin-triplet superconductivity. First, the authors show how the normal-state properties of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ are quantitatively described in terms of a quasi-two-dimensional Fermi liquid. Then they summarize its phenomenological superconducting parameters in the framework of the Ginzburg-Landau model, and discuss the existing evidence for spin-triplet pairing. After a brief introduction to the vector order parameter, they examine the most likely symmetry of the triplet state. The structure of the superconducting energy gap is discussed, as is the effect of symmetry-breaking magnetic fields on the phase diagram. The article concludes with a discussion of some outstanding issues and desirable future work. Appendixes on additional details of the normal state, difficulty in observing the bulk Fermi surface by angle-resolved photoemission, and the enhancement of superconducting transition temperature in a two-phase ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}\ensuremath{-}\mathrm{Ru}$ system are included.

The superconductivity of Sr 2 RuO 4 and the physics of spin-triplet pairing

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

In a conventional superconductor, the binding of electrons into the paired states that collectively carry the supercurrent is mediated by phonons — vibrations of the crystal lattice. Here we argue that, in the case of the heavy fermion superconductors CePd2Si2 and CeIn3, the charge carriers are bound together in pairs by magnetic spin–spin interactions. The existence of magnetically mediated superconductivity in these compounds could help shed light on the question of whether magnetic interactions are relevant for describing the superconducting and normal-state properties of other strongly correlated electron systems, perhaps including the high-temperature copper oxide superconductors.

Magnetically mediated superconductivity in heavy fermion compounds

The response of the worldwide scientific community to the discovery in 2008 of superconductivity at T c = 26 K in the Fe-based compound LaFeAsO1−x F x has been very enthusiastic. In short order, ot...

The puzzle of high temperature superconductivity in layered iron pnictides and chalcogenides

We report the observation of heavy-fermion superconductivity in CeCoIn5 at Tc = 2.3 K. When compared to the pressure-induced Tc of its cubic relative CeIn3 (Tc~200 mK), the Tc of CeCoIn5 is remarkably high. We suggest that this difference may arise from magnetically mediated superconductivity in the layered crystal structure of CeCoIn5.

/pdf/heavy-fermion-superconductivity-in-cecoin5-at-2-3-k-2nco5b84iv.pdf

Heavy-fermion superconductivity in CeCoIn5 at 2.3 K

We report the observation of heavy-fermion superconducitivity in CeCoIn5 at Tc =2.3 K. When compared to the pressure-induced Tc of its cubic relative CeIn3 (Tc ~200 mK), the Tc of CeCoIn5 is remarkably high. We suggest that this difference may arise from magnetically mediated superconductivity in the layered crystal structure of CeCoIn5 .

Heavy-fermion superconductivity in CeCoIn5 at 2.3K

We report specific heat measurements of the heavy fermion superconductor ${\mathrm{C}\mathrm{e}\mathrm{C}\mathrm{o}\mathrm{I}\mathrm{n}}_{5}$ in the vicinity of the superconducting critical field ${H}_{c2}$, with magnetic fields in the [110], [100], and [001] directions, and at temperatures down to 50 mK. The superconducting phase transition changes from second to first order for fields above 10 T for $H\ensuremath{\parallel}[110]$ and $H\ensuremath{\parallel}[100]$. In the same range of magnetic fields, we observe a second specific heat anomaly within the superconducting state. We interpret this anomaly as a signature of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting state. We obtain similar results for $H\ensuremath{\parallel}[001]$, with the FFLO state occupying a smaller part of the phase diagram.

https://arxiv.org/pdf/cond-mat/0304420.pdf

Possible Fulde-Ferrell-Larkin-Ovchinnikov superconducting state in CeCoIn5.

CeIrIn5 is a member of a new family of heavy-fermion compounds and has a Sommerfeld specific-heat coefficient of 720 mJ/molK2. It exhibits a bulk, thermodynamic transition to a superconducting state at Tc = 0.40 K, below which the specific heat decreases as T2 to a small residual T-linear value. Surprisingly, the electrical resistivity drops below instrumental resolution at a much higher temperature T0 = 1.2 K. These behaviors are highly reproducible and field-dependent studies indicate that T0 and Tc arise from the same underlying electronic structure. The layered crystal structure of CeIrIn5 suggests a possible analogy to the cuprates in which spin/charge pair correlations develop well above Tc.

https://iopscience.iop.org/article/10.1209/epl/i2001-00161-8/pdf

A new heavy-fermion superconductor CeIrIn5: A relative of the cuprates?

With only a few exceptions that are well understood, conventional superconductivity does not coexist with long-range magnetic order (for example, ref. 1). Unconventional superconductivity, on the other hand, develops near a phase boundary separating magnetically ordered and magnetically disordered phases. A maximum in the superconducting transition temperature T(c) develops where this boundary extrapolates to zero Kelvin, suggesting that fluctuations associated with this magnetic quantum-critical point are essential for unconventional superconductivity. Invariably, though, unconventional superconductivity masks the magnetic phase boundary when T 0 K magnetic field-pressure phase diagram of CeRhIn5 is well described with a theoretical model developed to explain field-induced magnetism in the high-T(c) copper oxides, but in which a clear delineation of quantum-phase boundaries has not been possible. These experiments establish a common relationship among hidden magnetism, quantum criticality and unconventional superconductivity in copper oxides and heavy-electron systems such as CeRhIn5.

Roman Movshovich

Papers

Heavy-fermion superconductivity in CeCoIn5 at 2.3 K

Heavy-fermion superconductivity in CeCoIn5 at 2.3K

Possible Fulde-Ferrell-Larkin-Ovchinnikov superconducting state in CeCoIn5.

A new heavy-fermion superconductor CeIrIn5: A relative of the cuprates?

Hidden magnetism and quantum criticality in the heavy fermion superconductor CeRhIn5.