Rebecca Flint (Rutgers U.): How Spin become pairs: composite pairing and magnetism in the 115 heavy fermion superconductors

articles Rebecca reports on:

Flint, Dzero and Coleman Nature Physics 4, 643 (2008)

Flint and Coleman arXiv (2009)

Outline of her talk:

* Why are 115 SC special?

* How do spins form pairs? two different pairing mechanisms:

magnetic pairing and composite pairing

* tool symplectic-N

* illustration: two-channel Kondo Heisenberg model

* experimental consequences

1.) Introduction: Why are 115 SC special?

Rebecca explained that a general theme in correlated systems is the distinction/competition between localized and itinerant electrons: localization vs. itineracy. For example, in the cuprates this competition is induced by doping and in the heavy fermions this competition is inherent in the interaction between local spin and the conduction electrons. This dichotomy leads to rich phase diagrams with magnetism, superconductivity etc.

She then continued by introducing the 115 family of unconventional superconductors. For example, CeMIn5 exhibits various phases as a function of doping: AFM, SC with many quantum critical points. The critical temperature for superconductivity can be raised by considering other 115 compounds like PuCoGa5.

2.) How do spins form pairs?

Next, the conventional picture for the formation of heavy Cooper pairs was explained.

Usually one considers the following sequence of mechanisms:

1. The local moments are quenched by means of the Kondo effect and the heavy electron liquid forms.

2. The Cooper pairs of heavy quasiparticles form; the glue is provided by the residual spin fluctuation, which is known as "magnetic pairing"

Rebecca explained that this two-stage pairing mechanism is reflected in the T-dependence of the magnetic susceptibility of various compounds. For example, in UPt3 there is a crossover from an Curie behavior at high temperatures reflecting the local spins to a Pauli behavior at low temperatures characteristic for a (heavy) Fermi liquid. In addition, the quenched entropy during this crossover is usually large, ie. on the order of R Log 2 so that the residual entropy attributed to the (quenched) local moments is usually small. The important aspect of this two-stage mechanism is that the energies associated with the quenching of local moments and the formation of Cooper pairs are well separated.

However, this seems to be different in CeCoIn5. There is in fact no Pauli susceptibility observed at lowest T and residual entropy is rather large. As a consequence, the nature of the Cooper pairs might be different in this 115 compounds. Rebecca explained that there is alternative scenario for Cooper pair formation, ie., "composite pairing" (going back to works of Abrahams, Balatsky Scalapino Schrieffer 1995). Here, the Cooper pair is not form by a pair of heavy electrons as for "magnetic pairing" but instead by a pair of (light) conduction electrons PLUS a spin flip of the local moment. In fomula the order parameter would read schematically as c+c+S-. Rebecca explained that whereas magnetic pairing is favoured by spin-fluctuations, the composite pairing is favoured by two channel Kondo physics.

Next, Rebecca motivated why a two-channel Kondo model might be important for the 115 compounds. The Ce3+ atoms are situated in a tetragonal cage of In atoms. This leads to several crystal field doublet Gamma6, Gamma7- and Gamma7+ as a function of decreasing energy.

The Gamma7+ doublet has the lowest energy and provides the effective local spin 1/2. There is a direct coupling of the conduction electrons to this effective spin providing a first screening channel. In addition, there is another orthogonal channel mediated by the other two crystal field doublets. (Did I get this correctly?)

There was a question, if it is known that Gamma7+ is indeed the lowest doublet. The answer was yes due to neutron scattering data.

Afterwards, Rebecca explained the important features of the two-channel Kondo effect (Noziere Blandin 1980). The important aspect for Rebeccas work is that this model exhibits a quantum critical point as a function of the ratio of the two couplings J1/J2 of the two channels. In the context of the two-channel Kondo lattice model, the strong fluctuations close to this critical point provide a strong glue for composite pairing leading to a dome of superconductivity as a function of J1/J2.

3.) tool symplectic-N

The analytical formalism that was used is the so-called symplected large N approach. The problem of Kondo lattice models in general is the absence of any small parameter that could be used as an expansion parameter. So one is forced to introduce an artifical one by for example enhancing the Hilbert space by generalizing the local spin 1/2 to something else like N/2 and use 1/N as a small parameter. However, Rebecca explained carefully that this procedure is not unique and that it is important to keep the essential physics intact upon this generalization. In particular, one should ensure that the following symmetries are not violated: (i) spin rotation symmetry, (ii) time reversal symmetry and (iii) charge neutrality (the spins are neutral objects). A simple SU(N) generalization of the local spin SU(2) in fact misses the discrete symmetries. A generalization that keeps these symmetries intact is the symplectic large N approach. Rebecca presented many formulae in this context, see here paper.

She then continued with a discussion how the Kondo lattice can be treated within the symplectic large N limit. A Hubbard-Stratonovich decoupling leads to two different pairs in the Hamiltonian: a hybridization term between the local spins and the conduction electrons and a pairing term that is important for superconductivity. She then argued that this large N treatment does not give a superconductiviting ground state if there is only a single Kondo screening channel present in agreement with known results. In the present of two channel, however, there is the possibility to obtain SC. Whereas the Kondo effect is an intra-channel effect, the SC arises from an effective inter-channel interaction. The spin provide an effective coupling that can be understood in terms of an resonant Andreev scattering finally leading to the composite pairing.

Rebecca continued with explaining that the nature/quantum numbers of the two channels arising from the crystal field splittings naturally explains the d-wave SC order parameter within the composite pairing mechanism.

A question was raised whether a self-consistent solution for composite pairing is already obtained for infinitesimal small coupling, ie., N->\infty, or if there is a threshold behavior as a function of coupling. This issue was further discussed at the end of the talk.

Rebecca then presented a phase diagram of the two-channel Kondo lattice. as a function of J2/J1 there are three phases: two heavy fermion phases HFL1 and HFL2 than sandwich a composite paired SC phase close to the critical point.

4.) Illustration: two channel Kondo-Heisenberg model

Now the presented discussion was extended to include also a Heisenberg term, ie., a direct spin interaction between the local spins. Such a term favours magnetic pairing so that a competition/coexistence of magnetic and composite pairing arises, which Rebecca also called "tandem pairing". The result of this extended model were compared to the experimental phase diagram. As a function of chemical doping, Rh-Ir-Co, one observes two SC phases (Sarrao, Thompson (2007)) These were interpreted as SC phases where different pairing mechanisms, magnetic or composite, prevail.

5.) Experimental consequences

Interestingly, the tandem condensate is electrostatically active. As the composite pairing redistributes f-electron charges, the condensate acquires an effective quadrupole moment. This moment will couple to tetragonal strain c/a that, as a consequenc, will correlate with the critical temperature Tc. Such relations are known, see Bauer PRL 93 147005 (2004). Furthermore, the quadrupolar moment could be directly probed with the help of nuclear quadrupolar resonance at the In position. Such a resonance signal close to the SC transition temperature is predicted by the theory.

Summary of the talk:

* spins quench as they pair in 115 and this must be incorparated in the condensate itself

* composite and magnetic pairing in tandem to drive SC

* composite pairing redistributes charge that is

observable as a sharp NQR shift at Tc

or as a sharp shift in the f-electron valence at Tc

Open issues:

* How does disorder affect the different mechanisms

* quantum criticality

* tandem pairing extended to other families of SCs

There were a couple of questions and discussion after the talk:

Q: Are there transitions between different FL phases possible at higher temperatures?

A: You have to discriminate between different symmetries. At high T, possible crossover between FL phases.

Q: Do 1/N corrections increase or decrease the SC

A: not considered, probably decrease it. Appearance of a pseudogap?

Q: Did you consider the magnetically ordered phases within this formalism?

A: not possible in large N

Q: Is this scenario relevant for other materials with high spin entropy at low temperatures?

A:

Then there was again a discussion about the stability of the composite paired SC phase in the large N limit, questions were raised by Eremin, Chubukov and Tesanovich.