Piers Coleman (CMT, Rutgers U.)
The unsolved problem of heavy fermion superconductivity
Blogged by Mike Norman
Piers apologizes for giving a talk since he was an organizer, but was covering for Gil Lonzarich, who unfortunately could not make it to the meeting.
Piers points out the amazing similarity of the phase diagrams for many classes of superconductors, with superconductivity often found near the boundary of magnetism. For heavy fermions, this was identified by Gil in CeIn3 in a famous paper in 1998. Piers next turns to NpPd5Al2, a heavy fermion superconductor with a Tc of 4.5K, which has a divergent Curie susceptibility as one approaches Tc from above, indicating that the f spins are involved in superconductivity.
He now introduces f electron physics. Ce has an f1 configuration, with the f electron having a J=5/2. This level will be split by crystal fields to a series of Kramers doublets. As one lowers the temperature, the single spin of the f1 configuration will be screened by the conduction electrons, forming Kondo singlets. Below some characteristic temperature TK, the susceptibility will flatten and the specific heat coefficient C/T will also saturate. For a lattice of spins, once the Kondo singlets start to communicate from site to site, one forms a Kondo lattice, where the resistivity drops, forming a heavy Fermi liquid.
Now, there are two things the spins can do on a lattice. They can form Kondo singlets, or they can interact between sites giving rise to local f magnetism mediated by the conduction electrons (RKKY interaction). Doniach proposed in 1976 that at some intermediate coupling, the two effects have the same value, implying a quantum critical point between magnetism and a Fermi liquid.
Now, in classic superconductors, magnetic impurities are pair breaking. But in 1975, a Bell labs group discovered superconductivity in UBe13, but because of the above, felt that it had to be an extrinsic effect due to U filaments. Later in 1983, Ott realized it was indeed a heavy fermion superconductor. But this was preceded by Steglich's discovery of superconductivity in CeCu2Si2 in 1979. As Frank pointed out, because TK is so low, the ratio of Tc to TK is large, implying "high temperature" superconductivity. Moreover, it was later realized that this material is near the boundary of magnetism. Returning to Ott, UBe13 was even more bizarre than CeCu2Si2, since Fermi liquid behavior never sets in before one hits Tc.
Then the LANL group discovered superconductivity in UPt3. This material exhibits Fermi liquid formation well above Tc. This material was the first where antiferromagnetic spin fluctuations were identified. In 1986, three theoretical groups showed that such fluctuations would give rise to d-wave pairing. Interestingly, UPt3 is now thought to be a p-wave (blogger takes this opportunity to say probably f-wave) superconductor.
Since then, a large number of superconductors have been discovered, some near the boundary of ferrromagnetism (like UGe2), some near antiferromagnetism (CeIn3), some where inversion symmetry is broken (which would give rise to mixed parity superconductivity), etc.
Piers now returns on NpAl2Pd5, which was discovered somewhat by accident by Aoki in 2007. In this system, the ratio of Tc to TK is of order 1, so the susceptibility is still diverging when Tc is hit. There is no question the spins are involved in the pairing. At Hc2, the magnetization jumps by 0.2 mu_B, indicated the "release" of the f spins when superconductivity is destroyed. So, how can neutral magnetic moments form a charged superconducting condensate?
Piers now turns to his theory of composite pairing. The heavy electron is a product of an f spin and a conduction electron (Kondo singlet). Cooper pairs involve pairs of electrons. So, Piers proposes that heavy Cooper pairs are a product of two conduction electrons and an f spin flip.
Q: Why do the two electrons have the same spin?
PC: Because to get an S=0 Cooper pair, I have to combine a triplet combination of the two conduction electrons with the spin flip of the f electron to get a net S=0.
Now, one way to realize this is by going back to the two channel Kondo model. This model is hard to solve, but one can make progress by taking the large N limit (where N is the degeneracy of the f orbitals). Such a model has a critical point as a function of couplings where one has a divergent tendency to form composite pairs.
One consequence of composite pairs is that the f valence and f charge distribution will change at Tc, leading to a shift in the NQR frequency, which has been recently seen. Piers also points out that the spin resonance in CeCoIn5 has been seen to split into two by a field (Collin Broholm), implying a doublet, not a triplet. Is this an S=1/2 excitation instead of S=1?
After the talk, there were many questions, but as I was the chairman, I was unable to blog them.
The unsolved problem of heavy fermion superconductivity
Blogged by Mike Norman
Piers apologizes for giving a talk since he was an organizer, but was covering for Gil Lonzarich, who unfortunately could not make it to the meeting.
Piers points out the amazing similarity of the phase diagrams for many classes of superconductors, with superconductivity often found near the boundary of magnetism. For heavy fermions, this was identified by Gil in CeIn3 in a famous paper in 1998. Piers next turns to NpPd5Al2, a heavy fermion superconductor with a Tc of 4.5K, which has a divergent Curie susceptibility as one approaches Tc from above, indicating that the f spins are involved in superconductivity.
He now introduces f electron physics. Ce has an f1 configuration, with the f electron having a J=5/2. This level will be split by crystal fields to a series of Kramers doublets. As one lowers the temperature, the single spin of the f1 configuration will be screened by the conduction electrons, forming Kondo singlets. Below some characteristic temperature TK, the susceptibility will flatten and the specific heat coefficient C/T will also saturate. For a lattice of spins, once the Kondo singlets start to communicate from site to site, one forms a Kondo lattice, where the resistivity drops, forming a heavy Fermi liquid.
Now, there are two things the spins can do on a lattice. They can form Kondo singlets, or they can interact between sites giving rise to local f magnetism mediated by the conduction electrons (RKKY interaction). Doniach proposed in 1976 that at some intermediate coupling, the two effects have the same value, implying a quantum critical point between magnetism and a Fermi liquid.
Now, in classic superconductors, magnetic impurities are pair breaking. But in 1975, a Bell labs group discovered superconductivity in UBe13, but because of the above, felt that it had to be an extrinsic effect due to U filaments. Later in 1983, Ott realized it was indeed a heavy fermion superconductor. But this was preceded by Steglich's discovery of superconductivity in CeCu2Si2 in 1979. As Frank pointed out, because TK is so low, the ratio of Tc to TK is large, implying "high temperature" superconductivity. Moreover, it was later realized that this material is near the boundary of magnetism. Returning to Ott, UBe13 was even more bizarre than CeCu2Si2, since Fermi liquid behavior never sets in before one hits Tc.
Then the LANL group discovered superconductivity in UPt3. This material exhibits Fermi liquid formation well above Tc. This material was the first where antiferromagnetic spin fluctuations were identified. In 1986, three theoretical groups showed that such fluctuations would give rise to d-wave pairing. Interestingly, UPt3 is now thought to be a p-wave (blogger takes this opportunity to say probably f-wave) superconductor.
Since then, a large number of superconductors have been discovered, some near the boundary of ferrromagnetism (like UGe2), some near antiferromagnetism (CeIn3), some where inversion symmetry is broken (which would give rise to mixed parity superconductivity), etc.
Piers now returns on NpAl2Pd5, which was discovered somewhat by accident by Aoki in 2007. In this system, the ratio of Tc to TK is of order 1, so the susceptibility is still diverging when Tc is hit. There is no question the spins are involved in the pairing. At Hc2, the magnetization jumps by 0.2 mu_B, indicated the "release" of the f spins when superconductivity is destroyed. So, how can neutral magnetic moments form a charged superconducting condensate?
Piers now turns to his theory of composite pairing. The heavy electron is a product of an f spin and a conduction electron (Kondo singlet). Cooper pairs involve pairs of electrons. So, Piers proposes that heavy Cooper pairs are a product of two conduction electrons and an f spin flip.
Q: Why do the two electrons have the same spin?
PC: Because to get an S=0 Cooper pair, I have to combine a triplet combination of the two conduction electrons with the spin flip of the f electron to get a net S=0.
Now, one way to realize this is by going back to the two channel Kondo model. This model is hard to solve, but one can make progress by taking the large N limit (where N is the degeneracy of the f orbitals). Such a model has a critical point as a function of couplings where one has a divergent tendency to form composite pairs.
One consequence of composite pairs is that the f valence and f charge distribution will change at Tc, leading to a shift in the NQR frequency, which has been recently seen. Piers also points out that the spin resonance in CeCoIn5 has been seen to split into two by a field (Collin Broholm), implying a doublet, not a triplet. Is this an S=1/2 excitation instead of S=1?
After the talk, there were many questions, but as I was the chairman, I was unable to blog them.
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