Discussion+reports

This page contains brief reports on discussions that have occurred so far. Reporters: please add your notes by editing this page. Please contact Clifford Hicks if there are points here which are incorrect and need correcting. Talk slides and recordings of the talks and discussion are available at http://online.kitp.ucsb.edu/. Speakers: please upload your talk slides to [|http://online.kitp.ucsb.edu/online/author/.]

toc =10 December= **Edge current session** **After talk by G. Luke:**

Q: What other materials show TRSB sigantures in muSR experiments? A: All that show evidence are also considered TRSB candidates for other reasons, but are not firmly established as such. The most relevant materials are UPt3, Sr2RuO4, PrOs4Sb12, and some other doped compound.

Q: What is the nature of these other candidate materials, such as their order parameter symmetry? A: They are still under depate. The orbital symmetry of UPt3 seems to be E_2, but there is conflict between NMR and Hc2 on whether the d-vector is locked by SO coupling or not. UPt3 belongs to a high-dimensional representation and exhibits multiple phases with the low temperature phase widely believed to exhibit TRSB. It is possible that the field distribution leading to the muSR signal has relatively long tails, and the field scale could be somewhat larger if it occupies only a fraction of the sample volume.

Q: Could muons themselve create a local moment? A: This should produce a signal corresponding to a more homogeneous field, since there are only few non-equivalent muon stopping sites. Thus, it is not a likely explanation for the observed signal.

Q: Could on tune the muon energy? A: In principle yes, but it requires a different procedure for muon production with a lower yield. No one has attempted the integration of a He3 or dilution fridge into an appropriate beamline.

Q: Some other material break gauge symmetry before TR symmetry. Is it of any significance that TRSB sets in right at Tc for Sr2RuO4? The general consensus seemed to be that this is not the case. It was also noted that one enocunters different temperature dependences. The muSR TRSB signal varies linearly near Tc for Sr2RuO4, but as a square root for other materials.

After talk by J. Kirtley:
Q: Is there room for different surface state? The general consesus was that while the surface may have an effect through various measurements, it is unlikely to explain the apparent absence of chiral currents, since the surface state would have to extend several penetration depths into the sample in order for any lower lying edge currents to be fully screeened.

After talk by C. Hicks:
It was noted that a smooth cutoff in the gap Delta as a function of energy should not affect chiral currents. Similarly, edge scattering should not lead to a large change.

There was a general discussion on chiral currents in He3. They have no been detected directly, but there is one indirect magnetization measurement based on acoustic attenuation in a field, for which a small asymmetry was predicted. The experiment appeared to be troubled by hysteresis upon field reversal. If there were null-results, they were not published. The expected Faraday effect is still debated by one order of magnitude, and would be near the noise limit of the Kapitulnik group.

It was discussed whether the phase sensitive measurement by the Liu group imply small domains, and pointed out that many pi phase shifts would still give long range coherence. Ying Liu believes this scenario to be unlikely, and noted that there was no evidence of dynamic switching.

V. Yakovenko proposed a scanning experiment to directly probe the triplet pairing: Consider a junction between a singlet and a triplet superconductor, with d||z_hat for the latter. Assume paring amplitude in the off diagonal gap- matrix elements. -> diffetence between singlet and triplet pairing is just a sign in the gap matrix. The Andreev states (obtained from BdG) should have a well defined spin projection. Their energies for spin up and down, plotted as function of the phase difference across the junction, will have opposite signs because the sign difference in one of the off-diagonal paring amplitudes. A junction without external leads will minimize the energy w.r.t. the phase difference. Since this minimum depends on spins, the system should break summetry. Only Andreev states with the lower energy spin will be occupied, leading to a spin accumulation. Its magnitude might be on the order of 1 spin per surface atom. The temperature scale, i.e. difference between up and down energy, is set by the transparency of the junction.

Experimental evidence that the A-phase in He-3 is the ABM phase ~ d (px + ipy) - NMR frequency shifts - acoustic spectrum indicating collective modes. - vortex sheets in rotating 3He-A

=11 December= **Time reversal symmetry breaking II: Kerr effect** **During/After Talk by A. Kapitulnik**

For the field cooling (training) to polarize, it needs to be above a minimum of 5-10 Oe.

It is not known what amount of field is left inside the sample after turning of the field.

There is not enough sensitivity to say if the signal changes when the field is tuned off.

The new single data point, showing increased effect with narrower beam, shows a smaller effect than expected.

Take field cooling data as it cools was not done because of experimental problem (sample holder not cooled homogeneously, etc).

Q: Are the fluctuations in zero-field cooled related to warming up or are they observable if you stabilize the temperature. A. They have not stabilized the temperature. They have seen all possibilities of fluctuations but 7/10 of runs show full signal.

The effect is not seen in type II superconducting Aluminium thin films, lead and YBCO. For heavy fermions it depends which one. It is important to do both Al and lead because they reside on different sides of spin orbit interaction and that is important for magneto-optics.

There were comments mentioning the presence of collectives modes contributions to the signal.

After Talk by V. Yakovenko
Cannot calculate the absolute amplitude of the Kerr rotation because calculations (with additional terms) are now too complicated.

There are other ways to arrive at these results. This way used field language (and effective action) but it could be done for example using vertex corrections. The transverse part of the calculations is okay, the longitudinal part is the problem.

The first paper had a signal when using plane waves but that was because of dropping a term which actually cancels the effect. The term was dropped because at high frequency, past the cut-off energy, the supercurrent is not well defined anymore. But when including the term, the plane waves give no effect and only a non-zero q(parallel to surface) wave leads to the effect.

Kallin, Roy and Yakovenko seem to agree on results of calculations but maybe not with Mineev.

After Talk by V. Mineev
The calculations uses the largest in-plane plasma frequency.

The F used in the diagrams is obtained from gradient expansion of Gorkov's equation in an electromagnetic field. The vertex is an operator that acts on Green's functions. It gives zero on the superfluid Green's functions and produced the term introduced in the talk when applied to the normal Green's functions.

After Talk by R. Roy and about last 3 talks
The longitudinal calculations for s-wave superconductors has rarely been done right because you need to do it in a gage invariant way.

If the plasmon is excited by another beam then there is an effect on the Kerr rotation but only for a chiral system because the longitudinal-transverse coupling exists only for chiral, it does not exists for s-wave.

This is an interesting experiment that might be done in the future.

There was a discussion about equilibrium/non-equilibrium. This is not quite the right language since all the calculations are done in linear response. It refers to treating self-consistently or not the high frequency term when it is above the high energy cutoff. So to either drop or not the time derivative at high frequency. Another way to look at it at high frequency does the order parameter react to the fact the the electrons are oscillated at high frequency. Instead of dropping the term, above the cut-off you need to include the retardation and that will destroy the cancellation that appears in the new calculations.

The experiments are done at 1.55 µm which is where the hardware is easily available (optical communication frequency). The experiments can be done at twice the frequency (0.82 µm). The size of the signal could be larger or smaller. Other frequencies are not feasible right now.

The theories have the same results at low frequency (when dropping the time derivative term). If you need to keep the derivative above 1eV you need to consider the next order (i.e. include the effect of the time derivative).

In zero field Mineev Hs is zero in the bulk without domain walls.

The dj_s/dt term at high frequency is connected to the delta function in a superconductor at ω=0 in the real response and should not disappear because of causality so should have no reason to drop the term. There was mention of old measurements (at Berkeley?, monopoles) that showed the 1/ω term still present at very high frequency.

The Kerr effect calculations have opposite sign for opposite chirality which implies the measurements were seeing one domain (hence domain larger than 20 µm or of about that size) while µSR requires smaller domain walls.

The muons does not travel and land where there are inhomogeneities. They land in one or two sites in the unit cell on oxygen bonds.

Field cooling would produce a predominant domain direction so the signal should be bigger. Zero field cooling sees variations which can be due to domains smaller than the beam crossing. The ZFC data can be seeing a signal coming from many domains as long as there is an odd number (or different sizes for both chiralities) the effect is a reduced signal (just the residual from the cancellation is left).

After Talk by J. Kirtley
The samples with holes don't show any particular signals because the holes are not very big. The ac measurements on those samples were not done carefully but they certainly did not detect a signal as big as what was seen. They are confident to be able to detect the signal from a hole but certainly not as big as the signal from the inclusions.

There is nothing (no signal) around 3 K and you expect to see something. The fraction going superconducting is small but you see it in ac susceptibility measurements.

Part of the sample is pure Sr2RuO4 so you can see that the susceptibility is homogeneous in that region.

=12 December= **3K phase, and PrOs4Sb12, and magnetometry on Sr2RuO4** **after talk by M Sigrist**

Does frustration among Ru inclusions lead to phase gradients and spontaneous currents? Sigrist reckoned that this was probably a rarely occuring phenomenon, that the Ru inclusions are likely too dilute.

Ru inclusions have so far been regarded more as an experimental nuisance, but in fact they are interesting subjects for experimentation in their own right. They appear dilute in faces cut perpendicular to the inclusions, but in faces cut parallel they occupy a large fraction of the area.

Jc of the inclusions is made through bulk measurements and the features are very subtle, ~100nV, in the range where thermoelectric effects, for example, are significant, so it would be useful for this measurement to be repeated.

Why is Tc enhanced at Ru inclusions? Likely due to strain effects. A more specific description: strains in SRO are eased by rotation of the RuO6 octahedra, leading to a narrowing of the gamma band (the dominant SC band) and certainly some effect on the pairing.

Thousands of interfaces between superconducting materials have been studied; isn't enhancement of Tc like this very surprising? Why is it not more common. Apparently Zachary Fisk knows of another example. But still, how lucky a coincidence is the 3K phase?

Evaporating Ru onto a clean SRO surface does not lead to a 3K phase.

The Ge-Ag interface is superconducting (as is Ge by itself under strain (?)). A similar phenomenon?

After talk by Y Liu
Au/Sr2RuO4 interface: there may have been another experiment by a Japanese group in which the sharp change in the tunnel conductance with a temperature change of only .002K \ (at around .5K) was not observed.

The complex features in the Sr2RuO4 N-S junctions are reminiscent of the complex I-V curves that the van Harlingen group has seen in UPt3.

Instead of flakes of Ru in SRO, How about a flake of Sr2RuO4 embedded in Ru?

Cleaved, polished SRO: appears that one almost never gets a superconducting ab-plane surface. C Lupien managed is once in many cleaves of SRO, for STM measurements. Y Liu observed a superconducting surface once in a SRO214-327 eutectic, suggesting that strain in the eutectic prevented the RuO6 octahedra from rotating at the surface near the eutectic boundary. The IV curve was consistent with weak-coupling superconductivity.

After talk by C Hicks
A very large zero-bias conductance peak has been observed by J Wei, indicating a sign change in the order parameter.

The TRSB in PrOs4Sb12 may be multipole rather than chiral- analagous to d+is rather than p+ip.

After talk by K Machida
The quasiparticle contribution to the spin susceptibility observed by NMR is not actually known. In current NMR literature on SRO it is assumed that the orbital part of the Knight shift is constant in temperature and can be extracted by extrapolating to zero on the usual Knight shift - normal state susceptibility plot, but this is not o accurate in SRO and the van Vleck term (which varies with T) might be significant. So the expected form of the spin susceptibility in the case of singlet pairing is not known certainly.

NMR is a surface probe and may not be seeing the bulk d-vector.

Could features in gamma(H) actualy result from mutli-band effects?

There is not much doubt that the spin susceptibility is flat (with varying T) for in-plane fields. However the c-axis experiment is more difficult- the internal fields in the mixed state are much more inhomogeneous because lambda_ab is so much smaller than lambda_c, leading to a broad NMR resonance. The NMR shifts the experiment attempted to resolve are smaller than the resonance width.

In UPt3 there is also a conflict between NMR data and bulk magnetic properties. NMR only sees the surface. NMR sees a flat spin susceptibility but bulk magnetization data show strong Pauli limiting along the c-axis.

Neutron scattering has also observed no drop in susceptibility for in-plane fields, but this experiment has not been reported yet for c-axis fields.

Talk of Eun-Ah Kim
Key Points: 1- Superconducting phase changes by pi (not 2 pi as a usual vortex) as core is circled once, the missing minus sign is restored by rotating the in-plane d-vector by pi. 2- Microscopically, there is a 2 pi phase winding in the up-up pairing gap and no phase winding in the down-down pairing gap. 3- The BDG equations describe particle-hole mixing in the same spin state, leading to zero-energy majorana mode. 4- NMR c-axis and ab-plane NMR both see no change in spin susceptibility. The in-plane data is interpreted as having the d-vector along the c-axis. The c-axis data is interpreted as a c-axis magnetic field flipping to an in-plane d-vector, allowing for the possibility of the Phi_0/2 vortex. 5- The d-vector rotation is not screened, so half-flux quantum has energy that diverges as logarithim of system size. Pair of half-vortices has finite energy.

Questions during and after talk:

Q-How does a square vortex lattice ensure a chiral p-wave? A- The field distribution seen experimentally is consistent with chiral p-wave. Q- How can in-plane d-vector account for Josephson coupling? A-This needs more analysis. Q- What does c-axis dispersion do to zero energy states? A- Need 2D to have isolated majorana states for non-abelian statistics to be robust. Q- Is the origin of the Phi_0/2 energy cost purely kinetic? A-Yes Q- Can divergent energy cost be eliminated by placing fractional vortices in an array? A- Yes

Talk of Suk Bum Chung
Key Points: 1- A pair of Phi_0/2 vortices in a bulk system can separate more than a penetration depth if rho_sp<rho_s (meaning spin superfluid stiffness is less than usual superconductor stiffness). 2- Materials with typical lengths smaller than the penetration depth can also be used to stabilize Phi_0/2 vortices.

Questions during and after talk:

Q- Spin-orbit can perhaps lead to electric fields which may be bad for Phi_0/2 vortices? A - Maybe Q- Spin-orbit will probably lead to a confinement of vortices? A - The relevant spin-orbit coupling will be small, much smaller that spin-orbit that selects in-plane versus c-axis d-vectors. Q- How big is SO? A- The single-particle SO can be on order of 0.1 eV, but the relevant effect is the splitting of the Tc’s for the different directions of the d-vector and this is much smaller (perhaps negligible). The Fermi liquid parameters that define the difference of rho_s and rho_sp generated much discussion. Q - Can the Fermi liquid parameters not be measured? A- Perhaps, but it is reasonable to expect that generically rho_sp is less than rho_s. Q- How do electron-electron interactions play a role? A- If there are no correlation effects than rho_sp=rho_s. Otherwise expect rho_sp is less than rho_s

Talk of Hendrik Bluhm
Key Point: Distinct features in M(H) patterns can be used to observe fractional vortices.

Question following talk: Q – What is the role of the Josephson coupling? A – It leads to metastable soliton solutions.

Talk of Yukio Tanaka
Key point: Vortices in different chiral p-wave domains will have different density of states in the shadow region.

Questions following talk: Q- Does the vortex in different chiral domains sit at different distances from the wall? A- Yes, the Bean Livingston barrier differs. Q- Does this lead to an M versus H asymmetry. A- Yes. Q- Is the Doppler shift the origin of this effect? A - Yes.

=13 December= **Session: Multiple component order parameter** **After the talk by Lupien***

There were several questions about the data collection and analysis. What range was the power law seen? From lowest T (40 mK) to about 500 mK. Can the transverse signal pick up longitudinal response accidentally? Is there any mixing of transverse and longitudinal excitations in the transducer? The answers are that there should be no problems..

The attenuation data seems to suggest small in-plane gap anisotropy; Data on jump in velocity was published only in the Ph.D. Thesis. Ultrasound attenuation measurements performed on UPt3 suggested line nodes in basal plane.

After the talk by Sigrist
There are several questions on how much ultrasound measurements tell us about multiple component and chiral p-wave superconductivity. The ultrasound jump data suggests that the superconducting order parameter had to be of multiple components as a single-component superconducting order parameter does not lead to a transverse signal. However, whether it is chiral cannot be determined. There was also a question on whether one can distinguish chiral p- from chiral d-wave superconductors. The answer is no.

After the talk by Agterberg
There is a general theorem that there should in general no line nodes by symmetry consideration in p-wave superconductors. The answer is that when you write out the full form of order parameter (for example, including kz dependence) then one can remove line nodes. There was another question as to whether the square vortex structure requires cylindrical Fermi surface. The answer is you need a small deviation from the cylindrical structure.

Other questions: Can you get square vortex lattice within singlet. Yes the prediction is a quantitative prediction not protected by symmetry. Is it always square? Not necessary. It can be triangular at low temperature.

After the talk by Luke*,
The muon experiments suggest that there are no nodes on the gamma band. If there are nodes, they have to be on alpha or beta bands.

There was a question as to whether there are two transitions (between square and triangular lattice). The answer is may be.

There is also a question on how the data in time domain was analyzed to arrive at conclusion on lattice structure. The answer is that the conclusions are based on the qualitative instead of quantitative features of the data.

After the talk by Sigrist*
There was a question on whether the power-law behavior is the due to disorder. The answer is cautious no. There was also a question on whether all experiments can be explained by band dependent rather than line nodes. The answer is that this is difficult to determine experimentally.

What about the data on angle dependent thermal conductivity results which suggest very little in-plane anisotropy? The answer is that the lowest temperature of the measurements, 0.3 K, is probably not low enough.

Is there an upper limit in the gap anisotropy that could be obtained from the data? Not available at the present.

After the talk by Nomura
There was a question about how theory can be used to analyze data on the longitudinal sound velocity jump. The answer is that the jump is dominated by gamma band but there are 5 fitting parameters. Another question is whether there is an exponential part in the temperature dependence. The answer is that it is hard to know.

The perturbation theory is carried out down to the third order. The question is what parameter one needs to obtain the final results. The answer is that only U and J's.

Discussion on Hc2 suppression
Maeno's talk connected the double transition near Hc2 for fields in the ab-plane with the suppression of Hc2 and put forward a model where the order parameter chirality contributes to the Hc2 suppression. Typically one would expect this to be a small effect, so one would need to identify a mechanism for enhancing this effect.

In the discussion, it was pointed out that the order parameter symmetry classifications used for strontium ruthenate are relevant only for the case of strong spin-orbit coupling. While the atomic spin-orbit coupling is believed to be strong, the energy splittings of the various order parameters may be sufficiently small that the strong spin-orbit classifications are not appropriate. In particular, one should consider whether an order parameter with the d-vector in the plane might better explain the experiments in a magnetic field.

Agterberg pointed out how one expects different slopes for Hc2 near Tc for fields along c and fields in the ab-plane, for the proposed chiral p-wave order parameter. On the other hand, experiments see identical, or nearly identical, slopes and this requires some other explanation. Sauls pointed out that there might be a high magnetic field transition which influences the experiments.

Mineev pointed out that the 2-component chiral p-wave order parameter leads to an anisotropy of Hc2 in the ab-plane which could be measured as a function of field angle. Maeno stated that only two angles (100 and 110) had been measured so far.

Kittaka presented new data on the double transition near Hc2 for fields in the ab plane. Kittaka also showed how the data appeared to give a small anisotropy near Tc for fields along c and perpendicular to c, but that this anisotropy had the opposite sign to the anisotropy observed at lower temperature.

December 18
**Exotic Physics and Quantum Computing**

M.P.A. Fisher talked about the difference between edge excitations in quantum Hall states and SRO. He first introduced the 5/2 quantum Hall state and the Moore-Read Pfaffian wavefunction, which is the quantum Hall incarnation of a p+ip superconductor of spinless fermions. He discussed the neutral Majorana edge mode which is present at the boundary of such a quantum Hall state or a spinless p+ip SC; the physics of low-energy electrical charge modes is quite different. The quantized transverse thermal conductance was discussed in this context. Ong asked about experimental difficulties involved in making such a measurement. The difference between the tunneling of quasiparticles in the 5/2 QH state and the tunneling of vortices across a weak link in a p+ip SC was also discussed: the former are essentially quantum-mechanical but the latter are very classical.

M. Stone talked about how Majorana zero modes arise in the solution of the B-dG equations in the presence of vortices in a chiral p-wave SC. He began by using semiclassical arguments based on Andreev reflection and then showed the solution of the B-dG differential equations. The zero-energy solutions are Majorana fermions, and he discussed Majorana fermions and the Clifford algebra. The connection to Ising model fusion rules was explained: when two vortices are brought close together, either nothing will be left over or a single fermion will be left over.

M. Freedman talked about `measurement-based quantum computation'. This is a scheme by which one can prepare an entangled state (which doesn't depend on the particular computation) and perform a series of measurements to implement a computation rather than gates enacting unitary transformations. The talk began by drawing an analogy with sailboats tacking into the wind (and the defeat of the Spanish Armada by English). The concept of `forced measurement' was discussed and it was shown how a sequence of forced measurements could mimic a braid.

B. Seradjeh talked about a scheme for layering a SC on a 2DEG in an integer quantum Hall state. He argued that anyonic phases could be obtained by braiding such vortices.

Lessons from He3
Tony Leggett presented an alternative to the usual BCS wave function for a chiral p-wave superconductor. His wave functions starts from the filled Fermi sea, rather than the vacuum, and creates both electron and hole pairs in such a way that it reproduces the BCS wave function for s-wave pairing. However, for chiral p-wave pairing the angular momentum of the condensate is reduced by a factor of the square of gap over the Fermi energy. This dramatically reduces the magnitude of the predicted supercurrents at edges and domain walls. In response to a question about the experimental situation, Tony responded that the experiments on He3 are more compatible with this reduced superflow, than the prediction which follows from BCS. Jim Sauls talked about the collective modes in the B phase of He3 where theory and experiment are in excellent agreement. On Thursday, Jim will present a proposal for an experiment to detect collective modes in strontium ruthenate. The frequency requirement (GHz) makes it difficult to detect these collective modes and it appears that, to date, there is no experimental confirmation of the existence of the collective modes one would expect to result from the complex, multicomponent order parameter.

December 19
**Is it Triplet?**
 * Talk by Ishida: NMR experiments**

Q: Could the observed 1/T1 data be consistent with s-wave pairing states with line nodes? A: The coherence factors should still lead to a small Hebel-Slichter peak, which is never observed. Also impurity scattering would make the gap more isotropic, increasing the Hebel-Slichter peak, which is not seen even in reduced Tc samples.

Q: The evidence for line nodes from the T^3 temperature dependence of 1/T1 is mainly between 0.2 Tc and Tc. Is it consistent with a strongly anisotropic gap without true nodes? A: Possibly strong anisotropy could be consistent with the data.

Q: The c-axis field NQR experiments are in a field close to Hc1. Is there independent evidence that the field is penetrating the sample in these experiments? A: Not directly. The linewidth is dominated by inhomogenous broadening, and there is no significant extra broadening from the vortex lattice field distribution, for example the linewidth is similar above and below Tc.


 * Talk by Ong: Torque magnetometry experiments**

Q: The 50-60G field where vortex entry is first observed may not be Hc1 because of demagnetizing factors. A: The factors have not yet been accurately estimated in this geometry, but the observed field should be an upper bound for Hc1. Ac susceptibility measurements put Hc1 at about 30G.

Q: Could the unusual features of the torque curves be affected by inclusions of the 3K phase? A: No. The scale of all features shrink near to Tc and no hysteresis is observed above Tc.

Q: is there evidence for meta-magnetism in high fields? A: There is a clear signature in CeCoIn5, where M increases abruptly as soon as superconductivity is suppressed at Hc2. There is no corresponding effect in Sr2RuO4.

Q: Is there evidence for the edge current, or the texture current j=curl(rho_s l)? A: The regions of reversibility in the M-H curves appear to correspond to surface current, which changes reversibly with H for small changes in H. While the irreversible changes appear to be consistent with bulk trapped flux within the Bean model.

Q: Is there evidence for a 1st order transition at Hc2 or in the Deguchi phase transition? A: There is no observable jump in the data. The small jump in the preliminary data shown is probably due to the incomplete background subtraction.


 * Talk by Agterberg: Surface reorientation of the d-vector**

Q: If the gap d-vector structure becomes modified at the surface, what is the healing length over which it recovers to the bulk? A: It depends on the bulk energy differences between phases. If these are small then the healing length can be long. In the case the energy differences are zero, as in 3He, we have textures.


 * General discussion session**

Q: What are the essential experiments which rule out s-wave pairing? If we concentrate on the in-plane H Knight shift experiment as most decisive, are there other cases where no Yoshida function change in susceptibility is observed? What are the exceptional cases for spin singlet pairing? A: The c-axis Knight shift in YBCO is constant, despite d-wave singlet pairing. But this is an exceptional case, and this can be understood because chi_s is changing and there is the expected change in K_ab. K_c does not depend on chi_s and so it is not measuring the relevant spin susceptibility.

Q: The data shown earlier for UPt3 also showed constant susceptibility below Tc, but it is often claimed that this is a d-wave superconductor? A: The p-wave interpretation is more probable in this material.

Q: Can one do an ESR type experiment? A: There is no observable ESR signal in the normal state

Q: Is the Knight shift experiment consistent with neutron scattering? A: The Hayden spin-polarized neutron experiments repeated the Shull-Wedgewood experiment in V3Si confirming they can detect changes in spin susceptibility in s-wave materials, but again observed no change in chi_s below Tc in Sr2RuO4 for ab plane fields.


 * Second talk by Ishida: Recent muSR experiments**

Q: Do all groups agree on a Lorentzian lineshape, and the size of the field distribution? Do the three different experiments find consistent results? A: The raw experimental data are consistent, but not all groups interpret their data in the same way.

Q: Does the internal field observed have a preferred orientation? A: The Luke experiments tested this, and found similar results for different muon initial spin orientations, so no preferred direction for field.

Q: If Tc is suppressed by impurities, does the onset of the spontaneous field signal in muSR track changes in Tc. A: Yes it does.

Q: What is the volume fraction estimated where the internal field is non-zero? A: About 20% of the volume, corresponding to a 1 micron domain size.

****Normal state/nodes/mechanism****


 * Talk by** **Mackenzie: normal state and Spin orbit effects**


 * 1) ARPES and LDA do have an overall shape right. The scale of the effective mass is missed in LDA ( factor of 6 mismatch). This factor is present at all energy scales, not just near FS.
 * 2) To account for this mismatch Andie proposed to look at the electron- electron interaction that is very local in space.
 * 3) Tight binding fit to the ARPES data provides a starting point for theories trying to develop microscopic description of SC state.
 * 4) Effect of Spin-Orbit interaction need to be revisited. Andie referred to the Advances in Physics, v 59, p 639 (2003). In there data already contain the effects of SO interaction. They are manifested as a spin dependent bending of the LDA bands ( k-dependent Zeeman term).
 * 5) Provided estimate of the SP terms to be on the scale 70 micro eV /Tesla.


 * Talk by Nomura on Mutiband Supercondutivity**

used third order perturbation theory (U and J) to develop effective pairing interaction. secondary gaps open up at alpha, beta sheets. These secondary gaps are small and are on the scale 0.2 K and 0.3 T.
 * 1) Description of the effective Hamitonian and pairing interaction.
 * 1) Leading gap is on gamma sheet. No nodes in the gap albeit gap is anisotropic.
 * 1) One of the gaps has to have node (no topological reasons to protect it) to account for the power laws seen in ultrasound down to 40mK.
 * 2) Three bands fit can account for the complicated field dependence H || ab of the specific heat.


 * Talk by Annett**
 * Effects of spin orbit interaction and first order phase transition induced by magnetic field.**

this flip would cause a first order phase transition.
 * 1) Magnetic field can cause the ground state to flip between chiral p+ip state with d vector out of plan to d vector in plane.
 * 1) role of Spin Orbit interaction is discussed.
 * 2) James found that his LDA calculations are pointing to the much stronger ( 100 mev/T) spin orbit terms then the estimated by Andie


 * Talk by Maeno on multiband superconductivity.**


 * 1) Yoshi started with the discussion on the specific heat. Pointed out that the specific heat can be explained within the multiband model.
 * 2) As an example the model by Nomura and collaborators is used. Gamma band is driving the SC state. The multiband proximity effect induces gaps in alpha and beta bands. One needs a gap node on beta band. This node is not required by any symmetry and is accidental. At the same time this note is robust.
 * 3) Yoshi claims that specific heat is better fitted with the fully gapped gamma sheet gap.
 * 4) Question raised about the splitting of SC transition even in H||c geometry since the effective mass and coherence length would be different for different gaps. And why this splitting is not seen experimentally.
 * 5) From questions and discussion it seems that there is no experiment that can rule out horizontal nodes.


 * Talk by Victor Yakovenko on surface state in p+ip superconductor.**


 * 1) Victor revisited the surface midgap states in d-wave superconductor. Discussed the role of the order parameter reversal and formation of the intragap state as a function of the qp momentum along the surface.
 * 2) In tunneling experiments one always finds the sharp cusp sat zero bias in tunneling conductance. One can explain it by looking at tunneling into surface Andreev bound states. These states produce a peak in conductance at zero bias. If one takes into account the dispersion of the gap along k_z one gets a distribution of gaps that tunneling electrons see. Summing over all gaps one gets singularity at zero energy that leads to the cusp in total conductance.
 * 3) Question raised about the point contact vs planar tunneling and presence/absence of the insulating layer. Theory is applied to both cases.

=20 December= **Semi-Exotic Vortices** **Talk by Klaus Hasselbach** Hasselbach talked about muSQUID measurements done at Grenoble to look at vortex physics in Sr2RuO4. The point was made that anisotropy is important in SRO perhaps similar to BSSCO. The measurement incorporated an AFM device and a compact dilution fridge. A tuning fork was used to control the distance from the sample. The method was benchmarked with NbSe2. Strong flux expulsion was observed in SRO implying weak pinning, unlike the cuprate materials. Measurements at low field showed weak vortex repulsion. Different behavior was observed in areas separated by a defect or trench. The trenches were found by inspection. An in-plane field of 10 G was enough to align the vortices so defects were thought not to play a role in linear clustering. Number of vortices in the lines depends linearly on in-plane field. They could be rotated with a rotating in-plane field. Vortex chains are present at low fields and could coalesce.

Q: Contradicting statements about strong pinning were reported earlier by Ong. A: It was noted surface barrier may act for entry and not exit.

Q: Effect of thermal cycling? A: Similar patterns were observed with nucleating at the same spots.

Q: Photographs of the surface? A: The sample is cleaved and AFM images show very small roughness. Surface corrogation was about 3 A, smaller than NbSe2. 3K phase due to Ru inclusions was not seen in susceptibility measurements.

Q: Could the observed domains be due to easy path of entry rather than chirality? A: Can't be ruled out. Needs larger image sizes than the current 60mux30mu.

Q: Cooling in large field, so that if they are domains sing of field-induced flips can be seen? A: Need more data.

Q: What is the min. field required for rotating the chains? A: very low ~ a few G.

Q: Could vortices be sweeped out by in plane field as in BSSCO? A: Yes.

Q: Edge currents? A: Have not been looked for. Th SQUID has lower sensitivity than Kirtley's.

Q: K. Moler's group saw no effect when a deep hole was made into the sample. A: The depth of the trenches were not measured, but they may run to the edge of the sample.

It was noted that non-torque-magnetometry could be performed here and it would be interesting to compare the M(H) curves obtained.

Talk by Dan Agterberg
Agterberg talked about semi-exotic vortices with fractional value of flux. He used a simple model with a U(1)xU(1) symmetry, one for the usual phase and one for the in-plane spin rotations to describe such vortices. He derived a relation for the flux as a fraction of two superfluid densities for the two components. The simple theory does not take account of spin-orbit coupling, thought to be important in real materials. Such vortices have log-divergent energy costs. The breaking of the spin rotation symmetry from U(1) down to Zq would confine these vortices with a linear potential. The confinement is significant for SRO. However, Sigrist, Ueda and Rice argued in a '89 PRL that they might occur as line defects on domain walls of a chiral superconductor.

It was noted that the U(1)xU(1) symmetry could arise in FFLO superconductors, 3He/4He superfluid mixtures, in a rotating superconductor, or a neutron star! It was also noted that the energy cost may be lowered by solitons.

Talk by Belitz
Belitz talked about spatial 2D Skyrmions in the spin component of the gap function in a p-wave superconductor. Skyrmions could have a lower energy than the usual vortices for large values of kappa (LG paramter). The interaction was said to be 1/r, so a lattice of such defects would have a different stiffness. He described the results of their theory for the melting curve, good for H~Hc1. In contrast to the vortex lattice melting curve, there is no melting near Hc1.

The dependence of the enregy on kappa was questioned. An opposite behavior was said to be expected due to core energy.

The transition from the Meissner state to the Skyrmion lattice was noted to be first order.

Talk by Jim Sauls
Sauls talked about "Non-Equilibrium Dynamics of Superconducting Vortices." The point was made, quoting a Woody Allen line, they "they always come in pairs". In the time-reversal broken state of a p-wave superconductor with Lz=1 with cylindrical symmetry enforced at large distances a quantization relation was derived for the relative and center-of-mass phase. Various vortex types were tabulated: interesting cases were a "non-vortex vortex" with no overall phase winding but a core and a double vortex with homogeneous core.

Q: Stability? A: The GL calculation were done in the clean limit of mean free path ~ 5-10 coherence lengths and by tuning beta_2/beta_1 in the GL theory down to low values. A transition in the core and also the vortex lattice was seen. In SRO there is strong phase locking and beta_2/beta_1 is estimated around 0.5.

Afternoon session: new experiments
Jim Sauls: Suggestions for new experiments on SRO

The main topic of the talk was the possible signatures of BTRS in acoustic experiments. Jim started with a model of BTRS in the ground state assuming spin-singlet pairing. There was a long discussion of spin-singlet vs. spin-triplet order parameter. It was hard to reconcile the spin-singlet assumption with the Knight shift experiments on SRO. However, in other materials like URu2Si2, the spin-singlet model is more realistic. Jim reviewed scattering of quasiparticles on paramagnetic impurities and discussed transport coefficients in unconventional superconductors. Then, he discussed chiral Faraday effect in acoustic experiments.

Q: Do we believe in the possibility of interplane superconducting pairing ? A: There was a long discussion of the spin-singlet assumption and compatibility of it with the experimental data. The consensus was that the spin-singlet pairing is unlikely to describe the experiments on SRO.

Q: What assumptions are used in order to obtain the Faraday effect? A: The effect depends on the particle-hole asymmetry and is zero otherwise.

Q: What happens within the interplane coupling model under the compression? A: Experiments show that Tc goes down under uniform compression and goes up under pressure along c-axes.

Q: If there are accidental zeros in the gap, will the results be the same? A: No, the effect (the Faraday rotation) is zero in this case.