Girsh Blumberg (Rutgers): Raman spectroscopy of multiband superconductors with competing order parameters

Girsh started by a remark that his talk will be devoted to the many-body aspects of multiband superconductivity as seen from Raman spectroscopy.

First example given is a Raman study of layered system, NbSe_2, by Sooryakumar & Klein, PRL 45, 660 (1980), the material with coexisting CDW (T_CDW ~ 9K) and (multiband) superconductivity (T_c ~ 2K). The first challenge for Raman spectroscopy was to keep the material below the sc transition temperature as laser heats the sample [remark about the Burch's talk earlier today].
On the theory side the story began with the study by Abrikosov and Falkovskii in 1961.

What is interesting on the side of multiband superconductors? Following Littlewood and Varma in 1982 there are two possible modes in a usual superconductor: amplitude mode (amplitudon) and the phase (Bogolyubov-Anderson ) mode. In a multiband SC there is an additional Legget's mode associated with the phase difference of the sc gaps on different bands.

Next Girsh has reviewed the classical work by Klein and Dierker, PRB 1984. In the normal state
the only electronic excitations Raman spectroscopy is able to see is a particle-hole continuum with a small (almost zero) momentum transfer. In a superconductor due to renormalization of the electron bands the continuum will be gaped up to a twice of the sc gap. Observed by Hackl (at a time graduate student) in V_3Si for the first time. HOWEVER: this is all for non-interacting electrons: in case the residual interaction is involved the peak at 2\Delta could be shifted to the lower energies and whether it happens or not depends on the symmetry of the OP, Raman vertices and so on. Special example is a long-range Coulomb interaction. The excitation driven by light are electron charge densities which should be screened by the long-range Coulomb interaction especially in the fully symmetric A_1g channel.

Then he moved to cuprates, and has shown experimental examples of Raman scattering in the various (B_2g, B_1g, and A_1g) symmetry channels. Due to the fact that Raman vertices are momentum dependent and have maximums and minimums at the various parts of the Fermi surface you realize that B_1g probes mostly quasiparticles around the M point of the BZ, while in B_2g you taking mostly the excitations around the diagonal of the BZ. Naturally if the gap is d-wave the largest effect comes in the B_1g channel [few curved from YBCO]. Then he moved to the story of interaction and reminded about the work by Chubukov and Deveraux on the final-state interaction effects in the B_1g channel (below T_c). Comments by Chubukov: first work is with Girsh. Comment by Nevidomskii yielded the understanding among the audience that what we hear today is only the electronic Raman scattering. [no two magnon, no phonons]. Hirschfied pointed out that in the data the peak is hardly distinguishable from usual 2\Delta peak, Chubukov replied that the story actually is that the peak in Raman is BELOW 2\Delta and the latter is measured by other techniques and this is what effect of the interaction is: shifting the peak to energies below 2\Delta.

Then Girsh turned to the electron-doped cuprates (PCCO) and the story of electron and hole pockets there. Blogger is busy typing but notices that the story itself is quite interesting and for non-expert probably heavy to follow with one slide that Girsh has shown. Anyway if you accept that there are pockets you understand the asymmetry of Raman spectroscopy in electron and hole-doped cuprate superconductors.

Ok now we are back at the Legget's mode as Girsh comes up with the paper by Klein, PRB 2010 where he
analyzes Raman in MgB_2 (by now classical two-band superconductor). By looking in E_2g symmetry we notice two separate 2\Delta structures associated with pair-breaking of the correspodning gaps [temperature dependece, coupling to phonons]. Now if you look at the A_1g you see an extra (unexpected) feature at 9.4 meV which, as Girsh argues, is a collective mode effect. To understand this you look into the theory of a two-band superconductors:
For two order parameters the phases of the order parameters are arbitrary but if there is an interaction you can have in phase locking for an attractive interaction (V_interband>0) and out-of-phase locking of the phases for the repulsive interaction (V_interband<0). Klein pointed out that in MgB_2 the interband interaction is large and positive. The former shifts the collective mode associated with this phase locking to higher energies (into continuum) which yields damping.

Now iron-based supercondctors (from 2 to 5 bands). The idea about collective mode goes back to Chubukov, Eremin, Korshunov, PRB79 (2009) [thanks Girsh!]. They story is that if the symmetry is extended s-wave and these are electron and hole pockets involved then the effect of the final state interaction will be to create a collective mode below 2\Delta. Now the apparent contradiction [after discussion of Chubukov, Hirshfield, Fernandes, and Nevidmoskii, blogger also liked to contribute but had to continue typing] was that the collective modes Girsh has introduced earlier had nothing to do with the collective mode in B_1g in cuprates and in the A_1g channel of iron-based superconductors which he discussed now. These are all density-density excitations (excitons) shifted to lower energies due to interference of the the gap and Raman vertices. So these are neither Leggett's or amplitudon modes.

Finally in the last few minutes Girsh comes back to NbSe_2. He discussed some STM and ARPES data by Hanaguri et al., and Borisenko et al., respectively. What about Raman? Well, it seems that you see 2\Delta features only (sc and CDW). However, it is bit controversial because Girsh suggests that it might be an amplitude mode.

Questions: 1 ) blogger: why one should believe that the intreband intreaction in NbSe_2 is repulsive, Answer: the system is complicated not that much is known about the system.
2) questions raised by Nevidmoskii produced some discussion which has moved to a lunch and basically concerned the symmetry representation of the various channels in the B1g, B2g and A1g symmetry representations for iron-based superconductors. It seems that to correctly interprete the data of Muschel et al you have to work in the unfolded BZ.