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.

Yoshihiro Iwasa (Tohoku U): Electric field induced superconductivity with electric double layer transistors

Outline:

• electric field induced SC
• double layer Transistor
• oxides
• increase of carrier density
• layered ZrNCl
• summary

Intro:

charge accumulation in capacitor lead to MOSFET by replacement of one electrode structure, however, difficult to make in the past

at the same time (Glover 1960) electric field control of SC was investigated (In)

field effect on high-Tc cuprates (YBCO): by applying gate voltage increase of Tc

dream: gate control of localization-SC transition (e.g. a-Bi, Parendo PRL 2005)

best would be SC in an insulator by gating

conventional FET with weak electric field ~1 MV/cm, 10^13 cm^-2 which is too little, therefore attempt to use liquid gate (ionic), this leads to charge accumulation devices like Li battery or electric double layer capacitor

comparison of capacitance: double layer capacitor b/w electrolytic capacitor and battery, in double layer capacitor voltage drop right at the electrode

application of EDLT to organic conductors: sharp raise of conductance --> low operation voltage, but conductance in order of 4 microS therefore switch to inorganics


made of ZnO and patterned, ZnO shows large increase of sheet conductance at about 1.7 V, carrier densities are several 10^13 cm^-2, the capacitance is 7.8 microF/cm^2, e. i. half that as on Au

low T measurements;

crossover from insulator to metallic behavior at 0.7 V
now STO/PEO(KClO4) is being used, current two order of magnitude larger, insulator to metal transition at around a few volts

electric field induced SC was then found at V_g = 3 V, first field induced SC without doping, critical magnetic field about 30 mT, H_c2 is smaller than in the bulk due to interface which is not working as a pinning center

increase of carrier density:

uniqueness of STO:
STO is lowest carrier density SC, also atomically flat surfaces can readily be made

higher carrier density in ionic liquids: polymer electrolyte (solvent + salt) but large solvent molecules are bad, therefore solvent is to be removed --> melting at RT (organic material)

now accumulated carrier density is in range of 10^14 cm^-2, gate voltages of 0.5 V needed at room temperature, gate V goes up with T --> enhanced electric charging at low temperature, that should be advantageous for SC



Device:


ZrNCl:

discovered about ten years ago, layered material, cleaveable and interesting phase diagram

very small specific heat capacity if compared to other SC but relatively high Tc of ~15 K (goes down with Li-doping, pairing interaction increases which is strange, magnetic fluctuation are present but it is not clear where they come from, crossover from isotropic gap to an anisotropic one

try to explain these strange properties by a fluctuation exchange approx. theory, afm fluctuation develops causing d pairing even in doped band insulator







device fabrication:

exfoliating single crystals, electrodes by e-beam lithography, TiAu electrodes, single crystal size some 10 micrometer,

sigma kicks in at around 1,5 V at 220 K, goes up to 1.5 mS, by increasing the gate voltage remarkable decrease of resistivity, at about 4 V SC is found below ~14 K, however it is not clear how much volume of the sample turns SC

doping study: Tc goes down to below 12 K but there seems to be a maximum at ~0.04 as shown by recent low-doping studies

novel materials:

also, KTaO_3 turns SCbelow 0.04 K

• new tunable 2D systems
• challenges: increase Tc, discover new SC
• new states at interface which are inaccessible by conventional chemistry

Ken BURCH (U. Toronto): Tuning Materials with Mechanical Exfoliation

In order to tune properties - how to tune carrier densities without affecting purity, homogeneity etc.

OUTLINE:

• Introduction
  
• Method: exfoliation. A very expensive glove-box is (almost) all one needs.

• Materials: BSCCO, Bi2Se3. Using spectroscopy (Raman) in order to characterize the tickness of the layers.

E.g. in BSCCO. Characteristic features in the Raman spectrum: a low and a higher energy peaks. Changing the doping level enhances the intensity of the higher-energy (3-phonon) peak.

• Future directions

I. Introduction.
Disorder vs. doping.
E.g. STM work in BSCCO-2212 (McElroy, Science 309, 1048 (2005)) shows a lot of disorder on the surface (and presumably the bulk too). One would like to tune the doping without affecting the disorder. Exfoliation technique is promising.

Spectroscopy is a powerful tool to study materials, e.g.:
- ps-gap in the cuprates. Optical studies (Basov and Timusk, RMP 77, 721 (2005)) were one of the first to show the existence of the ps-gap. Also Fermi-arcs were observed in ARPES (Tanaka, Science 314, 1910 (2006)). Raman studies (Blumberg, Science'1997).
- Fe-pnictides - a new exciting direction.

Interfaces and surfaces (epitaxially grown)
- Ohmoto et al, thin films of BaTiO3/ Nature ()
- ferroelectrics

Field-effect transistor.
Consider SiO2 grown on top of Si:P.
There are few examples of combined thin layer materials (e.g. LaAlO3/LaVO3 etc), but material and growth issues are daunting. Lattice mismatch is important and prevents one from growing arbitrary combination of the film/substrate.
The exfoliation technique, on the other hand, is free from this drawback - the same thin film can be exfoliated onto a number of different substrates.

II. A new way: exfoliation technique
Pioneered by Andrew Geim for graphene. A.K.A. "skotch-tape" technique

- graphene
E.g. Tony Heinz's group showed that if grown on MICA, the graphene layer is very flat, unlike if grown on e.g. silica.
(The blogger did not know what MICA was - as far as I understood (please correct in incorrect) it is a substrate typically used in AFM for calibration. The surface of it is covered with Na aroms, leaving an atomically flat surface underneeth it)

- topological insulators
See Peng, Nat. Mater 9, 225 (2009); D. Hsieh, Science (2009)
e.g. Bi2Se3, Bi2Te3
Since MICA is transparent, the speaker used it for exfoliation, and then measured Raman on it.

- NbSe2
Raman A1g mode shifts depending on the thickness of the layers.

- MoS2
A. Splendiani.., Nano Lett. 4, 1271 (2010)

III. Results on BSCCO-2212
Bi2Sr2Ca0.6Dy0.4Cu2O(8+x)
x = 0.3, 0.4, in the ps-gap regime

Depending on the film thickness, the colour of the crystal is changing. Where does it come from? Chemistry is unchanged! Turns out - interference effect by reflection from different layers. Plot so-called contrast depending on the layer thickness - convincing.

Lab Tour: 9 T magnet, ellipsometer, Raman scattering ...

History of Raman: sunlight from a telescope, passed through a polarizer, filters to a single wave-length, and scatters it from the sample. The shift in frequency (Raman shift) is what measured.

Sharp features in Raman - 2-phonon joint density of states.
Broad features: two-magnon excitations. Review: T. Deveraux and R. Hackl RMP 79, 175 (2007)
E(1 magnon) = 2J;
E(2 magnon)=3J - most pronounced signal, since one breaks 6 spin-spin bonds by flipping two adjacent spins, paying energy cost J/2 for each.
Note: Other frequencies are possible (e.g. E(2 magnon) = 4.5 J).

The 2-magnon excitations have definite selection rules. E.g. B1g excitation corresponds to XX or X'X' polarization. The intensity of the Raman signal from thin films (exfoliated direcltly on the SiO2 substrate) greatly enhances compared to the bulk (See data in: Sandilands, PRB (2010)).

NOTE: Raman signal, even from the bulk, always has interference correction from reflection off different layers. (See Y. Wang, APL 92, 043121 (2008) ).

So what is the reason for much enhanced intensity of the B1g 2-magnon peak?
It turns out - this is the effect of the changed doping level. In fact, the bulk data show that reducing concentration of holes (under-doping) hardens the 2-magnon peak (i.e. shifts it to higher frequency). This is precisely what we observe in our exfoliated thin film flakes.

SUMMARY:

• using exfoliation technique allows to create very thin films without worrying about the interaction with the substrate, lattice mismatch etc.
• optical studies are a very powerful method
  
• thinning out the BSCCO films seems to result in increasing under-doping, judging from the 2-magnon Raman peak frequency.

Questions:
Q: P. Hirschfeld. Presumably, the reason for under-doping in exfoliated films is that you lose O atoms from the surface. However, don't you think that only few top layers would be affected?
A: It may well be true. Our data show however that the effective doping level, as measured by Raman 2-magnon peak position, reduces. We are not quite sure at present, due to what microscopic mechanism.

Q: H. Alloul. Are data taken at room temperature
A: Yes. The low-temperature data can be different

Q: A. Chubukov. Were all the measurements done for one doping level?
A: Yes, so far we started from overdoped O-concentrations. We would like in future to do exfoliation starting from optimally doped samples. We have also experimented with different Dy doping (not shown in this talk).

Q: G. Blumberg.
What was the laser power
A: a few miliwatts.
Blumberg's comment: concentrating this much power on a tiny surface area would lead to heating of the sample, and hence oxygen diffusion off the surface.

Q: P. Coleman: what do you know about the dependence of exfoliation on temperature?
A: we heat the substrate before exfoliation. We haven't yet done the exfoliation at low temperatures.
Q: Is the size of the flakes sufficient to attach leads?
A: The flakes are too small. It would be great to be able to make them larger.

Q: A. Schofield. What are the prospects of this exfoliation technique?
A: Exploring the phase diagram of e.g. cuprates, without affecting the purity of the crystals.

Q: Y. Grin. What do you know about the real structure of the spacer? Can you do TEM?
A: TEM proves hard. We do AFM, showing very flat surfaces. We'd like to do other structural probes in the future.

Q: [someone]. Can one see a gradual change in the Raman B1g position from bulk to thin film, by gradually increasing the film thinkness?
A: No, it's very hard to control the film thickness during exfoliation process. Somewhat of a black art.

Q: P. Hirschfeld. How important is lattice mismatch with the substrate? E.g. other studies on epitaxially grown films?
A: We hope that we are not stretching the film, but we cannot really be sure. We tried different substrates to try to answer this question.