Serguei Borisenko: Fermiology and Order Parameter of Fe Based Superconductors

SVBorisenko(Institut fuer Festkorper Physik, Dresden, Germany)
Fermiology and Order  Parameter of Fe based superconductors (FeSC)

–      Blogged by Saurabh Maiti

Blogger’s notation-
SV Borisenko (SVB)

Superconductor (SC)

Anti Ferro Magnetism (AFM)

Spin Density Wave (SDW)

SVB starts by advertising 1-cubed ARPES that can reach to temperatures below 1K. He explains how low energy excitations can be angle resolved by rotating the sample. ARPES can be used to probe-

(*)Fermiology— get information abt:Fermi Surface (FS), band structure, reconstruction due to (e.g magnetic) ordering

(*)Self Energy- Get information abt: V_F renormalization, scattering, coupling const. (these last two are related to imaginary and real parts of the self energy respectively)

(*)Order Parameter (mostly talks abt extracting SC order parameter)

SVB mentions this was very useful for the cuprates in all the three above mentioned aspects [although Self energy study was a little involved because the bosonic mode was likely to be of electronic origin]. For the cuprate case it was clearly established that there was no 3D and the gap was d-wave in character with clear nodes – max gaps of 20-30mev.

SVB mentions then talks abt how comparing ARPES band structure  and LDA band structure can be used to measure correlations, velocity renormalizations…

Having mentioned the success in Cuprates, SVB now moves on to FeSC-specifically the pnictides. He reminds us that the photoemission data is a product of

<f|p.A|i> A(k,e)f(e) X R(k,E)---the last term is resolution

Explains step by step how the matrix elements, polarization, resolution convolutions are taken care of and finally we get A(k,e)*f(e) and then final division by the Fermi-function gives the electronic spectral function which is used to extract info abt self energy and gap structure.

SVB then talks about LiFeAs-mentions presence of one large hole pocket and two crossed elliptical electron pockets at (\pi,\pi) in the two iron unit cell Brilliouin zone. But what happens very close to \Gamma point its more involved [different results for different polarizations---resolved by scanning across kz---he concludes that in a particular region of kz there is hole pocket… kind of like cigar shaped. Points out the 3D nature of this material.]

SVB now talks abt Co-NaFeAs shows ARPES results- combines results from different polarizations and concludes presence of two crossed elliptical electron pockets and 3D small hole pocket at \Gamma point.

SVB now moves to K-BaFeAs

Three hole pockets at \Gamma point—for optimally doped material

But !! Result!!  At corner there are 4 hole barrels [blogger’s note- star shaped] with an electron band crossing in the centre.

KFeAs          

Same as above but no central electron band crossing; So three hole pockets  at \Gamma and 4 hole barrels at the corner —

Co-BaFeAs

Two crossed elliptical electron pockets

One clear hole pocket, but two other bands possibly cross the FS. Its complicated due to hybridization of xz /yz.

FeSe-

Very tiny two elliptical electron pocket

And very tiny hole pocket at \Gamma point of xz/yz character

Rb-FeSe

Rb expels iron and causes vacancy ordering but will not discuss this.

Want to discuss the metallic behavior of  RbFe2Se2

Tiny hole pocket and two large elliptical electron pockets

In this case the disordered vacancies give metallic regions.

Two electron pockets at corner and 3D ELECRON pocket at gamma point (does not cross for all Kz values)

MAIN MESSAGE is that the standard picture of 2 circular hole pockets and two circular electron pockets is never experimentally realized.

Also points out that conventional mapping of FS topology to phase diagram is not realized experimentally…[insert picture].

SVB now discusses probing order parameter.

Start with FeSe (T_c=8K)—remind yourself that it has tiny electron pockets and tiny hole pocket. Then moves on to K-BaFeAs

Message- the gaps are strongly orbital dependent and kz dependent.

Points out that---

-xy band is irrelevant (gaps are small and some times give large FS, sometimes small, etc)

-xz/yz are the important bands

-Wherever the xy content is present the gap has a minima---

-Absence of xy character—large gap

SVB returns to his favorite material  ‘LiFe As’ to discuss its order parameter—The important results is the anisotropy of the SC gap which was claimed to be isotropic before. [blogger’s note: The oscillations are conts+cos4(\theta) type as expected from the A1g symmetry]

Electron pockets—also anisotropic.

The tiny hole pockets; cannot probe for anisotropy. [but gap is large]

[blogger’s note—the pocket is of xz/yz character; the outer FS is of xy character and the gap structure anisotropic and weaker]

SVB believes that it is likely to be s++ gap. He tried the fitting with usual form factors for the s+- wave gap structure like cosKx + cosKy and cosKx*cosKy. The only consistency he finds is with the gap structure predicted by Kontani et al. which describes the in-phase oscillations of the electron pockets. And since this required phonon mechanism in the theory, it might well be that electron-phonon mechanism is likely in this material.

Nevertheless, SVB points out that it can also be explained by S+- picture (S. Maiti et al. PRB 85, 014511 (2012)).

SVB thus invites the theorists to investigate this material more thoroughly because the self energy is known, band structure is known orbital characters are known, gaps are known; and this should be enough to find the right theory for this material.

SVB stresses on the fact that \Gamma point has cigar like features of the hole/electron pocket and suggests it  be taken into account instead of simply considering cylindrical FS. Simply put 3D is very likely important for SC. Life becomes hard but needs to be dealt with.---

Thanks collaborators and restates conclusions—

Q. Did you observe gaps induced by SDW gap in your?

A. Yes. It is clearly seen. But involves a lot of work.

Q. Are there data below Tc which show change electronic spectrum above and below Tc

A. Yes. No problem. Can be provided.

Q. Can your Spectroscopy give insight into the local  quantum chemistry of these materials?

A. Ok. Periodic potential gives good qualitative picture.

Local picture needs special attention and seems to be theorist dependent that is why I am not using that picture. Band structure picture seems to have some universal results that most people are getting. If I get a more or less universal local picture I don’t mind using it.

Q. 11 sample  FS looks like 122 (FeAs based); why? Even though the latter is heavily electron doped.

A. They are not really same. FeSe has a HOLE like  also the pockets are very Tiny. Doping with electrons makes electron pockets bigger.

Q. Is the phase diagram applicable to all pnictides.? What abt LiFeAs? No AFM… where does it fall?

A. The phase diagram is really for 122. 111 is different.

Q. Laser v/s your method; comparison?

A. Prof. Shin has an excellent technique. We have the same resolution as there’s.

Disadvantage of Laser is cannot scan kz and matrix elements can play crucial role in those measurements.

Q. In Li-111 what are the bands/orbitals responsible for SC?

A. xz and yz character of the inner pocket, I think is most relevant.

Q. Is there any criticality associated with change in FS topology?

A. It is interesting question—the main problem is that we don’t have data for continuous doping to probe that feature.