Hi Venkatesh,

the term "Pseudogap" is indeed complicated and often confusingly used.

In general, from the view of ARPES, when the cuprates where measured (see the 90ies papers by Ding, Campuzano or Shen) , they found below a pseudogap temperature T* (>T_C) a gap with a d_{x^2−y^2}-symmetry.

From these general findings, in my view, there are two reasons why the "Pseudo" is used:

(1) One meaning of "Pseudo" is that the gap is not in all direction but (crudely speaking) , in one direction the electrons behave as they do in a metal, whereas in the other direction they are more semiconductor-like.

(2) The other meaning of "Pseudo" is that People believe that the gap measured in ARPES must have something to do with the superconducting gap (why shouldn't it?). So then the meaning of  "Pseudo" is that this gap already exists above T_C.

Of which Pseudogap do we want to speak here? What is the other material?

best wishes

l.

Dear Lenart,

Thanks for your explanation. I am working in the research area belongs to the Fe2VAl intermetallic Heusler alloy. This alloy particularly said to be has a pseudo gap (ie. lower density of states at Fermi level) in the literature. But this material does not show any kind of strongly correlating behaviour that opens a gap below certain temperatures.

plz kindly see the following links for your reference.

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.57.14352

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.84.3674

thanks

venkatesh

Hi Venkatesh,

As Lenart already said, your question is a good one.  There are multiple definitions of what a pseudogap is in the literature, differing slightly depending on material or the field.

In the High-Tcs, I would define the pseudogap as:

- The loss of spectral density at the Fermi level, which occurs only for some portion of momenta in the Brillouin zone.   Thus, it is distinct from a superconducting gap which would apply to ALL momenta.  Thus, 'pseudo' refers to momentum dependence.

If you then compute the density of states from the spectral density, (average over momenta), you would see the pseudogap as a suppression, or incomplete gap at the Fermi surface.  So this is the second, but somewhat weaker, definition that you are referring to above.

Finally, while the pseudogap which appears in High-Tcs is widely believed to be due to strong correlations, there are many ways to create a directional anisotropy which does not involve electron-electron interactions.  In which case, you should not in your mind let 'pseudogap' mean anything specific.  Usually it is just an indication that people don't know what has caused the suppression. 

I guess the pseudogap may stem from elementary exciations within energy gap suggested by me attached as follows;

I would like to help more or less understanding of high T_C superconductivity as follows

The main reason of pseudogap above T_c may be based on electric field-induced attractive electron-electron interactions near above transition temperature.

A pseudogap has meaning outside of superconductivity but in the case of the high-Tc superconductors the general tendancy has been to call this observed partial gap in the normal state above Tc a "pseudogap" because it initially looked like a SC gap. So in the underdoped and optimally doped region the observed gap did not close at Tc but persisted to some higher temperature generally referred to as T*. For some it was quite natural to think of this as a residual SC pairing gap - hence "pseudogap". But quite early in its history the pseudogap was shown to compete with SC - so it is present above and below Tc. It took a long time for this to be widely recognised though opinion is now consolidating around this view. It is likely to arise from Fermi surface reconstruction arising from short-range spin correlations so that the large Fermi surface which is observed on the overdoped side reconstructs into electron and hole pockets with a narrow energy gap in between. IN this view the electron pockets lift above the Fermi level with decreasing doping opening a gap at the Brillouin zone boundary - the so-called antinodal regions. Currently evidence for this is rapidly gaining momentum but this view is yet to receive universal acceptance.

@James P.F. LeBlanc : thanks for you answer. As you suggested that there is a sharp decrease in the density of states indicative of a narrow gap like character in some materials (ex: quasicrystals (Al-Pd-Re)), giving negative temperature co-efficient of resistivity although the alloy is formed with elemental metallic constituents.

@ Je Huan Koo :  I also wants to know the physics of high temperature superconductivity. Particularly, i want to know the electron -electron coupling mechanism in both Cupprate and Fe-based superconductors. Thanks for your references. I will go through them and will make a massage if i have any doubts.

@Jeffery L. Tallon : Dear sir, thanks for your answer.  I have one doubt. Is origin of pseudogap mainly responsible for the superconducting behaviour of Cupprates and other Fe-based superconductors...? or any material having pseudogap may show superconducting behaviour....?...do you have any comments on this..?

 Its a complicated issue which is difficult to summarise without the background.  I have just submitted a paper to Phys.Rev.X on the issue which is available as a preprint _https://www.researchgate.net/publication/266851012.   Apologies for referencing one of my own papers but i think it might help your question.

Regards

Philip

Article The origins of macroscopic quantum coherence in high tempera...

Hello Venkatesh,

Generally I do not like to be negative, but I expect that Dr. Turner's reference will be mostly confusing, rather than helpful.

To follow up on your other questions:   "Is origin of pseudogap mainly responsible for the superconducting behaviour of Cupprates and other Fe-based superconductors...? or any material having pseudogap may show superconducting behaviour....?"

To the first:  While there is no definitive proof that the pseudogap is not preformed superconductivity, the scenario of pocket formation mentioned by Tallon above is a strong supporter that the pseudogap is a competing phase.  So in that view, a popular one which I also support, the pseudogap is NOT responsible for the superconducting behaviour in the cuprates.  Other materials might be a different story, and this is not my expertise.

To the second question:  There are theories in which the pseudogap emerges out of what is called a quantum critical point, near T=0.  There are scenarios where these quantum critical points are necessarily surrounded by a superconducting region.  There are many papers on this topic.  So in some scenarios, IF a material has a pseudogap, and IF that pseudogap vanishes at T=0 at a quantum critical point, THEN one should expect a superconducting dome in the vicinity.  It could however be vanishingly small.

I assigned quantized phonon-enhanced spin fluctuation to Kim spinon.

This mode as elementary excitation can drive a pseudo gap.

The reason of higher temperature than superconducting one is electric-induced  preformed superconducting states.

Je Huan, I am not sure exactly what you are saying here but you seem to be saying that the pseudogap is a form of preformed pairing state i.e. let's call it precursor superconductivity. But the key feature of pseudogap phenomenology is that it is also present at T=0, competing with the ground-state superconductivity. At T=0 thermal fluctuations are absent and so the full condensate should have developed at T=0 if it were merely a precursor pairing state. But in the pseudogap regime the ground state is severely weakened by the competing pseudogap which is still present at T=0. THis is seen in the abruptly reduced condensation energy, superfluid density and critical fields; and most notably for application purposes it is seen in the severely reduced T=0 critical current density immediately when p is reduced below 0.19 holes/Cu. JLT

Apologies if i have added confusion to the discussion.  I should have made it clear that my comment was related to the the specific question "Is origin of pseudogap mainly responsible for the superconducting behaviour of Cupprates and other Fe-based superconductors...? ".  The paper attempts to offer an explanation as to the connection between the pseudogap and superconducting state based on a robust published data set which to date does not have commonly agreed explanation. I agree that some parts of the paper might appear complex in addressing the specific question but I hope the underlying concepts address the question.

Regards

Philip

This discussion is becoming mucky. I still hold the view that unearthing pseudogap phenomenon will explain high temperature superconductivity. The existence of Cooper pairs (in condensate state) in a sea of electrons (in excited state), raises the question where is the start and end of the pseudogap? The indistinguishability of electrons that form Cooper pairs, the distance between two Cooper pair electrons in comparison to two adjacent electrons are unanswered questions. Literature shows that not more than 5% of electrons in a superconducting material forms Cooper pair.