Talk:BCS theory

..caused by Bose-condensation ...

As was reading the paper by Bardeen, Cooper and Schrieffer some days ago, I want to ask if there were new results for the state of the electrons, since the BCS-Theory tells, that the condensation isn't a Bose-Einstein condensation. In the first sentence this is said and I am going to change it into "... caused by a condensation of pairs of electrons into a boson like state."

"Theory of Superconductivity" by J.Bardeen,L.N.Cooper and J.R.Schrieffer, Phys. Rev. 108, 1175 (1957)

--Xeltok (talk) 15:41, 11 January 2009 (UTC)

Nowdays BCS theory is unified with Bose-Einstein condensation: [1], [2], [3], and so on. It is right to say, that condesation of Cooper pairs is a Bose-Einstein condensation. Andrius.v (talk) 10:40, 18 January 2009 (UTC)

"Condensation" in BCS is not a usual Bose condensation, because pairs are nor elementary bosons, but composite bosons. Commutation relations for pair desctructon and creation operators are different from purely bosonic ones. One can say that pairs have a mixed nature: in some aspects they are similar to fermions, but other features make them close to bosons. These are bosonic properties, which are responsible for superconductivity. In particular, BCS wave function has a "bosonic" structure: all the pairs are "condensed" into the same state. In some sense, you are right - there is no simple Bose condensate, but something much more complicated, this "something" however having bosonic features. —Preceding unsigned comment added by 93.123.157.13 (talk) 17:25, 19 October 2009 (UTC)

Point one: Cooper pairs are no Bosons. The operators (bogolubov quasi particle operators) which are describing the cooper pairs do not fit the commutation relation of bosons. Cooper pairs are: Majorana_fermion

Point two: All cooper pairs are in the same state (have the same wave function). In a BEC one has the same effect, that all electrons have the same wave-function. This is why it is often compared to each other.

--130.149.114.218 (talk) 08:20, 18 May 2011 (UTC)

Bogoliubov operators are quasiparticle creation and destruction operators. They are not "Cooper pair" operators. Bogoliubov operators correspond to excitations, which are absent in the ground state, by definition. Pair creation and destruction operators can be introduced (as done in BCS paper or Schrieffer's book) without any link with Bogoliubov approach. They do violate both bosonic and fermionic commutation rules. — Preceding unsigned comment added by 93.123.157.13 (talk) 09:59, 15 February 2012 (UTC)

Intuitive picture is wrong (?)

The BCS theory page has an intuitive explanation of how Cooper pairs are formed (see below). I think this picture is not suitable, as it is wrong.

Cooper pairs are formed between electrons with opposite spin, and opposite k-vector. This means they have to be travelling in opposite directions! The energy of such a system is lowered compared to the two separate systems, because the center of mass is at rest.

It's not really true. Cooper pars can be formed between electrons with same spin, but formation of such pair has very small probability. Andrius.v (talk) 10:40, 18 January 2009 (UTC)

Text from article

Roughly speaking the picture is the following:

An electron moving through a conductor will attract nearby positive charges in the lattice. This deformation of the lattice causes another electron, with opposite "spin", to move into the region of higher positive charge density. The two electrons are then held together with a certain binding energy. If this binding energy is higher than the energy provided by kicks from oscillating atoms in the conductor (which is true at low temperatures), then the electron pair will stick together and resist all kicks, thus not experiencing resistance.

Cleanup tag

I notice the cleanup tag on the article since July 2007. I agree that the article needs improving; however, tags should not just be added with no explanation on the talk page, so I'll remove the tag for now. What are some specific suggestions for improving this article?--Gloriamarie 17:12, 11 September 2007 (UTC)

I feel its a bit too wordy. And even so, the explanations given are too short for anyone to clearly understand.

Eg: The ratio between the value of the energy gap at zero temperature and the value of the superconducting transition temperature (expressed in energy units) takes the universal value of 3.5, independent of material.

I'm pretty sure the first qns asked of that line would be: what is that 3.5 of what universal value of what zero temperature gap?

Put simply, there are many descriptions about the bcs theory in the article, but its jus not organized into a simple understandable way.

I support the cleanup tag reinstated--Venny85 17:13, 29 March 2008 (UTC)

Suggested material

There is a section dedicated to the successes of BCS theory, but none describing its shortcomings. It seems that the article would be more balanced if such a section were introduced. I currently do not have the expertise to write such an addition. Could anyone else give it a start? zipz0p (talk) 00:58, 16 March 2009 (UTC)

Debye

I've added a {{dn}} to "In its simplest form, BCS gives the superconducting transition temperature in terms of the electron-phonon coupling potential and the Debye cutoff energy". I don't think that a link to the unit debye is correct, but am not sure what the right target would be. Maybe Debye frequency?--ospalh (talk) 12:04, 8 July 2010 (UTC)

Debye temperature? Modest Genius ^talk 23:40, 10 January 2011 (UTC)

Debye frequency seems more likely ? relates to the max phonon energy ? - Rod57 (talk) 18:31, 31 August 2019 (UTC)

Yurin's paper

I've removed the reference to the alternative theory developed by I.M. Yurin. Although it does cite one paper, that paper does not seem to be widely accepted, and does not meet the standards for inclusion here. All other references I have found to Yurin's theory are posted by the author himself, who appears to have a bit of an axe to grind. Until there's more secondary sources referring to this theory, I don't think it warrants inclusion here. PianoDan (talk) 19:10, 18 November 2012 (UTC)

BCS Gap Equation

I am correcting the asymptotic versions of the gap equation near T=0 and near T=T_c, which appear to be wrong. I have no idea whether or not the references afterward remain valid, but would appreciate it if someone wants to check them out. Csmallw (talk) 19:05, 26 March 2014 (UTC)

Should mention that BCS used to predict max Tc of 30 K

Other articles say this and need a source yet it is not clearly covered here. Who/when made the prediction from BCS that the max Tc would be about 30 K ? - Rod57 (talk) 19:09, 21 December 2015 (UTC)

This is pre-1980s activity. Way outdated.--Ymblanter (talk) 19:23, 21 December 2015 (UTC)

Maybe so, but it should be covered eg in a history section, and say when/how/who showed it to be an incorrect prediction. - Rod57 (talk) 13:22, 16 February 2016 (UTC)

BCS theory motivated testing hydrogen sulphide under pressure

Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system. Sept 2015 says " the Bardeen–Cooper–Schrieffer theory of conventional superconductivity gives a guide for achieving high Tc with no theoretical upper bound — all that is needed is a favourable combination of high-frequency phonons, strong electron–phonon coupling, and a high density of states[4]". - Rod57 (talk) 13:22, 16 February 2016 (UTC)

Superconductivity discovered in Bismuth / BCS might need revision?

Might the theory require a revision?

The properties of the 83rd element of the periodic table, namely, Bismuth (Bi) have been studied for more than a century and still continues to draw enormous scientific interests due to its anomalous electronic properties. Bulk rhombohedral Bismuth (Bi) at ambient pressure is a semi-metal and it remains in the normal state down to 0.010 K. Unlike metals where there is roughly one mobile electron per atom, in a semi-metal like Bi, the concentration of mobile electrons is extremely low (100,000 atoms share a single mobile electron). Hence, the superconductivity (SC) in bulk is thought to be very unlikely due to this extremely low carrier density. Now, a group of TIFR scientists have discovered superconductivity of a high quality single crystal of Bi (99.998% pure) at 0.00053 K with a critical field of 0.000005 Tesla (nearly 1/8 of earth’s magnetic field). The discovery was made by observing a diamagnetic signal using a home made ultra sensitive magnetometer which is housed in a state of the art TIFR copper nuclear refrigerator built in 2011. This discovery cannot be explained by standard models of superconductivity. A new theory is necessary since the assumption that the electronic (Fermi) energy is much larger than the lattice (vibration) energy used in standard models fails in Bismuth. This exciting discovery has recently been published in Science (online 1 Dec 2016 http://science.sciencemag.org/content/early/2016/11/30/science.aaf8227) and has generated significant interest in the media.

http://www.tifr.res.in/TSN/news_detail.php?id=108 DOI: 10.1126/science.aaf8227
- added by [ 101.56.247.247 ] 16:33, 12 December 2016

Nonscientific language

An exponential rise in heat capacity near the critical temperature for some superconductors

What does "exponential" mean to this writer? "Big"? How can you observe exponential increase of a function f(t) as t approaches a finite value a?

188.154.140.131 (talk) 10:45, 7 September 2018 (UTC)