Physics of High Temperature Superconductivity

SCy

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>What\'s the latest in the search to understand the secrets\nof high temperature superconductivity which can\'t be\nexplained by the BCS theory of cooper pairs bonded\nby phonons? What\'s the leading theory or best candidate\nthat has ample scientific and experimental support?\n\nSCy\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>What's the latest in the search to understand the secrets
of high temperature superconductivity which can't be
explained by the BCS theory of cooper pairs bonded
by phonons? What's the leading theory or best candidate
that has ample scientific and experimental support?

SCy

Igor Khavkine

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On 2005-06-21, SCy <magnetofeynman@yahoo.com> wrote:\n> What\'s the latest in the search to understand the secrets\n> of high temperature superconductivity which can\'t be\n> explained by the BCS theory of cooper pairs bonded\n> by phonons? What\'s the leading theory or best candidate\n> that has ample scientific and experimental support?\n\nThe latest is: still searching.\n\nOne of the main problems is the sheer complexity of the phenomenon and\nits rich phenomenology. The unit cell of a YBCO crystal, one of the\nfirst discovered high-Tc superconductors, contains on the order of 100\natoms. Elementary excitations on top of the superconducting state are\nwell described by BCS-like quasiparticles with a d-wave gap (4-fold\nrotational symmetry, nodes along the diagonals of the Brillouin zone\nalong wich the gap vanishes). There are important structures in 1D (Cu-O\nchains), in 2D (Cu-O planes, considered most important), and 3D\n(coupling between Cu-O layers). The presence of superconductivity\ndepends on a certain amount of disorder. The phase diagram of high-Tc\nmaterials contains unusual regions such as an antiferromagnetic\ninsulator, the mysterious "pseudogap" state, a non-metallic normal\nphase, as well as a doped conductor phase.\n\nAs superconductors, high-Tc materials don\'t differ much from Type-II\nsuperconductors described by BCS theory. So many believe that the\nsuperconducting state is due to Cooper-like pairing, except that it is\nmediated not by phonons, but by as yet an unknown agent.\n\nThere are many proposals for a microscopic theory of high-Tc\nsuperconductivity. But none of them are yet successful. One reason is\nthat the important properties of these materials stem from strong\ncorrelations between their electrons. In other words, the electrons\ncannot be treated as non- or weakly interacting, like in normal metals.\nThis imposes difficulties theoretically since simple models with weak\ncoupling are not expected to be appropriate, and strongly coupled\ninteracting systems are always difficult to work with. Instead, there\nare many phenomenological theories describing different phases in the\nphase diagram, with varying degrees of success. But no theory has come\nclose to, say, accurately predicting the transition temperature.\n\nA recent review article focusing on the state of the theory is\ncond-mat/0309094 by Yanase et al.\n\nHope this helps.\n\nIgor\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On [itex]2005-06-21,[/itex] SCy <magnetofeynman@yahoo.com> wrote:
> What's the latest in the search to understand the secrets
> of high temperature superconductivity which can't be
> explained by the BCS theory of cooper pairs bonded
> by phonons? What's the leading theory or best candidate
> that has ample scientific and experimental support?

The latest is: still searching.

One of the main problems is the sheer complexity of the phenomenon and
its rich phenomenology. The unit cell of a YBCO crystal, one of the
first discovered high-Tc superconductors, contains on the order of 100
atoms. Elementary excitations on top of the superconducting state are
well described by BCS-like quasiparticles with a d-wave gap (4-fold
rotational symmetry, nodes along the diagonals of the Brillouin zone
along wich the gap vanishes). There are important structures in [itex]1D (Cu-O[/itex]
chains), [itex]in 2D (Cu-O[/itex] planes, considered most important), and 3D
(coupling between [itex]Cu-O[/itex] layers). The presence of superconductivity
depends on a certain amount of disorder. The phase diagram of high-Tc
materials contains unusual regions such as an antiferromagnetic
insulator, the mysterious "pseudogap" state, a non-metallic normal
phase, as well as a doped conductor phase.

As superconductors, high-Tc materials don't differ much from Type-II
superconductors described by BCS theory. So many believe that the
superconducting state is due to Cooper-like pairing, except that it is
mediated not by phonons, but by as yet an unknown agent.

There are many proposals for a microscopic theory of high-Tc
superconductivity. But none of them are yet successful. One reason is
that the important properties of these materials stem from strong
correlations between their electrons. In other words, the electrons
cannot be treated [itex]as non-[/itex] or weakly interacting, like in normal metals.
This imposes difficulties theoretically since simple models with weak
coupling are not expected to be appropriate, and strongly coupled
interacting systems are always difficult to work with. Instead, there
are many phenomenological theories describing different phases in the
phase diagram, with varying degrees of success. But no theory has come
close to, say, accurately predicting the transition temperature.

A recent review article focusing on the state of the theory is
http://www.arxiv.org/abs/cond-mat/0309094 by Yanase et al.

Hope this helps.

Igor

Richard Saam

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>SCy wrote:\n> What\'s the latest in the search to understand the secrets\n> of high temperature superconductivity which can\'t be\n> explained by the BCS theory of cooper pairs bonded\n> by phonons? What\'s the leading theory or best candidate\n> that has ample scientific and experimental support?\n>\n> SCy\n>\nOne possibility:\n\nSuperconductivity is a Bose Einstein Condensate\n\nh^2/(2 pi m lambda^2) = kTc\n\nin simplicity\naided\nbut mostly masked\nby molecular topology.\n\nRichard Saam\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>SCy wrote:
> What's the latest in the search to understand the secrets
> of high temperature superconductivity which can't be
> explained by the BCS theory of cooper pairs bonded
> by phonons? What's the leading theory or best candidate
> that has ample scientific and experimental support?
>
> SCy
>
One possibility:

Superconductivity is a Bose Einstein Condensate

[itex]h^2/(2 \pi m \lambda^2) =[/itex] kTc

in simplicity
aided
but mostly masked
by molecular topology.

Richard Saam

Igor Khavkine

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Richard Saam wrote:\n> SCy wrote:\n> > What\'s the latest in the search to understand the secrets\n> > of high temperature superconductivity which can\'t be\n> > explained by the BCS theory of cooper pairs bonded\n> > by phonons? What\'s the leading theory or best candidate\n> > that has ample scientific and experimental support?\n\n> One possibility:\n\nHardly a leading theory, though.\n\n> Superconductivity is a Bose Einstein Condensate\n\nThe BCS phase is different from the BEC phase. The study of the\ncross-over between the two regimes is a hot topic at the momnent, but\nin cold atomic gases. I don\'t think any superconductors have been found\nto have a BEC as the underlying phase.\n\n> h^2/(2 pi m lambda^2) = kTc\n\nReference?\n\n> in simplicity\n> aided\n> but mostly masked\n> by molecular topology.\n\nThis statement makes little sense, so I can\'t comment on it.\n\nIgor\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Richard Saam wrote:
> SCy wrote:
> > What's the latest in the search to understand the secrets
> > of high temperature superconductivity which can't be
> > explained by the BCS theory of cooper pairs bonded
> > by phonons? What's the leading theory or best candidate
> > that has ample scientific and experimental support?

> One possibility:

Hardly a leading theory, though.

> Superconductivity is a Bose Einstein Condensate

The BCS phase is different from the BEC phase. The study of the
cross-over between the two regimes is a hot topic at the momnent, but
in cold atomic gases. I don't think any superconductors have been found
to have a BEC as the underlying phase.

> [itex]h^2/(2 \pi m \lambda^2) =[/itex] kTc

Reference?

> in simplicity
> aided
> but mostly masked
> by molecular topology.

This statement makes little sense, so I can't comment on it.

Igor

Richard Saam

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Igor Khavkine wrote:\n> Richard Saam wrote:\n>\n>>SCy wrote:\n>>\n>>>What\'s the latest in the search to understand the secrets\n>>>of high temperature superconductivity which can\'t be\n>>>explained by the BCS theory of cooper pairs bonded\n>>>by phonons? What\'s the leading theory or best candidate\n>>>that has ample scientific and experimental support?\n>\n>\n>>One possibility:\n>\n>\n> Hardly a leading theory, though.\n>\n>\n>>Superconductivity is a Bose Einstein Condensate\n>\n>\n> The BCS phase is different from the BEC phase. The study of the\n> cross-over between the two regimes is a hot topic at the momnent, but\n> in cold atomic gases. I don\'t think any superconductors have been found\n> to have a BEC as the underlying phase.\n>\n>\n>>h^2/(2 pi m lambda^2) = kTc\n>\n>\n> Reference?\n>\nThere is some work:\n\nhttp://scienceworld.wolfram.com/physics/Bose-EinsteinCondensation.html\n\nJournal : PHYSICA C: SUPERCONDUCTIVITY\nISSN : 0921-4534\nVol./Iss. : 301 / 3-4\nBose--Einstein condensation in finite-length channels\ncomposed of weakly interacting filaments\nEagles , D.M.\npp.: 165-172\n\nJournal : PHYSICA C: SUPERCONDUCTIVITY\nISSN : 0921-4534\nVol./Iss. : 305 / 1-2\nd-wave Bose--Einstein condensate and tunnelling in\nsuperconducting cuprates\nAlexandrov , A.S.\npp.: 46-56\n\nJournal: Physica C: Superconductivity\nISSN : 0921-4534\nVolume : 325\nIssue : 1-2\nDate : 26-Nov-1999\npp 35-40\nD-wave Bose-Einstein condensation and the London penetration depth in\nsuperconducting cuprates\nAS Alexandrov\n\nIt is not a leading theory,\nbut if room temperature superconductivity is ever to be achieved,\na mechanism based on very small (~electron mass) (quasi?) particles\nmust be found/engineered generally aligned with:\n\nkTc = hbar^2 K^2/(2m)\n\nm associated with atomic mass will not do the job.\n\nRichard Saam\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Igor Khavkine wrote:
> Richard Saam wrote:
>
>>SCy wrote:
>>
>>>What's the latest in the search to understand the secrets
>>>of high temperature superconductivity which can't be
>>>explained by the BCS theory of cooper pairs bonded
>>>by phonons? What's the leading theory or best candidate
>>>that has ample scientific and experimental support?
>
>
>>One possibility:
>
>
> Hardly a leading theory, though.
>
>
>>Superconductivity is a Bose Einstein Condensate
>
>
> The BCS phase is different from the BEC phase. The study of the
> cross-over between the two regimes is a hot topic at the momnent, but
> in cold atomic gases. I don't think any superconductors have been found
> to have a BEC as the underlying phase.
>
>
[itex]>>h^2/(2 \pi m \lambda^2) =[/itex] kTc
>
>
> Reference?
>
There is some work:

http://scienceworld.wolfram.com/phys...densation.html

Journal : PHYSICA C: SUPERCONDUCTIVITY
ISSN [itex]: 0921-4534[/itex]
Vol.[itex]/Iss[/itex]. : 301 [itex]/ 3-4[/itex]
Bose--Einstein condensation in finite-length channels
composed of weakly interacting filaments
Eagles , D.M.
pp.[itex]: 165-172[/itex]

Journal : PHYSICA C: SUPERCONDUCTIVITY
ISSN [itex]: 0921-4534[/itex]
Vol.[itex]/Iss[/itex]. : 305 [itex]/ 1-2[/itex]
d-wave Bose--Einstein condensate and tunnelling in
superconducting cuprates
Alexandrov [itex], A.S.pp.: 46-56[/itex]

Journal: Physica C: Superconductivity
ISSN [itex]: 0921-4534[/itex]
Volume : 325
Issue [itex]: 1-2[/itex]
Date : 26-Nov-1999
[itex]pp 35-40[/itex]
D-wave Bose-Einstein condensation and the London penetration depth in
superconducting cuprates
AS Alexandrov

It is not a leading theory,
but if room temperature superconductivity is ever to be achieved,
a mechanism based on very small (~electron mass) (quasi?) particles
must be found/engineered generally aligned with:

kTc [itex]= \hbar^2 K^2/(2m)[/itex]

m associated with atomic mass will not do the job.

Richard Saam

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