superconductivity and superfluidity mgb 2 since 1973 the limiting transition temperature in...

Superconductivity and Superfluidity

MgBMgB22

Since 1973 the limiting transition temperature in conventional alloys and metals was 23K, first set by Nb3Ge, and then equaled by an Y-Pd-B-C compound in 1994

In February 2001 superconductivity was found in MgB2 at just below 40K Ironically this compound was routinely available in most laboratories.

Although the critical field is modest (10T) it may well find applications - it is relatively easy to make into wires.

The high transition temperature has led to suggestions that the superconductivity may be unconventional

However, it appears that it is the phonons themselves that are perhaps a little out of the ordinary

Lecture 13


The breakthrough -1986The breakthrough -1986

George Bednorz

Alex Muller

Lecture 13


The breakthrough-1986The breakthrough-1986

“BaxLa5-xCu5O5(3-y)”

actuallyLa2-xBaxCu2O4

Lecture 13


…….and higher.and higher

Lecture 13


……..and higher.....and higher...

YBa2Cu3O7

Lecture 13


The High Temperature SuperconductorsThe High Temperature Superconductors

The high temperature superconductors are all mixed valent cuprates based upon the perovskite structure, usually associated with BaTiO3

Ba

O

TiMany minerals take the perovskite structure - it is extremely stable to substitution and many, much more complex, crystal forms (such as the high Tc cuprates can be derived from it

Lecture 13



Bednorz and Muller’s original HiTc was soon shown to be based upon La2CuO4 which is derived from the basic perovskite structure

However La2CuO4 itself is found to be an anti-ferromagnetic insulator with a Neel point of over 240K, only when doped with M=Ba or Sr, giving La2-xMxCuO4 (ie hole-doped) is superconductivity found

AF

SC

tetragonal

orthorhombic

Metal

insulator

x0.125

Lecture 13



The 90K Y-Ba-Cu-O superconductor - in which there are two CuO2 planes rather than one - shows similar behaviour.

YBa2Cu3O6 YBa2Cu3O7

Y

Ba

BaCu

Y

Ba

BaCu

O

Here introduction of O in the chains provides the hole doping directly:

AFSC

tetragonal orthorhombic

Metalinsulator

x

YBa2Cu3O6+x

0 10.5

400K

90K

Lecture 13


DopingDoping

The onset of superconductivity, and the optimisation of the transition temperatures of all of the high temperature cuprates is associated with doping….

……..usually (but not always) with holes

This can be seen by examination of the formal valences:

Y3+ + 2Ba2+ + Cu1+ + 2Cu2+ + 6O2- insulating antiferromagnetic YBa2Cu3O6

Y3+ + 2Ba2+ + 3Cu2.3+ + 7O2- superconducting YBa2Cu3O7

1.875La3+ + 0.125Ba2+ + Cu2.125+ + 4O2- superconducting La2-xBaxCuO4

2La3+ + Cu2+ + 4O2- insulating La2CuO4

Overdoping, as well as underdoping, can lead to a reduction in Tc. Usually the optimal doping is 0.2 holes per Cu atom

We can therefore draw a generic phase diagram

Lecture 13


Generic phase diagram for the High TGeneric phase diagram for the High Tccss

Non Fermi Liquid

Fermi Liquid

superconducting

pseudogap

Tc

antif

erro

mag

netic

tem

pera

ture

0.20 Doping level (holes per CuO2)underdoped optimally

dopedoverdoped

Lecture 13


Generic phase diagram for the High TGeneric phase diagram for the High Tccss

Non Fermi Liquid

Fermi Liquid

superconducting

pseudogap

Tc

antif

erro

mag

netic

tem

pe

ratu

re

0.20 Doping level (holes per CuO2)

In a so-called Landau-Fermi liquid the properties of single electrons are "renormalized" by interactions with other electrons to form "quasiparticles". The properties of the material can then be understood in terms of the weak residual interactions between the quasiparticles and their excitations. A key feature of the quasiparticle concept is that low-energy single-particle excitations have very narrow linewidths: Dw~w2 where w is the energy of the excitation.

In the non-Fermi-liquid region the thermodynamic properties are unexceptional and, within experimental uncertainties, are similar to the behaviour of a Fermi liquid. However, this region is characterized by exceptionally simple but unusual power laws in all of its transport properties as a function of temperature. These transport properties include the resistivity, the optical conductivity, the electronic Raman-scattering intensity, the thermal conductivity, various nuclear relaxation rates, the Hall conductivity and the magnetoresistance.

The so-called pseudogap regime is not well understood - evidence for its existence comes,eg, from the coefficient of electronic specific heat which starts to decrease at temperatures well above Tc. The region is characterised by spin and/or charge stripes and fluctuations

Lecture 13


Other high TOther high Tc c phasesphases

La2-xBaxCuO4 35KLa2-xSrxCuO4 38K(La2-xSrx )CaCu2O660K

YBa2Cu3O7 92K

Bi2Sr2CuO6 20KBi2Sr2CaCu2O8 85KBi2Sr2Ca2Cu3O10 110K

TlBa2CaCu2O7 80KTlBa2Ca2Cu3O9 110KTlBa2Ca2Cu4O11 122K

HgBa2CuO4 94KHgBa2Ca2Cu3O8 135K

214

123

220122122223

112

2

123

123

13

Number of CuO2 layers

HgBa2Ca2Cu3O8

Lecture 13


Layered cupratesLayered cuprates

La2-xSrxCuO4 YBa2Cu3O7 HgBa2Ca2Cu3O8

N=1 N=2 N=3

Lecture 13


Other propertiesOther properties

Highly anisotropic conductivity and superconductivity

In plane conductivity much higher than out of plane

Resistivity proportional to T at all temperatures above Tc

Close proximity to magnetic transition

Low temperature (few K) magnetic order when Y is replaced by Gd, Dy, Er, Ho etc

Very high critical upper critical fields (>60T), very low lower critical fields (mT)

Very long penetration depths (>120nm) but very short coherence lengths (1nm and less)

Very small isotope effect

Probably d-wave superconductors

Are they BCS superconductors?

Lecture 13

superconductivity and superfluidity mgb 2 since 1973 the limiting transition temperature in...

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