Transcript Superconductivity and Superfluidity PHYS3430 Professor Bob

MgB2
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
Superconductivity and Superfluidity
The breakthrough -1986
George
Bednorz
Alex
Muller
Lecture 13
Superconductivity and Superfluidity
The breakthrough-1986
“BaxLa5-xCu5O5(3-y)”
actually
La2-xBaxCu2O4
Lecture 13
Superconductivity and Superfluidity
….and higher
Lecture 13
Superconductivity and Superfluidity
…..and higher...
YBa2Cu3O7
Lecture 13
Superconductivity and Superfluidity
The High Temperature Superconductors
O
The high temperature superconductors
are all mixed valent cuprates based
upon the perovskite structure, usually
associated with BaTiO3
Many 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
Ti
Ba
Superconductivity and Superfluidity
The High Temperature Superconductors
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 antiferromagnetic 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
insulator
tetragonal
orthorhombic
AF
Metal
SC
0.125
Lecture 13
x
Superconductivity and Superfluidity
The High Temperature Superconductors
The 90K Y-Ba-Cu-O superconductor - in which there are two CuO2 planes rather
than one - shows similar behaviour.
Here introduction of O in the chains
provides the hole doping directly:
YBa2Cu3O6
YBa2Cu3O6+x
400K
tetragonal
Ba
YBa2Cu3O7
orthorhombic
Ba
90K
Y
Y
Metal
insulator
Ba
Cu
Ba
AF
Cu
O
SC
0
Lecture 13
0.5
1 x
Superconductivity and Superfluidity
Doping
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
2La3+ + Cu2+ + 4O2-
insulating La2CuO4
1.875La3+ + 0.125Ba2+ + Cu2.125+ + 4O2-
superconducting La2-xBaxCuO4
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
Superconductivity and Superfluidity
temperature
Generic phase diagram for the High Tcs
antiferromagnetic
Non Fermi Liquid
pseudogap
0
underdoped
Lecture 13
Tc
Fermi Liquid
superconducting
0.2
optimally
doped
Doping level (holes per CuO2)
overdoped
Superconductivity and Superfluidity
Generic phase diagram for the High Tcs
Non Fermi Liquid
antiferromagnetic
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
temperature
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.
pseudogap
Tc
Fermi Liquid
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 singleparticle excitations have very
narrow linewidths: Dw~w2 where w
is the energy of the excitation.
superconducting
0
Lecture 13
0.2
Doping level (holes per CuO2)
Superconductivity and Superfluidity
Other high Tc phases
214
La2-xBaxCuO4
La2-xSrxCuO4
(La2-xSrx )CaCu2O6
35K
38K
60K
1
1
2
123
YBa2Cu3O7
92K
2
2201 Bi2Sr2CuO6
2212 Bi2Sr2CaCu2O8
2223 Bi2Sr2Ca2Cu3O10
20K
85K
110K
1
2
3
TlBa2CaCu2O7
TlBa2Ca2Cu3O9
TlBa2Ca2Cu4O11
80K
110K
122K
1
2
3
HgBa2CuO4
HgBa2Ca2Cu3O8
94K
135K
1
3
Number
of CuO2
layers
Lecture 13
HgBa2Ca2Cu3O8
Superconductivity and Superfluidity
Layered cuprates
La2-xSrxCuO4
N=1
Lecture 13
YBa2Cu3O7
N=2
HgBa2Ca2Cu3O8
N=3
Superconductivity and Superfluidity
Other 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