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

The breakthrough -1986 George Bednorz Alex Muller Lecture 13

The breakthrough-1986 “BaxLa5-xCu5O5(3-y)” actually La2-xBaxCu2O4 Lecture 13

….and higher Lecture 13

…..and higher... YBa2Cu3O7 Lecture 13

The High Temperature Superconductors The high temperature superconductors are all mixed valent cuprates based upon the perovskite structure, usually associated with BaTiO3 Ba O Ti 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

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 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 x 0.125 Lecture 13

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 YBa2Cu3O7 AF SC tetragonal orthorhombic Metal insulator x YBa2Cu3O6+x 1 0.5 400K 90K Y Ba Cu Y Ba Cu O Lecture 13

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

Generic phase diagram for the High Tcs Non Fermi Liquid Fermi Liquid superconducting pseudogap Tc antiferromagnetic temperature 0.2 Doping level (holes per CuO2) underdoped optimally doped overdoped Lecture 13

Generic phase diagram for the High Tcs 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 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. Non Fermi Liquid Fermi Liquid superconducting pseudogap Tc antiferromagnetic temperature 0.2 Doping level (holes per CuO2) Lecture 13

Other high Tc phases 214 123 2201 2212 2223 La2-xBaxCuO4 35K La2-xSrxCuO4 38K (La2-xSrx )CaCu2O6 60K YBa2Cu3O7 92K Bi2Sr2CuO6 20K Bi2Sr2CaCu2O8 85K Bi2Sr2Ca2Cu3O10 110K TlBa2CaCu2O7 80K TlBa2Ca2Cu3O9 110K TlBa2Ca2Cu4O11 122K HgBa2CuO4 94K HgBa2Ca2Cu3O8 135K 1 2 3 Number of CuO2 layers HgBa2Ca2Cu3O8 Lecture 13

Layered cuprates La2-xSrxCuO4 YBa2Cu3O7 HgBa2Ca2Cu3O8 N=1 N=2 N=3 Lecture 13

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