CUPRATE SUPERCONDUCTORS 11/15/2005 12:00am room B361 Valentin Stanev Intermediate seminar Department of Physics and Astronomy Johns Hopkins University |
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Contents INTODUCTION DIFERENT PHASES OF CUPRATES
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The discovery of high-temperature superconductivity (SC) in 1986 by Georg Bednorz and Alex Muller (working at the IBM Research laboratory in Zurich) came as a shock to the physicists. Surprising was not only the high value of the critical temperature – 30 K (previous record was 23.3K, achieved more than a decade before that) but also the compound that was used – LaBaCuO. It’s a ceramic oxide that in normal state is not a conductor but an insulator. However when doped (replacing some of the lanthanum atoms with strontium) it first turns into a reasonable conductor and at some level of doping becomes superconducting. |
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| This unexpected result prompted intense activity and has led to the synthesis
of compounds from the copper oxides family with increasingly higher Tc (current
record at about 150K.) Today the cuprates are arguably the best studied material
(with possible exception of the semiconductors) and have more than 100 000
research papers devoted to them. The main result is that all members of the
family have similar phase diagram (with T and doping on the axis). Superconductivity
is only one aspect of this diagram. Despite the efforts the main problems are
still unresolved. The microscopic mechanism of superconductivity is unknown
and there is lacking general understanding of the origin and nature of the
different phases. The first important step in understanding cuprates was made by Anderson (Science 235, 1196-1198). He identified the key feature of the new superconductors - the essential structural element in all of them is CuO plane with very weak interplane coupling. Thus effectively the physics is quasi-two-dimensional. This and some other factors lead him to the believe that those materials are in fundamentally new phase unknown in conventional materials. The theories proposed to explain that new behavior have been getting increasingly sophisticated (with some really peculiar examples – anyon superconductivity and charge and spin separation for example) But we are still missing one big theory to combine and explain most of the properties and give a unified picture of the phase diagram of cuprates. 1) MOTT INSULATOR: With no doping the cuprates are poor conductors. They are believed to be an example of the so called ‘Mott insulator’. The Mott insulator is fundamentally different from a conventional (band) insulator. In the latter conductivity is blocked by the Pauli Exclusion Principle. In a Mott insulator conductivity is blocked instead by the electron-electron Coulomb repulsion. To minimize the potential energy electrons try to be as far as possible from each other and each electron takes a minimum of the ionic potential. To generate a current we have to create a doubly occupied sites which costs too much energy. So the electrons are frozen on their respective positions. There is however a virtual hopping between the sites that decreases the kinetic energy without increasing the potential energy too much. Thus there is a magnetic (antiferromagnetic) ordering in the system (two electrons must have opposite spins when on the same site.) There are several models that exhibit that type of behavior and it’s very well understood. With the increase of the doping and temperature this ordering will be lost. The problem is that the nature of this transition and the new phase that arises are very poorly understood. Most of the theoretical effort in the field has been aimed to understand and describe that new phase (so far with moderate success.) 2) PSEUDOGAP: The most mysterious part the phase diagram of cuprates comes after the loss of the antifferomagnetic ordering because of doping. Commonly known as the ‘pseudogap’ this phase it is a conductor but with properties much different from the properties of the usual conductors (generally Fermi liquids). This includes unusual algebraic decay of correlations, resisitivity linear in T and many others. Pseudogap state actually shares many common properties with the superconducting state – for example the form (d-wave) of the gap in the electron spectrum is the same (nothing ‘pseudo’ about it.) The common view is that this is the region where the battle between two different types of order (Mott insulator and SC) is fought. On the opposite side of the phase at a very high doping and temperature there is a cross-over to the ‘normal’ (Fermi liquid) behavior. 3) SUPERCONDUCTOR: Increasing the doping in the pseudogap state leads eventually to the SC (unless the temperature is too high.) Tc becomes higher and higher until it reaches maximum (optimal doping) and then starts decreasing. Like conventional SC the current carriers are electron pairs (Cooper pairs). According to the conventional BSC theory after forming the condensate of Cooper pairs there is a uniform (hence the name s-wave) gap in the k-space electron spectrum. In High-Tc SC there is still a gap but it is anisotropic with d-wave symmetry. After modifying the BSC theory to incorporate those differences it turns out that it is a pretty good description of the d-wave SC. However the microscopic mechanism of the SC is still uncertain. It is clear that the electron-phonon interaction that is responsible for the conventional SC is way to weak to do the same in the cuprates – the temperature is too high (this is one of the reasons for the surprise in 1986 – nobody was expecting such a high Tc.) 
PERSPECTIVES The problem of High-temperature SC is one of the central problems in modern physics. Before solving it new theoretical approaches most probably will be needed since the system is build of strongly interacting particles with strong fluctuations.
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