"Mottness" Might Help to Explain Cuprate Behavior

One of the biggest problems in condensed matter physics is the effort to understand the behavior of copper oxide (or cuprate for short) superconductors. One of the most studied materials in all of science, cuprates are layer cakes consisting of copper-oxygen planes alternating with planes in which other elements, such as strontium or lanthanum, are stocked in varying ratios. For instance, the alternating layer might consist entirely of La, or it might contain 10% Sr. Like chefs looking for just the right recipe of spices, physicists have tried different levels of doping in an effort both to understand the underlying physics and to enhance the movement of electrons through their samples. At moderate doping levels, the cuprates are superconducting: moving electrons pair up and constitute a resistance-less current of electricity. Ironically, the cuprates are much less hospitable to electricity at ultra-low doping levels. In fact, they are insulators when they are not doped. A material's conductivity is determined by the ease with which electrons can move around. In a conductor, there is an abundance of free electrons. (Hotel analogy: there are plenty of guests and plenty of hotel rooms.) In an ordinary insulator electrons are bound two by two (the Pauli exclusion principle insures that no two electrons, except those with opposite values of spin, can occupy the same state) and there are very few if any free electrons. (In an insulating hotel all the rooms are filled with two guests, with no room for more guests.) In a Mott insulator (named for Sir Nevill Mott) conditions are even more inhospitable: all electron energy states are filled with single electrons, and these interact so strongly as to preclude even the arrival of a second electron. (In a Mott hotel all the rooms are single rooms, and all are filled.). Many scientists believe that one of the keys to understanding why the cuprates are such good superconductors in the cold regime is to learn why they are Mott insulators in the warm regime and how such physics manifests itself when they are doped. One more oddity about the cuprates is the issue of "pseudogaps." In a superconductor, the energy required to break up a pair of electrons is termed the "energy gap." But in the cuprates, a partial gap still persists even when superconductivity is destroyed. Some have interpreted this as evidence that some pairs can exist even when the material is warmed above its superconducting transition temperature (see figure). However, the pseudogap is observed in Mott insulators that never became superconducting in the first place, indicating that the pseudogap is of a more general origin. Maybe there is more to superconductivity than the pairing of electrons. (See Nature, 4 January 2001 for background on this topic.)

Now, a new theory addresses the problem of cuprate superconductivity by suggesting that the existence of the curious pseudogap behavior can be explained by the same physics that makes cuprates Mott insulators. Tudor Stanescu (Rutgers Univ) and Philip Phillips (Univ Illinois) argue that "Mottness," involving the collective interaction among many electrons, is still present even when some of the hotel rooms are empty, to use the hotel analogy. They propose that the pseudogap arises simply because transport of electrons in a doped Mott insulator will still involve two electrons temporarily occupying the same site (the same room in the hotel analogy). Such events remind the doped state of its Mottness and this produces a pseudogap. They argue that such an effect disappears when roughly 25% of the hotel rooms are vacant. At such an occupancy rate, an electron can move, on average, throughout a layer without the inhospitability of Mottness. (Tudor Stanescu and Philip Phillips, Physical Review Letters, 4 July 2003; contact Philip Phillips, 217-244-2003)