Pseudogap in a real energy spectrum.
Image courtesy of Benjamin Sacepe (Neel Institute, Grenoble, France)
Superconductors with a normal gap fit in well with the BCS theory, which explicitly links Cooper pairs with the formation of a gap in an energy distribution diagram. According to this theory, superconducting current density is directly proportional to the magnitude of the superconducting gap: ρs ~ Δ, the more Cooper pairs formed per unit volume, the larger the gap in the energy spectrum, i.e. the size of the gap.
Superconductors with a pseudogap do not fit in with the BCS theory, but they can be described using the theory proposed earlier by Mikhail Feigel’man and Lev Ioffe and their colleagues. In their new paper, the scientists used their theory to calculate the dependence of superconducting current density on pseudogap width for a pseudogapped superconductor.
The key is in the disorder
Studying the structure of pseudogapped superconductors at microscopic level showed that these materials are strongly disordered. This means that their atoms are not arranged in a perfect crystal lattice, or the structure of this lattice is strongly impaired. Examples of pseudogapped superconductors given by the authors of the new paper are thin films of titanium nitride (in which the crystal lattice is impaired in many places) and indium oxide (which can be completely amorphous, like glass).
The dome of this church is coated in a thin layer of titanium nitride. The same material is used to coat cutting tools, and if cooled strongly, titanium nitride film can be converted into a pseudogapped superconductor.
Disorder plays a key role because the transition to a superconducting state does not happen at the same time as the formation of Cooper pairs. The electrons that are bound to each other in these materials appear before electrical resistance disappears because the numerous variations in the substance’s microscopic structure from the ideal order can impede a Cooper pair, which in ordered crystals would move freely without interference.
It should be emphasized that Cooper pairs in a pseudogapped superconductor cannot be described as motionless. As a result of quantum effects, their behaviour is slightly more complex: obeying the uncertainty principle, they do not freeze motionless in one place, but “spread out” over a rather large (dozens of interatomic distances), but finite region. If they could move, this region would cover the entire substance: the illustration below will help to better understand the process.
The difference between conventional superconductors and pseudogapped superconductors. In normal superconductors, when the temperature rises above critical level superconductivity disappears due to the breakdown of the Cooper pairs, but in pseudogapped superconductors this happens because the disordered arrangement begins to impede the movement of Cooper pairs, and they become localized in a particular region of the lattice.
Deducing electrical parameters of pseudogapped superconductors from quantum properties is important both from a fundamental point of view (scientists are beginning to have a better general understanding of superconductors), and a practical point of view. The researchers note that using indium oxide, a typical pseudogapped superconductor, it has already been possible to create a superconducting quantum device that can be used as a prototype component for a quantum computer.
Having considered the movement of Cooper pairs in a substance with varying degrees of disorder, the scientists deduced the theoretical dependence of the density of Cooper pairs ρs in the substance on pseudogap width. This is an important characteristic, as it is inversely proportional to the inductance of the film (the materials described are obtained in film form) in the superconducting state. Films such as this with high inductance and zero resistance are needed to produce qubits, the fundamental units of quantum computing devices.
In conventional superconductors, the dependence of the density of Cooper pairs on pseudogap width is linear (ρs ~ Δ), however, in the test substances the dependence is squared (ρs ~ Δ2). This fact is easy to verify experimentally in a more detailed study, and, if that happens, the theory developed previously by the authors will receive further confirmation.
The authors would like to thank Benjamin Sacepe for useful discussions while writing the paper. The study was supported by a grant from the Russian Science Foundation.