The superconducting transition temperature is a point above which a material exhibiting superconductivity becomes a normal conductor. Researchers are striving to raise the superconducting transition temperature so practical applications can be realized.
This image shows cooper pair wavefunctions with different symmetry. On the left the sign of the wavefunction remains the same under 90o rotation while the sign reverses for the wavefunction on the right. (©Science China Press)
Researchers discovered a superconducting material with a transition temperature above liquid nitrogen’s boiling point in 1987. Today, several groups of closely related superconducting materials, some of which have even higher transition temperature, are identified. These compounds are dubbed as the "cuprates", with copper-oxides as their common building blocks.
A new class of high temperature superconducting material was discovered in 2006, triggering a new wave of excitement in the scientific community. This material consists of iron-pnictides as its building blocks. Pnictogens represent members of the group V elements in the periodic table. However, until recently, the superconducting transition temperature had fallen short of the boiling point of the liquid nitrogen.
Electrons form pairs in the superconducting state by binding together. The existence of pairs was first hypothesized by Leon Cooper and therefore, they are dubbed as "Cooper pairs." A superconductor has pairs as its current carriers. The binding energy of Cooper pairs reveals the robustness of a superconducting state. The superconducting transition temperature will be higher when the binding energy is larger. In 2012, a research team headed by Qi-Kun Xue at Tsinghua University observed an anomalously large pair binding energy at the interface between an iron selenide (FeSe) film. This atomically thin film was grown over the strontium titanate (SrTiO
3) substrate. This interface is known as FeSe/SrTiO 3. From the binding energy value, the superconducting critical temperature (Tc) is suggested to be higher than the liquid nitrogen boiling point.
A Stanford team headed by Zhi-Xun Shen demonstrated a strong coupling between the electrons in the FeSe film and the atomic vibrations in SrTiO
3 by conducting an angle resolved photoemission spectroscopy experiment, suggesting that the high superconducting transition temperature could be caused by such strong coupling.
However, subsequent advancements revealed the existence of another factor causing the high Tc of FeSe/SrTiO
3 in addition to the electron-phonon coupling. Phonon represents a quantum of atomic vibration energy. Electron doping, the process of injecting additional electrons into a system, can make the Tc quite high for systems consisting of FeSe building blocks but without the SrTiO 3 substrate. Nevertheless, the superconducting critical temperature of those free of the SrTiO 3 substrate remains considerably lower in comparison with the critical temperature of FeSe/SrTiO 3. The reason for the high TC for electron-doped systems free of the SrTiO 3 substrate is yet to be known.
Theoretical research in high temperature superconductivity suggests a strong correlation between the electron systems, copper-oxides, and iron-based superconductors. Theoretically, a strong correlation is considered as a cursed phrase, meaning that reality is far off from all ideal limits, where understanding is easy. Under such conditions, it is meaningless to attempt to gain knowledge about the realistic situation using the knowledge about the simple limits. This reason is partially why the mechanism causing the large pair binding energy in copper-oxide superconductors remains a mystery.
Strongly correlated system can be studied by brute-force using a numerical method called quantum Monte-Carlo simulation. Although this technique is perplexed with the renowned fermion sign problem for most realistic situations. This issue is ultimately related to the Fermi statistics of electrons, i.e., sign is changed by the quantum mechanical wavefunction subsequent to the exchange of two electrons. The low temperature properties of a system comprising various elections cannot be reliably computed in the case of the minus sign problem. Strongly correlated electron problems typically have such fermion sign problem unless the existence of a symmetry to ensure pairing up of minus signs to provide plus sign, i.e. -1 × -1 = + 1.
For the problem of FeSe/SrTiO
3, such a symmetry is realized to exist. This allowed Li et al. to analyze several electron-electron and electron-phonon interactions, which are considered as the potential cause of Cooper pair formation. Determining the interaction that is responsible for electron pairing is called the pairing mechanism problem. Especially, the symmetry of pair wavefunctions and the size of the binding energy were determined by the researchers.
There is a very close similarity between the Cooper pair wavefunction and the molecular wavefunction. This wavefunction is a Cooper pair’s quantum mechanical wavefunction as a function of the relative coordinates between those two electrons. The phase behavior of the pair wavefunction upon rotation of the relative coordinate is referred to as the symmetry of the pair wavefunction. Li et al. made a comparison to experiments and suggested the most likely interaction triggering superconductivity in the absence of the SrTiO
3 substrate, using the estimated binding energy and symmetry of the pair wavefunction.
The researchers determined the improvement of the pair binding energy in the presence of the SrTiO
3 substrate, caused by the FeSe electron-SrTiO 3 phonon interactions, and corroborated that such interaction actually raises Tc considerably. A phase diagram is created using these results, reflecting the enhancement of the Tc by the substrate phonons.
Besides providing insights into the high Tc in FeSe/StTiO3, these results also indicate two individual but cooperative mechanisms that drive the high temperature superconductivity. These findings are expected to provide clues for where to identify other higher temperature superconductors.
According to the researchers, they have carried out
"the first numerically-exact sign-problem-free quantum Monte Carlo simulations to study the pairing mechanism in iron-based superconductors."