The cause of high Tc superconductivity at the interface between FeSe and SrTiO3
Raising the superconducting transition temperature, the temperature above which a superconductor turns into a normal conductor, to a point where applications are practical is a dream in modern science and technology. In 1987 a superconductor with transition temperature above the boiling point of liquid nitrogen was discovered. Today several families of closely related superconducting compounds (some with even higher transition temperature) are known. They are called the "cuprates", for copper-oxides are the common building block among them. In 2006 another wave of excitement hits the scientific community due to the discovery of a different family of high temperature superconducting compound. This time the building blocks are iron-pnictides (pnictogens are members of the group V elements of the periodic table). However the superconducting transition temperature fell short of the liquid nitrogen boiling point, until quite recently.
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
In the superconducting state electrons bind together to form pairs. They are called "Cooper pairs" named after Leon Cooper who first theorized their existence. These pairs are the current carriers in a superconductor. The binding energy of Cooper pairs is a measure of the robustness of the superconducting state - larger binding energy implies higher superconducting transition temperature. In 2012 an anomalously large pair binding energy was observed by a research team lead by Qi-Kun Xue at Tsinghua University in Beijing at the interface between an atomically thin iron selenide (FeSe) film grown on the strontium titanate (SrTiO3) substrate. In the literature such interface is abbreviated as FeSe/SrTiO3. The value of the binding energy suggests that the superconducting critical temperature, Tc, can exceed the boiling point of liquid nitrogen.
Later on an "angle resolved photoemission spectroscopy" experiment done by a Stanford team lead by Zhi-Xun Shen provided compelling evidence that the electrons in the FeSe film couple strongly with the atomic vibrations in SrTiO3, hence raises the intriguing possibility that such coupling could be responsible for the high superconducting transition temperature.
However subsequent developments shows that aside from the above electron-phonon coupling (phonon is a quantum of atomic vibration) there is another factor contributing to the high Tc of FeSe/SrTiO3. For systems composed of FeSe building blocks but free of the SrTiO3 substrate, Tc can also be made quite high by injecting extra electrons into the system or in short by "electron doping". (Incidentally it turns out the FeSe in FeSe/SrTiO3 is also electron doped.) However when compared with the critical temperature of FeSe/SrTiO3 the Tc of those without SrTiO3 substrate are still considerably lower. Thus what causes the high Tc in systems with electron doping but without SrTiO3 also becomes a question scientists seek answer for.
At this point we would like to switch gear and discuss the situation of theory research in high temperature superconductivity. It turns out both copper-oxides and iron-based superconductors are "strongly correlated" electron systems. In theory "strong correlation" is like a cursed phrase. It means reality is far away from all ideal limits where understanding is simple. Under such situation it is hopeless to try to understand the realistic situation based on the knowledge on the simple limits. This reason is partly why the mechanism that causes the large pair binding energy in the copper-oxide superconductors is still regarded as an unsolved problem.
A numerical technique, known as quantum Monte-Carlo simulation, allows one to study strongly correlated system by brute-force. However for most realistic situations such method is plagued with the famous "fermion sign problem". This problem is ultimately associated with the Fermi statistics of electrons, namely the quantum mechanical wavefunction changes sign when two electrons are exchanged. In the presence of the minus sign problem it is practically impossible to compute the low temperature properties of a system consisting of a large number of elections reliably. Unfortunately such fermion sign problem is generally present for strongly correlated electron problems unless there is a symmetry to ensure minus signs pair up to give plus sign, i.e. -1 × -1 = + 1.
What is realized is that such a symmetry exists for the problem of FeSe/SrTiO3. Because of it Li et al. were able to examine a number of electron-electron and electron-phonon interactions that are potentially responsible for causing the formation of Cooper pairs. (Figuring out which interaction is responsible for the pairing of electrons is referred to as the "pairing mechanism problem").
In particular they were able to determine the size of the binding energy and the symmetry of pair wavefunctions. The Cooper pair wavefunction is very similar to the molecular wavefunction for, say, H2. It is the quantum mechanical wavefunction of a Cooper pair as a function of the relative coordinates between the two electrons. The symmetry of the pair wavefunction refers to its phase behavior upon rotating the relative coordinate. With the calculated binding energy and symmetry of the pair wavefunction Li et al. can make comparison to experiments and suggest the most likely interaction that triggers superconductivity when there is no SrTiO3 substrate.
In the presence of the SrTiO3 substrate they were able to determine the enhancement of the pair binding energy by the interaction between the FeSe electron and SrTiO3 phonons and confirm that such interaction indeed substantially raises Tc. Based on these results a "phase diagram" is constructed. There the difference between the red solid circles and open circles reflect the Tc enhancement by the substrate phonons.
In addition to its importance to the understanding of high Tc in FeSe/SrTiO3 these results also point out two separate but cooperative mechanisms driving high temperature superconductivity. Hopefully it will provide hints for where to find other higher temperature superconducting materials.
To the best of their knowledge, wrote by the four researchers, they have performed "the first numerically-exact sign-problem-free quantum Monte Carlo simulations to study the pairing mechanism in iron-based superconductors."
Original publication
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