Professor Amalia Coldea leads the Quantum Matter in High Magnetic Fields group, part of the quantum materials work in Oxford. Here, she takes a look at the basics of superconductivity research, advances made in understanding iron-based superconductors and the challenge of room temperature superconductivity.
Superconductivity is a fascinating state of quantum matter: it’s as close to magic as it can get. First of all, the electric current passes without any dissipation and the resistance completely vanishes. No dissipation means no energy loss and the supercurrent, once set up in the closed loop of a superconductor, can carry on forever. Making coils with such superconducting wires can allow MRI machines to scan the human body. The toroidal magnets can help to confine the plasma in fusion reactors. They can steer the particles in the right direction in particle accelerators. A superconductor can also fully expel magnetic fields and in certain high-temperature superconductors, quantum flux lines can tread through the material to form a vortex lattice. This enables superconductors to levitate above magnetic tracks but also the vortex lines keep them in a stable state which allows levitating trains to reach extremely high speeds close to flying. And then, when a current flows between two superconductors separated by a nanometre-sized metallic or insulating gap, it is generated by the phase difference between the two superconductors. This intriguing relation between the current and the phase of the superconductors, once implemented into circuits with the right energetic tuning, can bring the system in the stable conditions to perform the quantum tunnelling processes needed for quantum computation.
What does the quantum behaviour of unconventional superconductors look like? Imagine free electrons inside a solid, whizzing around at great speed; they are scattering all the time as they bump into the solid ions of the lattice and generating current when the flow of electrons is accelerated by an electric field. At low temperatures inside the superconducting phase, the electrons condense into the same energetic state and an energy gap opens up between this superconducting state and the normal metallic state from which they emerged. This condensed state occurs as the electrons form pairs; the energy of the system is lowered and thus, in the superconducting state, all electrons are in a condensed state of electron pairs. A pair of electrons would normally repel each other as they have similar negative charges. In a superconductor, the interaction between electrons can become attractive either via the interaction with the lattice that is felt by two electrons passing through the same trajectory, or via the interaction between the neighbouring magnetic fluctuating spins of the electrons that propagate through the lattice. The magnetically mediated interaction is believed to be another route that helps unconventional superconductors to achieve such large transition temperatures.
Understanding why the electrons decide to pair up in certain materials and not in others is the big challenge of creating new materials to superconduct at room temperature. It has been more than 14 years since iron-based superconductors were discovered as another family of unconventional superconductors. Before that, the previous breakthrough came in 1986 with the discovery of copper oxide superconductors – and only now have some of these cuprates reached their manufacturing potential to be used in powerful magnets that can operate with helium nitrogen, a much cheaper coolant, as compared with traditional systems using liquid helium. Superconductivity at room temperature is the holy grail and, once achievable at scale, will have myriad practical applications.
Room temperature superconductivity is believed to have been achieved recently in a mixture system based on carbon sulphur and hydrogen. The resulting system was subjected to extreme applied pressures, similar to those inside the core of the Earth. Surprisingly enough, their high temperature superconductivity can be understood using conventional theories of electron pairing via the lattice vibrations. As the vibrational energy is large for light elements, and additionally there is a large density of electronic states available for scattering under applied pressure, it creates the right conditions to enhance superconducting temperatures.
In unconventional superconductors, like iron-based superconductors, interaction with the lattice is always present. Electrons scatter to create their resistance at high temperatures, however, the attractive interaction is not sufficient to explain their large superconducting temperatures that are close to nitrogen temperatures. Instead, the proximity of superconducting phases to other unusual electronic orders are believed to play the important role of the glue in electron pairing. Among these exotic electronic phases from which superconductivity emerges, the nematic electronic phase, in which the electronic cloud becomes unusually elongated and breaks the symmetry of its lattice, and spin-density wave phase, with a periodic modulation in the density of the electronic spins across the lattice, are two important candidates that can provide the necessary conditions for pairing. Interestingly, under pressure their superconductivity can be strongly enhanced but it is still below liquid nitrogen temperatures. Even more unexpectedly, a single monolayer of a particular material, FeSe, grown on a suitable substrate can become a high-temperature superconductor above liquid nitrogen temperature.
Why a Fermi surface is relevant
The required attractive interaction binds together electron pairs such that their total momentum is usually zero for two electrons in different regions of the momentum space. To understand how this happens, one needs to know the Fermi surface of a conducting material which is a geometrical representation of the occupied electronic states in momentum space; knowing this helps us to work out the symmetry and the mechanism for electron pairing. When electrons pair up, a superconducting gap opens at the Fermi surface and separates the condensate from the normal unpaired states. Another useful measure of the strength of electronic interaction is given by the effective mass of the electrons; this originates from the band dispersion in momentum space – strong electronic interactions often leads to very large effective masses.
To find out more about Fermi surfaces and the behaviour of these quasiparticles, we use different techniques. One of them is quantum oscillations in high magnetic fields, a powerful technique that enables the understanding of the electronic behaviour of all metals and sets up the foundation of solid-state physics. This technique relies on the quantisation of the energy levels in the magnetic field and oscillations occur in the density of electronic states; as the magnetic field changes, different Landau levels cross the chemical potential of the system. Having a Fermi surface is a fundamental concept of a metal which is a useful start for a theory of superconductivity: in copper oxide superconductors it took more than 20 years to improve the sample quality to be able to access their Fermi surface in ultra-high magnetic fields. In iron-based superconductors, this was possible soon after their discovery due to the high quality of the single crystals and relatively smaller upper critical fields. Another technique, is the use of angle-resolved photoemission spectroscopy performed mainly at synchrotron facilities; light shining on the sample extracts photoelectrons and their energy and the momentum distribution can be probed directly.
Highly crystalline superconductors in extreme conditions
Using these two techniques, my group has been engaged in studies to understand the electronic and superconducting behaviour of iron-based superconductors. The electronic properties originate from square planes of iron atoms and they depend strongly on the orbital flavour that make the electronic bands. Interestingly we have found that depending on the orbital character of these bands, the electrons are exposed to different strengths of interactions which can be tuned by chemical substitution; we have discovered the signatures of nematic electronic phases. This orbital differentiation also influences how electron pairing takes place. By combining the experimental observation from quantum oscillations and angle-resolved photoemission spectroscopy, we have been able to identify the different pockets of the Fermi surface that contribute to the pairing of electrons.
Another important part of our research is to identify which electronic phase provides the attractive pairing; to do this, we use different tuning parameters like applied pressure and applied strain. We have developed different single crystalline materials, tools and techniques to be able to explore these phenomena both in Oxford and at international high magnetic field facilities. These complex studies on submillimetre-sized crystals coupled with the extreme environment of low temperatures, ultra-high magnetic fields and high pressure allows us to fully disentangle and separate the competing electronic phases and asses their relevance for superconductivity. The experiments involve tuning the quantum nature of electrons and observing the topological changes in the Fermi surface as well as the strength of electronic interactions in a single material. We discovered that nematic electronic phases have much stronger electronic interactions but superconductivity prefers much more isotropic and large Fermi surfaces. At the lowest temperature, we have searched for signatures of quantum critical behaviour at the nematic phase transition tuned by chemical and applied pressures. We have identified signatures associated with a quantum Griffiths phase, in which nematic islands are strongly fluctuating inside a tetragonal background which are rather unique. Furthermore, we found that a strong impurity in the iron plane is detrimental both to superconductivity and the nematic phases.
From fundamentals towards applications
In order to establish the relevance of iron-based superconductors for practical applications, their critical superconducting properties need to be measured. We have identified a highly promising material, CaKFe4As4; it has a huge upper critical field close to 100T; in addition, it can carry a larger critical current than any other material; and it can be developed in superconducting wires. As many iron-based superconductors are isotropic materials, they are ideal candidates to create extremely large magnetic fields that can be used in many different settings.
Our research has also explored how two-dimensional devices can be created by exfoliating highly single crystalline materials of FeSe. The superconducting properties of these devices are strongly reduced as the flakes become thinner which is in contrast to the case in which a single monolayer is created on top of a suitable substrate that donates electrons.
Looking towards an exciting future
The future of research of novel superconductors looks very promising. Certain materials like iron-based superconductors can combine the Dirac-like dispersion surface states with bulk superconductivity and have been predicted to host the right conditions to be a good candidate for topological superconductivity1. Inside the vortex core of these systems, one can create new quasiparticles: Majorana fermions. Majorana fermions are fermions with their own antiparticles and, if they can be moved and manipulated, are one of the keys to unlocking quantum computation. Furthermore, two-dimensional devices developed on thin flakes or films of iron-chalcogenides can be gated and provide an ideal platform as tunable superconducting and electronic devices.
Another important avenue of exploration is looking at novel advanced materials which could superconduct at temperatures above liquid nitrogen temperature. As well as the effort required to synthesise and develop new materials, the use of machine learning looks to be another useful tool in accelerating the search of new chemical and structural combinations. The machine learning input will still make use of the details of the Fermi surfaces and the electron-phonon interactions of conventional superconductivity to accelerate the discovery of new materials. The unconventional superconductivity still required experimental and theoretical effort to be understood by humans before the machines and quantum computing can make a difference for these complex systems.
The magic and allure of superconductors continues to inspire my group’s work – and the belief that the careful combining of the different experimental and computational tools at our disposal brings us closer towards exciting new discoveries.