Go with the FFLO
In a recent study carried out at HFML, a team of scientists investigated the iron-based superconductor FeSe and found compelling evidence of a distinct high-field superconducting phase which is separated from the usual superconducting phase via a first-order phase transition. This high-field phase is attributed to an exotic state, the so-called FFLO phase, first predicted in 1964. The research, carried out as part of an international collaboration involving Japanese and German researchers and two EMFL laboratories, was published in the journal Physical Review Letters.
Exotic high-field superconducting state
Superconductivity is destroyed at high magnetic fields. Usually, the highest field up to which this state can exist is the so-called Pauli paramagnetic limit, when the Zeeman energy of the itinerant electrons becomes larger than the superconducting condensation energy. Superconductivity may, however, survive even beyond the Pauli limit in a distinct state with spatially modulated order. This so-called FFLO state was already predicted in 1964, independently by Fulde and Ferrell as well as Larkin and Ovchinnikov and describes the state in which the flux-line lattice (caused by the magnetic field penetrating the superconductor) is segmented into periodic planes. Despite tremendous efforts in the search for the FFLO states in the past half century, indications of its experimental realization have been reported in only a few candidate materials.
Iron Selenide – a binary marvel
FeSe is a remarkable material that exhibits a host of exotic phenomena, both in its metallic and superconducting states. At room temperature, FeSe has a tetragonal crystal structure, but as it cools below around 100 K, the system undergoes a structural phase transition and becomes orthorhombic. This subtle structural change induces a profound change in its electronic properties, making them become strongly asymmetric, or ‘nematic’, within the conducting plane. Most other nematic electron fluids are also magnetic, but FeSe is unique in having a purely nematic ground state.
While its metallic properties may be fascinating in their own right, what makes FeSe truly stand out are its superconducting properties. At ambient pressure, FeSe undergoes a superconducting transition at about 9 K. Squeeze it a bit, inside a pressure cell, and its transition temperature rockets to 40 K. This already puts it into the elite class of high-temperature superconductors. Deposit a single atomic layer of FeSe onto a substrate of SrTiO3 however, and the superconducting transition temperature can be elevated up to 100 K, unprecedented for a monolayer superconductor.
With the discovery of its FFLO phase, the superconducting properties of FeSe just got even fancier.
High-field phase diagram of FeSe for field aligned parallel to the layers. Blue circles and green crosses show the irreversibility field, Hirr, and peak field, Hp, determined by resistivity measurements. Orange and yellow circles show the fields Hk and H*, where thermal-conductivity data show either a kink or downward jump, respectively. Above the first-order phase transition field H*, a distinct field-induced superconducting phase emerges at low temperatures.
It pays to be curious
During his PhD research at HFML, Dr. Salvo Licciardello was studying the electrical resistivity of high-quality single crystals of FeSe grown by the Japanese team in magnetic fields up to 35 T applied parallel to the layers. Some of these measurements, related to the evolution of the metallic properties of FeSe doped with S, had already been published in the journal Nature, but Salvo wasn’t content to leave it there. While he was re-analysing his data, he spotted something interesting in the transition from the superconducting (zero-resistive) to the resistive state. Normally, the transition is broadened in a magnetic field as the dynamics of the flux line come into play. However, in FeSe, Salvo noticed that as the sample was cooled below 1 K, the transition became extremely sharp, as though the phase transition from superconducting to normal state became first-order. At the same time, the onset field for the transition shifted to higher fields. Both features were possible signatures of the exotic FFLO phase, but on their own, they would not be enough to convince the community. More evidence was required.
Dr. Shige Kasahara, a collaborator working at the University of Kyoto, recognized that the best way to confirm whether or not the feature Salvo saw was the FFLO phase was to carry out a thermal, rather than an electrical measurement. Shige and his PhD student Yuki Sato duly came to Nijmegen to carry out a series of high-field thermal conductivity measurements on FeSe, assisted by Dr. Matija Čulo and a Radboud Masters student Thom Ottenbros using a probe first developed at HFML by Dr. Stevan Arsenijević, a former postdoctoral researcher now working at the Dresden High Field Laboratory (HLD-EMFL). Sure enough, upon cooling the sample down below 2 K, the team discovered the ‘smoking gun’ they were looking for, a discontinuous downward jump in the thermal conductivity at about 24 T. These measurements confirmed Salvo’s initial findings and provided strong evidence for the distinct high-field superconducting phase in FeSe predicted by Fulde, Ferrell, Larkin and Ovchinnikov all those years ago. Prof. Jochen Woznitsa, director of HLD-EMFL and a world-expert in FFLO physics, also provided invaluable input into the interpretation of the data.
Further high-field measurements are planned to explore this exotic phase, and while for Salvo, the journey is over, his curiosity definitely left an indelible mark on the field. “It was great to have the opportunity to witness in FeSe the occurrence of unique phase transitions and the formation of new states, that can only be observed in very high magnetic field strengths. I think that one of the most fun parts about having done my PhD research at HFML, is that it provided me with the tools that I needed to let my curiosity get the better of me!”
Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe, S. Kasahara, Y. Sato, S. Licciardello, M. Čulo, S. Arsenijević, T. Ottenbros, T. Tominaga, J. Böker, I. Eremin, T. Shibauchi, J. Wosnitza, N. E. Hussey, and Y. Matsuda, Phys. Rev. Lett. 124, 107001 (2020).