Observation of a novel state with broken time reversal symmetry in multiband superconductors

With the help of muon spin relaxation measurements physicists have observed spontaneous magnetic fields emerging inside the superconducting state of the metallic compounds Ba1−xKxFe2As2 within a certain range of K doping level (0.7≲x≲0.85). The presence of spontaneous magnetic fields and their spatial direction within the crystal lattice are the signatures of the novel s+is superconducting phase which breaks the time reversal symmetry while preserving other symmetries of the crystal lattice. These experimental findings together with thermodynamic data showing the connection between s+is state and a change in the topology of the Fermi surface (Lifshitz transition) was published in Nature Physics in April 2020. Part of the international team was Academy Research Fellow Mikhail Silaev from Ģֱ.
In upper panel: Schematic structure of the Brillouin zone in multiband superconductor Ba1−xKxFe2As2. For the low doping level it consists of one electron and two hole Fermi pockets. With the increase of the doping level the electron pockets disappear so that the Fermi surface undergoes the so called Lifshitz transition. In lower panel: Structure of spontaneous magnetic field generated around spherically symmetric inhomogeneity shown by the black sphere at the origin in s+is and s+id superconducting...
Published
20.5.2020

Worldwide many research groups explore new forms of superconductivity in various iron-based materials. An interesting property of such systems is that their band structure can be significantly changed without destroying superconductivity. This can be done by controlling the electronic doping level, for example via the amount of K atom substitutions in the crystal lattice of Ba1−xKxFe2As2.
Surprisingly it occurs that this system remains superconducting even when the Fermi surface changes its topology by closing one of its pockets as shown schematically in the Figure 1, upper panel. Moreover, this topological transition leads to the interplay of several superconducting channels mediated by the interband repulsion of electrons. This leads inevitably to the formation of a so-called frustrated state with a non-trivial phase difference between the wave functions of Cooper pairs formed by the electrons from different Fermi surface pockets (Figure).

Thermodynamically, this non-trivial interband phase difference is developed via an additional phase transition which occurs below the superconducting critical temperature and breaks the time-reversal symmetry of the system.

Superconducting states with broken time reversal symmetry have been observed earlier in other systems.

“However, the state that we have found in this study has a unique property of preserving the crystal lattice symmetry and breaking only the time reversal one. Physicist call it an s+is state because it is formed by the two complex order parameter functions with a phase difference equal to half of p between each other. Our theoretical prediction confirmed by the muon spin relaxation experiment was that in the s + is state the spontaneous magnetic fields generated near impurities or the doping level inhomogeneities are polarized mainly in the ab crystal plane. In other possible states, for example the crystal-symmetry breaking s + id state all spatial directions of the spontaneous fields are possible (Figure, lower panel). This result combined with the specific heat measurements provides a clear indication of the s+is state which appears during the topological Lifshitz transition driven by the change of the doping level”,  explains Academy Research Fellow Mikhail Silaev from the University of Finland.

This finding opens various directions for further theoretical and experimental explorations. For example, one can try to find signatures of the domain walls separating two energetically equivalent superconducting states related to each other by the time reversal transformation. Also technological applications are possible, for example exploiting the sensitivity of spontaneous magnetic fields to the local inhomogeneities which can be controllably generated inside the superconducting sample using various external perturbations.

The work by Mikhail Silaev is supported by the Academy of Finland.

Link to the publication in Nature Physics April 2020:
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For further information:
Mikhail Silaev, mihail.a.silaev@jyu.fi

Communications officer Tanja Heikkinen, tanja.s.heikkinen@jyu.fi, tel. 358 50 581 8351
The Faculty of Mathematics and Science:
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