| Project Detail |
Summary: Superconductivity and magnetism usually don’t go along together. But there is a notable exception, the family of type II superconductors, for which a Nobel prize was awarded to A.A. Abrikosov in 2003. In these materials, superconductivity and magnetic fields peacefully coexist in the form of topological excitations or quantum vortices. In the mixed state, vortices that exhibit a long-range repulsion, form a triangular Abrikosov lattice. The Berezinskii-Kosterlitz-Thouless transition, a new kind of phase transition in two dimensions that is due to the proliferation of vortices, gained another Nobel prize in 2016.The ability of type II superconductors to sustain very high magnetic fields is at the heart of most of the relevant applications of superconductivity, e.g., high-field magnets used for particle accelerators in high-energy physics or magnetic resonance imaging in medicine. It is the phenomenon of vortex pinning by material defects that determines the properties of all technically relevant superconducting materials, e.g., their dissipation-free transport or magnetic response. Thermal fluctuations of vortices lead to the melting of the Abrikosov lattice at high temperature and to flux creep, implying the appearance of finite voltages and dissipation. The physics of disordered systems and of fluctuations has been the subject of the 2021 Nobel prize awarded to G. Parisi.Another major application of superconductivity is in electronics; its basic functional element is the Josephson junction. Examples of such devices range from the most sensitive SQUID magnetometers measuring magnetic fields with highest precision, to superconducting quantum processors such as Google’s Sycamore chip or the Zuchongzhi quantum processor (UST China) that achieved quantum supremacy. Vortex matter and Josephson junctions are thus of great interest, both for fundamental science and for modern technology; vortex pinning and the Josephson effect are the subjects of the research project presented here.The pinning of topological defects poses a complex problem that has been attacked within two paradigms, weak-collective and strong pinning. The strong pinning theory allows to gain quantitative predictions for a number of measurable quantities. Up to now, use has been made of two crucial approximations, a radial symmetry of the pinning centers and an elastic description of the vortex lattice. As a result of these approximations, the complex many-body problem with disorder can be elegantly reduced to a one dimensional single-particle problem. In the present project, we will go beyond these approximations: we will develop the strong pinning theory for arbitrary anisotropic potentials and elucidate the new concept of unstable domains in the pinning landscape and their fascinating topological properties. Next, we will extend the applicability of the theory to regimes where several neighboring vortices interact, e.g., the high-field situation, thus going beyond the standard elastic approximation. Third, by applying strong pinning ideas to the pinning of a single vortex line (aka the directed polymer problem), we encounter an interesting relation to the problem of shock-wave formation and Burgers turbulence.Josephson junctions are the core elements in superconducting electronics. Involving un- conventional superconductors adds new functionality that can be used in technological appli- cations, e.g., the Josephson battery or quiet qubits. On the fundamental science side, the Josephson effect with its phase sensitivity has been crucial in unravelling the (d-wave) nature of the superconducting state in cuprate high-temperature superconductors. Also, over many years, the Strontium Ruthenate superconductor was considered the prototype candidate for a ‘topological’ superconductor with p-wave symmetry; if true, this material may hold a great potential for the realization of topologically protected quantum computing. Recent Knight shift experiments, however, claim to rule out triplet pairing, implying that the pairing sym- metry in this material remains controversial. Phase sensitive experiments on this and other ‘unconventional’ superconductors are therefore most desirable in order to arrive at unambiguous answers. Surprisingly, not that much is known what to expect for a classic superconductor- normal-metal-superconductor (SNS) junction with unconventional superconductors. We are going to explore this ‘terra incognita’, addressing basic questions about the magnitude of the junction’s Josephson current and its current-phase relation. We will focus on SNS junctions involving leads made from conventional (s-wave) and unconventional spin-singlet (d-wave) and spin-triplet (p-wave) superconductors that will help in the design of new electronic devices and phase-sensitive experiments; the latter should help to unravel the symmetry of the order parameter in Sr2RuO4. |
