Tensor Monopoles in superconducting systems

Abstract

Topology in general but also topological objects such as monopoles are a central concept in physics. They are prime examples for the intriguing physics of gauge theories and topological states of matter. Vector monopoles are already frequently discussed such as the well-established Dirac monopole in three dimensions. Less known are tensor monopoles giving rise to tensor gauge fields. Here we report that tensor monopoles can potentially be realized in superconducting multi-terminal systems using the phase differences between superconductors as synthetic dimensions. In a first proposal we suggest a circuit of superconducting islands featuring charge states to realize a tensor monopole. As a second example we propose a triple dot system coupled to multiple superconductors that also gives rise to such a topological structure. All proposals can be implemented with current experimental means and the monopole readily be detected by measuring the quantum geometry.

Ground state topology of a four-terminal superconducting double quantum dot

“…[27][28][29]. With such approach the dimensionality of the phase space and the related topology is in principle unlimited and only depends on the number of superconducting terminals [30][31][32]. The non-trivial topology of the bound states results in a quantized transconductance [13] in units of 4e 2 /h when applying voltages to the superconducting terminals.…”