Realizing and manipulating space-time inversion symmetric topological semimetal bands with superconducting quantum circuits

Symmetries of space-inversion (P), time-reversal (T), as well as the joint space–time inversion (PT) are fundamental and significantly important in physics. Here we have experimentally realized the joint PT invariant $${\Bbb Z}_2$$ -type topological semimetal-bands, via an analogy between the momentum space and a controllable parameter space in superconducting quantum circuits. By measuring the whole energy spectrum of the system, we clearly imaged an exotic tunable gapless band structure typical of topological semimetals. Two topological quantum phase transitions, from a topological semimetal to two kinds of insulators, can be manipulated by continuously tuning the different parameters in the experimental setup, one of which captures the $${\Bbb Z}_2$$ topology of the PT semimetal via merging a pair of nontrivial $${\Bbb Z}_2$$ Dirac points. Remarkably, the topological robustness was demonstrated unambiguously, by adding a perturbation that breaks only the individual T and P symmetries but keeps the joint PT symmetry. In contrast, when another kind of PT-violating perturbation is introduced, a topologically trivial insulator gap is fully opened. A special topological semimetal phase is realized in superconducting quantum circuits via mimicking the momentum space with a controllable parameter space. A team led by Haifeng Yu and Yang Yu from Nanjing University and Z. D. Wang from The University of Hong Kong measured the whole energy spectrum of a square lattice made by superconducting quantum circuits. They imaged a tunable gapless band structure typical of topological semimetals. By tuning parameters, they induced a special quantum phase transition from a space-time semimetal, which is a special topological semimetal via merging a pair of Dirac points, to an insulator. They further proved the robustness of such space-time semimetal phase by breaking individual time reversal or inversion symmetry while keeping space–time symmetry intact. These results represent the first experimental realization of space–time inversion symmetric topological semimetal phase.