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 Z₂ 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 Z₂ Z 2 topology of the PT semimetal via merging a pair of nontrivial Z₂ 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.