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We have experimentally realized novel space-time inversion (P-T) invariantZ2-type topological semimetal-bands, via an analogy between the momentum spaceand a controllable parameter space in superconducting quantum circuits. Bymeasuring the whole energy spectrum of system, we imaged clearly an exotictunable gapless band structure of topological semimetals. Two topologicalquantum phase transitions from a topological semimetal to two kinds ofinsulators can be manipulated by continuously tuning the different parametersin the experimental setup, one of which captures the Z2 topology of the PTsemimetal via merging a pair of nontrivial Z2 Dirac points. Remarkably, thetopological robustness was demonstrated unambiguously, by adding a perturbationthat breaks only the individual T and P symmetries but keeps the joint PTsymmetry. In contrast, when another kind of PT -violated perturbation isintroduced, a topologically trivial insulator gap is fully opened.

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