Possible Spin-Triplet Excitonic Insulator in the Ultraquantum Limit of HfTe_{5}

More than 50 years ago, excitonic insulators formed by the pairing of electrons and holes due to Coulomb interactions were first predicted [A. N. Kozlov and L. A. Maksimov, Sov. J. Exp. Theor. Phys. 21, 790 (1965); L. V. Keldysh and Y. V. Kopaev, Sov. Phys. Solid State 6, 2219 (1965)SPSSA70038-5654; D. Jérome, T. M. Rice, and W. Kohn, Phys. Rev. 158, 462 (1967)PHRVAO0031-899X10.1103/PhysRev.158.462]. Since then, excitonic insulators have been observed in various classes of materials, including quantum Hall bilayers, graphite, transition metal chalcogenides, and more recently in moiré superlattices. In these excitonic insulators, an electron and a hole with the same spin bind together, and the resulting exciton is a spin singlet. Here, we report the experimental observation of a spin-triplet excitonic insulator in the ultra-quantum limit of a three-dimensional topological material HfTe_{5}. We observe that the spin-polarized zeroth Landau bands dispersing along the field direction cross each other beyond a characteristic magnetic field in HfTe_{5}, forming the one-dimensional Weyl mode. Transport measurements reveal the emergence of a gap of about 250  μeV when the field surpasses a critical threshold. By performing the material-specific modeling, we identify this gap as a consequence of a spin-triplet exciton formation, where electrons and holes with opposite spin form bound states, and the translational symmetry is preserved. The system reaches charge neutrality following the gap opening, as evidenced by the zero Hall conductivity over a wide magnetic field range (10-72 T). Our finding of the spin-triplet excitonic insulator paves the way for studying novel spin transport including spin superfluidity, spin Josephson currents, and Coulomb drag of spin currents in analogy to the transport properties associated with the layer pseudospin in quantum Hall bilayers.