High Temperature Fermi Statistics from Majorana Fermions in an Insulating Magnet

Majorana fermions, particles that are their own anti-particles, can emerge in insulating magnets as excitations with fractions of the constituent's quantum numbers. Interest in Majoranas is driven by their potential for quantum computation, and as evidence of novel topological states. Observations have been limited to liquid helium temperatures as edge modes in topological superconductors and quantum spin liquids (QSL) without combined evidence of particle-hole symmetry, Fermi statistics, and presence in the bulk. Here we report all three in $\alpha$-RuCl$_{3}$, at temperatures exceeding liquid nitrogen via new energy gain as well as loss Raman spectra and a unique framework to identify the statistical properties of the Kitaev QSL. $\alpha$-RuCl$_{3}$ is close to the Kitaev QSL, where bond-dependent Ising interactions produce excitations that are non-local in terms of spin flips. Consistent with particle-hole symmetric excitations obeying Paul-exclusion, the sum of the energy loss and gain responses are nearly temperature and energy independent. This is in excellent agreement with new quantum Monte Carlo (QMC) calculations of the Kitaev QSL. The new data allow unambiguous separation of the bosonic thermal fluctuations from the continuum due to the Majoranas, further establishing their presence above liquid nitrogen. Our new method can be used to identify the unique properties of QSLs, and demonstrates the promise of $\alpha$-RuCl$_{3}$ for efforts in topological phases and quantum computation.