Half-integer thermal quantum Hall effect in a Kitaev spin liquid: A signature of Majorana edge modes and non-Abelian excitations

Kitaev quantum spin liquid (QSL) displays the fractionalization of quantum spins into Majorana fermions. In magnetic fields, the emergence of Majorana edge current is predicted to manifest itself in the form of thermal quantum Hall effect. Here we report on thermal Hall conductivity κ_xy measurements in α-RuCl₃, a candidate material for Kitaev QSL on two-dimensional (2D) honeycomb lattice. In magnetic field perpendicular to the 2D honeycomb planes, positive κ_xy develops in a spin-liquid state below the temperature characterized by the Kitaev interaction J_K/k_B ∼80 K, demonstrating the presence of highly unusual itinerant excitations. Although the zero-temperature property is masked by the magnetic ordering at T_N = 7 K, the sign, magnitude, and T-dependence of κ_xy at T_N< T < J_K/k_B follows the predicted trend of the itinerant Majorana fermion excitations. The application of a tilted magnetic field suppresses the AFM order, leading to a field-induced QSL ground state. In this QSL state, the 2D thermal Hall conductance per honeycomb plane κ_xy^2D/T shows a plateau behavior as a function of applied magnetic field and has a quantization value of π²k_B²/6h, which is exactly half of κ_xy^2D/T in the integer quantum Hall state and fractional quantum Hall state that hosts Abelian anyons. This half-integer thermal Hall conductance provides direct evidence of a non-Abelian phase and topologically protected chiral edge modes of charge neutral Majorana fermions (particles that are their own antiparticles), which have half degrees of freedom of conventional fermions. Above a critical field, the quantization disappears and κ_xy^2D/T goes to zero rapidly, indicating a topological phase transition.


In collaboration with T. Ohnishi, Sixiao Ma, Y. Matsuda (Kyoto Univ.), K. Sugii, M. Shimozawa, M. Yamashita, Y. Mizukami, O. Tanaka, Y. Motome, T. Shibauchi (Univ. of Tokyo), N. Kurita, H. Tanaka, and J. Nasu (Tokyo Institute of Technology).