Thermodynamic evidence for a field-angle-dependent Majorana gap in a Kitaev spin liquid

The exactly solvable Kitaev model of two-dimensional honeycomb magnets has a quantum spin liquid phase characterized by the emergence of fractionalized Majorana fermion excitations. In the paramagnetic state of α-RuCl 3 at high magnetic fields, a half-integer quantization of thermal Hall conductivity has been reported as a signature of edge currents carried by Majorana fermions, but the bulk nature of this state remains unconfirmed. Here, by measuring the heat capacity for different in-plane rotations of an applied magnetic field, we find strongly angle-dependent low-energy excitations in bulk α-RuCl 3 . The excitation gap has a sextuple node structure, and the gap amplitude increases with the field, as expected for itinerant Majorana fermions in the Kitaev model. Our thermodynamic observations of the opening and closing of the bulk gap according to the magnetic-field direction fully correspond with changes in the edge transport. Moreover, the behaviour at higher magnetic fields where the quantum thermal Hall effect vanishes is consistent with a nematic quantum spin liquid state with two-fold rotational symmetry.