Field-angle dependent Majorana gap in a Kitaev spin liquid state of α-RuCl₃

An exactly solvable model of two-dimensional honeycome lattice proposed by Kitaev, in which the bond-dependent Ising interactions act as an exchange frustration, leads to a quantum spin liquid (QSL) ground state characterized by Majorana fermions relevant for fault-tolerant topological quantum computations. Recent efforts to search the Kitaev QSL states revealed that in an antiferromagnet α-RuCl₃ with layered honeycome structure, the zigzag magnetic order can be suppressed by in-plane magnetic fields, leading to a paramagnetic ground state. In a limited range of this paramagnetic state, thermal Hall transport studies report a half-integer quantized plateau behavior [1,2], a signature of Majorana fermions whose degrees of freedom are half of electrons. However, the bulk nature of this state is still elusive. Here we report on detailed heat capacity measurements of α-RuCl₃ under rotated fields in the honeycome plane, which reveal strongly angle-dependent low-energy excitations in the bulk. The excitation gap has a sextuple node structure, and the gap amplitude increases with field, exactly as expected for itinerant Majorana fermions in the Kitaev model [3]. Our thermodynamic results are fully linked with the transport quantization properties, providing the first demonstration of the bulk-edge correspondence in a Kitaev QSL. Moreover, we find the possible emergence of a nematic QSL state with two-fold rotational symmetry at high fields, which may be relevant to the vanishing of quantum thermal Hall effect.

[1] Y. Kasahara et al., Nature 559, 227-231 (2018). [2] T. Yokoi et al., arXiv:2001.01899. [3] O. Tanaka et al., arXiv:2007.06757.