Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid

Abstract

The quantum Hall effect in two-dimensional electron gases involves the flow of topologically protected dissipationless charge currents along the edges of a sample. Integer or fractional electrical conductance is associated with edge currents of electrons or quasiparticles with fractional charges, respectively. It has been predicted that quantum Hall phenomena can also be created by edge currents with a fundamentally different origin: the fractionalization of quantum spins. However, such quantization has not yet been observed. Here we report the observation of this type of quantization of the Hall effect in an insulating two-dimensional quantum magnet, α-RuCl, with a dominant Kitaev interaction (a bond-dependent Ising-type interaction) on a two-dimensional honeycomb lattice. We find that the application of a magnetic field parallel to the sample destroys long-range magnetic order, leading to a field-induced quantum-spin-liquid ground state with substantial entanglement of local spins. In the low-temperature regime of this state, the two-dimensional thermal Hall conductance reaches a quantum plateau as a function of the applied magnetic field and has a quantization value that is exactly half of the two-dimensional thermal Hall conductance of the integer quantum Hall effect. This half-integer quantization of the thermal Hall conductance in a bulk material is a signature of topologically protected chiral edge currents of charge-neutral Majorana fermions (particles that are their own antiparticles), which have half the degrees of freedom of conventional fermions. These results demonstrate the fractionalization of spins into itinerant Majorana fermions and Z fluxes, which is predicted to occur in Kitaev quantum spin liquids. Above a critical magnetic field, the quantization disappears and the thermal Hall conductance goes to zero rapidly, indicating a topological quantum phase transition between the states with and without chiral Majorana edge modes. Emergent Majorana fermions in a quantum magnet are expected to have a great impact on strongly correlated quantum matter, opening up the possibility of topological quantum computing at relatively high temperatures.

Magnon bound states versus anyonic Majorana excitations in the Kitaev honeycomb magnet α-RuCl3

“…The discontinuous evolution observed through 10 T in our data admittedly may be expected in our data due to the slightly different experimental conditions between the high-field and the magneto-cryostat setups, the small temperature dif- ference of ≈ 3 K cannot account for a jump of 1 meV. We also recall that the vanishing thermal Hall conductance around 10 T parallels the disappearance of the MB mode 13 .…”

High-field quantum disordered state in α−RuCl3 : Spin flips, bound states, and multiparticle continuum

“…1(a)]. In particular, for 8 T, where evidence for a separate intermediate phase has been reported in recent thermodynamic measurements [28,29], we find a sharp peak m 1α at 2 meV in the Raman spectrum. Consistent with reported THz results [12,22], this mode hardens continuously in higher fields above B c (Fig.…”

Effect of quenched disorder on the quantum spin liquid state of the triangular-lattice antiferromagnet 1T−TaS2

“…Therefore, it is crucially important to measure the thermal conductivity and the heat capacity on the same crystal. To measure the heat capacity of tiny crystals used for the thermal conductivity experiments, we used a long relaxation method [31]. For both mea- surements, the crystals were cooled down very slowly, as the first-order CDW transition is sensitive to the cooling rate and transition is smeared out by a rapid cooling.…”