Half-integer quantized anomalous thermal Hall effect in the Kitaev material $α$-RuCl$_3$

Abstract

Heat transport mediated by Majorana edge modes in a magnetic insulator leads to a half-integer thermal quantum Hall conductance, which has recently been reported for the two-dimensional honeycomb material α-RuCl 3 . While the conventional electronic Hall effect requires a perpendicular magnetic field, we find that this is not the case in α-RuCl 3 . Strikingly, the thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The field-angular variation of the quantized thermal Hall conductance has the same sign structure of the topological Chern number, which is either ±1, as the Majorana band structure of the pure Kitaev spin liquid. This observation of a half-integer anomalous thermal Hall effect firmly establishes that the Kitaev interaction is primarily responsible and that the non-Abelian topological order associated with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in α-RuCl 3 .

Identification of Magnetic Interactions and High-field Quantum Spin Liquid in $α$-RuCl$_3$

“…9(b) and (c), for H a and b, respectively. From there we observe the spin gap (E 1 − E 0 ) changes its behavior at an intermediate field, which can be estimated as the transition field h c [11 2] and h c [1 10] , and the spectra appear differently along a and b directions, consistent with the observation in recent experiments [30,52]. entropy is defined as…”

“…For example, large [28,61] or even half-quantized thermal Hall conductivity was observed at intermediate fields and between 4-6 K [30,31,62]. However, it has also been reported that the thermal Hall conductivity vanishes rapidly when the field further varies or the temperature lowers below approximately 2 K [63].…”

“…Furthermore, experimental probes includ-ing the nuclear magnetic resonance (NMR) [17,20,21], Raman scattering [22], electron spin resonance (ESR) [23], THz spectroscopy [24,25], and magnetic torque [26,27], etc, have been employed to address the possible Kitaev physics in α-RuCl 3 from all conceivable angles. In particular, the unusual (even half-integer quantized) thermal Hall signal was observed in a certain temperature and field window [28][29][30][31], suggesting the emergent Majorana fractional excitations.…”

Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid

“…The observation of the half-quantized thermal Hall effect, which is a signature of chiral Majorana fermions, has been reported (49). Although further experimental observations which support the half-quantization of the thermal Hall effect in α-RuCl 3 are accumulating (49)(50)(51), it is still an important issue to confirm the existence of Majorana fermions from different and more direct approaches.…”

Quantum liquid crystals in the finite-field K$Γ$ model for $α$-RuCl$_3$

“…Among many possible realizations of the proximate Kitaev model [18][19][20][21][22][23][24], α-RuCl 3 is an outstanding material because a half-integer quantization of the thermal Hall conductivity has been observed [25,26]. At higher field, the breaking of the threefold rotation symmetry has been observed from the field angle dependence of the heat capacity at the same time as the disappearance of the thermal Hall effect [27].…”