Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid (1805.05022v2)

Abstract: The quantum Hall effect (QHE) in two-dimensional (2D) electron gases, which is one of the most striking phenomena in condensed matter physics, involves the topologically protected dissipationless charge current flow along the edges of the sample. Integer or fractional electrical conductance are measured in units of $e^2/2\pi\hbar$, which is associated with edge currents of electrons or quasiparticles with fractional charges, respectively. Here we discover a novel type of quantization of the Hall effect in an insulating 2D quantum magnet. In $\alpha$-RuCl$3$ with dominant Kitaev interaction on 2D honeycomb lattice, the application of a parallel magnetic field destroys the long-range magnetic order, leading to a field-induced quantum spin liquid (QSL) ground state with massive entanglement of local spins. In the low-temperature regime of the QSL state, we report that the 2D thermal Hall conductance $\kappa{xy}^{2D}$ reaches a quantum plateau as a function of applied magnetic field. $\kappa_{xy}^{2D}/T$ attains a quantization value of $(\pi/12)(k_B^2/\hbar)$, which is exactly half of $\kappa_{xy}^{2D}/T$ in the integer QHE. This half-integer thermal Hall conductance observed in a bulk material is a direct signature of topologically protected chiral edge currents of charge neutral Majorana fermions, particles that are their own antiparticles, which possess half degrees of freedom of conventional fermions. These signatures demonstrate the fractionalization of spins into itinerant Majorana fermions and $Z_2$ fluxes predicted in a Kitaev QSL. Above a critical magnetic field, the quantization disappears and $\kappa_{xy}^{2D}/T$ 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 major impact on strongly correlated topological quantum matter.

• The paper reports the observation of half-integer thermal Hall conductance, quantified as (π/12)(k_B²/ħ), evidencing fractional Majorana excitations.
• The study employs detailed thermal transport measurements under parallel magnetic fields to induce a quantum spin liquid state in α-RuCl₃.
• The findings confirm topologically protected chiral Majorana edge currents, highlighting potential applications in fault-tolerant quantum computing.

Majorana Quantization and the Half-Integer Thermal Quantum Hall Effect in a Kitaev Spin Liquid

The paper presented in this paper elucidates a notable advancement in the understanding of the thermal Hall effect, specifically within the context of a Kitaev spin liquid realized in the compound $\alpha$-RuCl$_3$. The research explores the intriguing phenomenon of Majorana quantization, providing empirical observation of a half-integer thermal quantum Hall effect (QHE) in a magnetic field-induced quantum spin liquid (QSL) state of $\alpha$-RuCl$_3$. This observation is made within a spin-orbit coupled Mott insulator environment, showcasing a 2D honeycomb lattice structure.

The primary discovery centers on the behavior of Majorana fermions, which are emergent quasiparticles theorized to arise in specific topological states of matter. Majorana fermions are characterized as particles that are their own antiparticles, possessing unique properties and half the degrees of freedom found in conventional fermions. In this paper, Majorana fermions are manifested in the edge currents of the Kitaev spin liquid, contributing to a quantized thermal Hall conductance.

Research Highlights

1. Quantized Thermal Hall Conductance:
   • The researchers report the quantized 2D thermal Hall conductance, $\kappa_{xy}^{\rm 2D}$, in units consistent with a half-integer value, specifically $(\pi/12)(k_B^2/\hbar)$. This value is notably half of what is recorded in established integer quantum Hall systems, indicating the presence of fractionalized excitations.
2. Observational Settings:
   • The experimentation involved subjecting $\alpha$-RuCl$_3$ crystals to parallel magnetic fields. The resulting field-induced QSL state exhibited topology-driven behaviors, crucial for the observed thermal Hall quantization.
3. Indication of Topological Phase Transition:
   • Above certain critical fields, the quantization of $\kappa_{xy}^{\rm 2D}/T$ rapidly diminishes, suggesting a topological quantum phase transition, one without the chiral Majorana edge modes.
4. Majorana Edge Currents:
   • The paper directly links the observed half-integer thermal Hall conductance to topologically protected chiral Majorana edge currents, reinforcing the theoretical predictions of spin fractionalization into itinerant Majorana fermions and static $Z_2$ fluxes, characteristics of a Kitaev QSL.

Methodological and Theoretical Implications

The methodology involved detailed thermal transport measurements and a comprehensive analysis of the quantum spin liquid behavior under varying magnetic field strengths and orientations. The use of $\alpha$-RuCl$_3$ as a host material for studying Kitaev interactions and Majorana fermions is validated, opening avenues for further exploration of topological quantum states and their potential applications in quantum computing and related fields.

Future Prospects

1. Further Exploration of Kitaev Materials:
   • Continued exploration of Kitaev materials, such as $\alpha$-RuCl$_3$, under varying magnetic fields and temperatures, can unravel more details about the interaction between spins and fractionalized excitations.
2. Technological Impacts:
   • The manifestation of Majorana fermions in solid-state materials holds promise for applications in fault-tolerant quantum computing, particularly in the field of topological qubits.
3. Enhanced Theoretical Models:
   • Enhancement of theoretical models to align with observed phenomena, especially in high-field regimes where experimental data diverge from predictions, could provide deeper insights into the interplay of interactions in spin liquids.

The paper makes a significant contribution to condensed matter physics by experimentally realizing theoretical predictions regarding Majorana fermions and the QSL state. It urges further research into the mysterious properties of these systems, both for fundamental science and potential practical applications in emerging quantum technologies.