Electrical Probes of the Non-Abelian Spin Liquid in Kitaev Materials

Abstract

Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin-liquid phase in the Kitaev material α-RuCl 3. Although the platform is a good Mott insulator, we propose experiments that electrically probe the spin liquid's hallmark chiral Majorana edge state and bulk anyons, including their exotic exchange statistics. We specifically introduce circuits that exploit interfaces between electrically active systems and Kitaev materials to "perfectly" convert electrons from the former into emergent fermions in the latter-thereby enabling variations of transport probes invented for topological superconductors and fractional quantum-Hall states. Along the way, we resolve puzzles in the literature concerning interacting Majorana fermions, and also develop an anyon-interferometry framework that incorporates nontrivial energy-partitioning effects. Our results illuminate a partial pathway toward topological quantum computation with Kitaev materials.

Honeycomb layered oxides: structure, energy storage, transport, topology and relevant insights

“…The discovery of high-temperature K-QSL (half-integer thermal hall conductivity) in a-RuCl 3 has brought such materials into the forefront of the pursuit of the non-Abelian K-QSL [231][232][233][234] and its related applications to topological quantum computing. 235 In particular, the magnetic spins, originating from the Ir 4+ ions or Ru 3+ surrounded by the ligand O 2À or Cl À ions respectively, lead to a K o 0 (ferromagnetic) Kitaev interaction via the celebrated Jackeli-Khaliullin mechanism. 236…”

Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries

“…For weak coupling strength, this interaction term is irrelevant and the boundary remains gapless. In the limit of a strong interaction strength, a gap opens in the spectrum [53,54]. At the mean-field level, this gap corresponds to the bilinear iχ LχR acquiring a nonvanishing expectation value.…”

Time-Domain Anyon Interferometry in Kitaev Honeycomb Spin Liquids and Beyond

“…Crucially, however, detection methods do not directly carry over from the quantum-Hall problem due to the host system's Mott-insulating character. While several recent works have nevertheless devised electrical spin-liquid probes [22][23][24][25][26][27], the problem certainly warrants renewed attention.…”

“…Throughout we assume for simplicity h z ≫ jh x j and h y ¼ 0. The third hybridizes the ancillary spins to the edge state via couplings λ j ðtÞ that descend from exchange interactions with the non-Abelian spin liquid [22,30]; these terms mediate energy shuttling between the ancillary spins by allowing each spin to locally absorb or deposit energy packets consisting of an even number of fermionic edge excitations. We assume that the λ j ðtÞ couplings, and hence shuttling of energy, are amenable to real-time control.…”

“…Here σðxÞ is the Ising-anyon field with conformal weight h σ ¼ 1=16, and x b − x t ≡ L a defines the path length enclosing quasiparticle a. We work in the regime where the dimensionless tunneling parametert σ ≡ t σ L 7=8 a =v admits a perturbative treatment [22].…”