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 materialα−RuCl3. 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.

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Plain Language Summary

Collections of interacting spins typically arrange themselves into ordered magnetic patterns at low temperature. Certain materials, however, evade ordering even at absolute zero, giving way to quantum spin-liquid phases supporting “fractionalized” excitations that behave like spins nontrivially diced into pieces. Recent experiments indicate that the insulating compoundα−RuCl3can produce a particularly enticing quantum spin liquid whose fractionalized excitations include so-called “non-Abelian anyons,” a class of quasiparticles that enable intrinsically error-resilient quantum computing. We provide a critical step toward harnessing this technological promise by introducing experiments that electrically probe the spin liquid’s fractionalized excitations even though the platform itself forms a good electrical insulator.

Electronic probes of fractionalization are well developed for many electrically active systems, but these tools do not naturally import to spin liquids because of their insulating character. We show that this barrier can be overcome by connecting conducting circuit elements to the quantum spin liquid in a manner that enables perfect conversion of electrons into fractionalized excitations and vice versa. Remarkably, nucleating even a single excitation in the spin liquid then qualitatively alters the circuit’s electrical conductance, providing unambiguous electrical fingerprints of fractionalized excitations as well as their nontrivial exchange statistics.

Our work spotlights quantum spin liquids as appealing contenders for fault-tolerant quantum-computing hardware. We anticipate further theoretical and experimental work aimed at developing a detailed road map toward applications in this arena.