Abstract
Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin liquid phase in the Kitaev material $\alpha$-$\mathrm{RuCl}_{3}$. 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 towards topological quantum computation with Kitaev materials.
Highlights
The field of topological quantum computation pursues phases of matter supporting emergent particles known as “non-Abelian anyons” to realize scalable, intrinsically fault-tolerant qubits [1,2]
We introduce a series of circuits that interface electronically active systems—notably proximitized ν 1⁄4 1 integer quantum-Hall states, though other choices are possible—with Kitaev materials realizing a non-Abelian spin liquid. Strong interactions at their interface can effectively “sew up” these very different subsystems, leading to a striking and exceedingly useful phenomenon: A physical electron injected at low energies on the electronically active side converts with unit probability into an emergent fermion in the spin liquid
The electrical conductance of these circuits changes qualitatively upon perturbing the Kitaev material, e.g., to add or remove even a single bulk emergent fermion or Ising anyon; we argue that this feature makes our predictions especially unambiguous
Summary
The field of topological quantum computation pursues phases of matter supporting emergent particles known as “non-Abelian anyons” to realize scalable, intrinsically fault-tolerant qubits [1,2]. We introduce a series of circuits that interface electronically active systems—notably proximitized ν 1⁄4 1 integer quantum-Hall states, though other choices are possible—with Kitaev materials realizing a non-Abelian spin liquid Strong interactions at their interface can effectively “sew up” these very different subsystems, leading to a striking and exceedingly useful phenomenon: A physical electron injected at low energies on the electronically active side converts with unit probability into an emergent fermion in the spin liquid. Our circuits exploit this perfect conversion process to electrically reveal (via universal conductance signatures) the spin liquid’s chiral Majorana edge state, bulk emergent fermions, and bulk Ising anyons, using variations of transport techniques developed for topological superconductors and fractional quantum-Hall states. Several Appendixes provide additional details and supplementary results on our circuits as well as interacting Majorana-fermion models
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