Gate-Controlled Anyon Generation and Detection in Kitaev Spin Liquids

Reliable manipulation of non-Abelian Ising anyons supported by Kitaev spin liquids may enable intrinsically fault-tolerant quantum computation. Here, we introduce a standalone scheme for both generating and detecting individual Ising anyons using tunable gate voltages in a heterostructure containing a non-Abelian Kitaev spin liquid and a monolayer semiconductor. The key ingredients of our setup are a Kondo coupling to stabilize an Ising anyon in the spin liquid around each electron in the semiconductor, and a large charging energy to allow control over the electron numbers in distinct gate-defined regions of the semiconductor. In particular, a single Ising anyon can be generated at a disk-shaped region by gate tuning its electron number to one, while it can be interferometrically detected by measuring the electrical conductance of a ring-shaped region around it whose electron number is allowed to fluctuate between zero and one. We provide concrete experimental guidelines for implementing our proposal in promising candidate materials like $\alpha \text{−}{\mathrm{RuCl}}_3$.

Figure 1

Top view (a) and side view (b) of the proposed experimental setup with the cross section shown in (b) corresponding to the dashed line in (a). The monolayer semiconductor (light gray), whose boundary is denoted by a thick line in (a), is gated with two electrodes of voltages $V_{\mathrm{disk}}$ and $V_{\mathrm{ring}}$ above (dark gray). The semiconductor contains dopant sites (large dots) that (a) form a closed loop of length $\ell$ (dotted line) in the ring region with two sites ${\mathbf{r}}_{\mathrm{\Lambda }}$ being in direct contact with the leads $\mathrm{\Lambda }=L$, $R$, and (b) are able to localize electrons $e$ and, hence, Ising anyons $\sigma$ in the disk region.

Figure 2

Electrical conductance $G$ of the ring region, in units of the conductance quantum $G_0=2e^2/h$, against the magnetic flux $\mathrm{\Phi }$ if the disk region inside contains a trivial boson 1 (solid line), a Majorana fermion $\psi$ (dashed line), or an Ising anyon $\sigma$ (dotted line). The conductance is computed via Eq. (9) for $\rho T_0^2=10\mathrm{meV}$, $\tilde{t}=1\mathrm{meV}$, $\delta E=10\mathrm{\mu }\mathrm{eV}$, ${\mathrm{\Gamma }}_L={\mathrm{\Gamma }}_R=0.1$, and $\mathcal{N}=\ell /d=100$.