Figure 1

Two superlayers of the heterostructure consisting of alternating layers of topological insulator (TI) and superconductor (SC). The external magnetic field induces vortices (green tubes) in the SC layers that terminate at the interface with the TI layers resulting in 3D anyons (orange balls). In addition to the obvious three-dimensional distribution of anyons in real space, these anyons provide a projective representation of the ribbon permutation group,[3] which further distinguishes them from the more well-known two-dimensional anyon system (which forms a representation of the braid group).Reuse & Permissions

Figure 2

Comparison of the temperature evolution with (a) and without (b) 3D non-Abelian anyons in the field-temperature plane. The superconductor layer thickness is set to $L=1000$ Å. The sign and magnitude of $\frac{dT}{dB}(B,T)$ determines the nature of the cooling or heating effect as the magnetic field is adiabatically increased. When 3D Majoranas are present (a), a sizable temperature window $T_L<T<T_U$ at intermediate fields (darker blue region labeled “Strong Cooling”) will exhibit a strong cooling effect. Without 3D Majoranas (b), the same parameter regime will demonstrate a heating effect. The yellow region below $T_L\left(B\right)$ is where the ground state degeneracy is split by Majorana-Majorana tunneling; oscillations are not shown for clarity. This interesting sector may include collective anyon excitations generalizing some ideas in 2D,[39] but these are not pertinent to this paper.Reuse & Permissions

Figure 3

Quantitative illustration of cooling via 3D non-Abelian anyons. The superconductor layer thickness is set to $L=1000$ Å. The orange and purple dashed lines are constant field cuts ($B=25B_{c1}\approx 33$ mT) of $\frac{dT}{dB}$ corresponding to the orange and purple dashed lines in Fig. 3 with (a) and without (b) anyons. Notice that $T_H\gtrsim T_U$, where $T_H$ is defined by the temperature below which $\frac{dT}{dB}>0$ in a system without 3D Majoranas, and $T_U$, the upper bound of the cooling window, is defined as the temperature below which the non-Abelian entropy strongly enhances the cooling effect in a system with 3D Majoranas.Reuse & Permissions