Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra

We demonstrate how to design various nonstandard types of Andreev-bound-state (ABS) dispersions, via a composite construction relying on Majorana bound states (MBSs). Here, the MBSs appear at the interface of a Josephson junction consisting of two topological superconductors (TSCs). Each TSC harbors multiple MBSs per edge by virtue of a chiral or unitary symmetry. We find that, while the ABS dispersions are $2\pi$ periodic, they still contain multiple crossings which are protected by the conservation of fermion parity. A single junction with four interface MBSs and all MBS couplings fully controllable, or networks of such coupled junctions with partial coupling tunability, open the door for topological band structures with Weyl points or nodes in synthetic dimensions, which in turn allow for fermion-parity (FP) pumping with a cycle set by the ABS-dispersion details. In fact, in the case of nodes, the FP pumping is a manifestation of chiral anomaly in 2D synthetic spacetime. The possible experimental demonstration of ABS engineering in these devices further promises to unveil new paths for the detection of MBSs and higher-dimensional chiral anomaly.

Figure 1

Majorana-bound-state (MBS) couplings for four MBSs appearing at the interface of a junction formed by two topological superconductors (TSCs). Each TSC provides a pair of decoupled or hybridized MBSs, before contact. The couplings are divided into intra-TSC $t_{12,34}$ and inter-TSC $t_{13,24,14,23}$. We focus on three representative scenarios I, II, and III, depending on the strengths of the couplings. The dark and light colored arrows denote the strong and weak MBS couplings. If a line is missing, the respective coupling is zero.

Figure 2

ABS spectra corresponding to the three types of scenarios shown in Fig. 1, when the two TSCs are biased by a phase difference $\mathrm{\Delta }\varphi$. In case (a), we obtain a fully gapped ABS spectrum, while in case (b), the lowest ABS branch contains two FP-protected linear crossings. Case (c) can be viewed as the critical situation where the two linear crossings of case (b) merge into a single quadratic band crossing. In case (d), the ${ϵ}_{-}$ branch has a sinusoidal form and contains two linear crossings at 0 and $\pi$. In (b), $t_{13}^{(0)}=t_{24}^{(0)}=1$ and $t_{34}^{(0)}=0.2$. In the rest, $t_{13}^{(0)}=t_{24}^{(0)}=0.1$ and $t_{34}^{(0)}=1$. In all panels, $t_{14,23}=0$.

Figure 3

(a) Junction of two TSCs, each one consisting of two coupled single-channel semiconductor nanowires (NWs) in proximity to conventional SCs. The NWs feel a spin-orbit coupling $(\mathit{\alpha }\times \mathit{\sigma }{)}_z{\widehat{p}}_z$. For specific values of fluxes ${\mathrm{\Phi }}_{\ell /r}$ and magnetic fields $B_z$, a pair of MBSs appears on each side of the junction. Each pair is protected by a Kramers degeneracy or a sublattice symmetry, which is violated away from the sweet spot. (b) Cross section of the lhs of a device, which is obtained by stacking two junctions shown in (a). (c) “Infinite” 1D network of identical TSC junctions described by the wave number $q$. FP pumping occurs by varying $\mathrm{\Delta }\varphi =\mathrm{\Phi }$ and an additional parameter, which in (a) is the interface flux ${\mathrm{\Phi }}_J$ (magnetization ${\mathit{M}}_J$), (b) is the flux $\sim B_z$ piercing the cross section, and in (c) is the phase of the interchain pairing [114].