Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires

One of the cornerstones for topological quantum computations is the Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such an exotic mode can also exist in a one-dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from interchannel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that a 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to realize such Majorana physics. By inserting magnetic flux, a DSM nanowire is driven into a 1D crystalline-symmetry-protected semimetallic phase. Interaction enables the emergence of boundary Majorana zero modes, which is robust as a result of crystalline symmetry protection. We also explore several experimental consequences of Majorana signals.

Figure 1

In (a), DSM nanowire is driven into a rotation-symmetry-protected 1D semimetal when flux $\mathrm{\Phi }=l{\mathrm{\Phi }}_0$ ($\frac{1}{2}<l<\frac{3}{2}$) is inserted. The emerging 1D Dirac points originate from $|\frac{3}{2},0,\uparrow ⟩$ (green line) and $|-\frac{1}{2},0,\downarrow ⟩$ (red line), as shown in (b). In (c), we show the process of pair-hopping interaction $g$, where two “red” electrons hop to the “green" electron states simultaneously. This process respects fourfold rotation symmetry, and enables the emergence of Majorana end states.

Figure 2

(a) We apply a step-function gate to DSM nanowire to fabricate the 2LL-LL configuration. (b) Tunneling phase diagram of 2LL-LL junction with $K_{-}<1$. In (c)–(e), we systematically plot the boundary conditions of the following fixed points: DFP, PFP, and $A_0\mathrm{FP}$. The dashed circle that contains a pair of electrons signals the pair-tunneling/backscattering process.