Crystalline symmetry protected Majorana mode in number-conserving Dirac semi-metal nanowires

One of the cornerstones for topological quantum computations is Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such exotic mode can also exist in one dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from inter-channel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that 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 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. Various experimental consequences of Majorana signals are discussed.