Nonperturbative phase diagram of interacting disordered Majorana nanowires

We develop a Gaussian variational approach in replica space to investigate the phase diagram of a one-dimensional interacting disordered topological superconducting wire in the strong-coupling regime. This method allows for a nonperturbative treatment in the disorder strength, electron-electron interactions, and the superconducting pairing amplitude. We find only two stable phases: a topological superconducting phase and a glassy, nontopological localized phase, characterized by replica symmetry breaking.

Figure 1

Effective gap $\Delta \left(\omega \right)$ as a function of $\omega /{\omega }_{\xi }$ for ${\Delta }_{0}a/v=0.01$, $\widehat{\Sigma }{a}^2=0.01$, and different values of the Luttinger parameter $K$. A pseudogap feature emerges below the scale ${\omega }_{\xi }$.

Figure 2

Phase diagram as a function of the dimensionless disorder parameter $\tilde{D}$ and the dimensionless pairing potential $\tilde{\Delta }$ for a repulsive interaction ($K=0.7$) as obtained from the free-energy calculation. A repulsive interaction stabilizes the glassy phase. The insets sketch the optical conductivity $\sigma \left(\omega \right)$ in both phases.