Class $D$ Spectral Peak in Majorana Quantum Wires

Proximity coupled spin-orbit quantum wires purportedly support midgap Majorana states at critical points. We show that, in the presence of disorder, these systems generate a second band center anomaly, which is of different physical origin but shares key characteristics with the Majorana state: it is narrow in width, insensitive to magnetic fields, carries unit spectral weight, and is rigidly tied to the band center. Depending on the parity of the number of subgap quasiparticle states, a Majorana mode does or does not coexist with the impurity peak. The strong “entanglement” between the two phenomena may hinder an unambiguous detection of the Majorana by spectroscopic techniques.

Figure 1

(a) Phase coherent scattering process $p\to h\to p$, (b) low-energy diffusion mode formed by the succession of such processes, and (c) cartoon of a higher order quantum interference process involving self-interacting diffusion modes.

Figure 2

Schematic profile of spectral density. The profile of the band center anomaly depends on the parity of the number of channels, $N$. Only for odd $N$ does the system support a genuine Majorana level, which is here represented as a broadened $\delta$ singularity.

Figure 3

Top: a sweep of an effective gap parameter generates a critical point at which the clean system goes gapless (cf. the schematic dispersion relations shown in the insets). Bottom: in the presence of disorder, an impurity band of semicircular local average DoS forms.