Majorana fermions in semiconductor nanowires

Abstract

We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor and calculate the topological phase diagram as a function of the chemical potential and magnetic field. The non-trivial topological state corresponds to a superconducting phase supporting an odd number of pairs of Majorana modes localized at the ends of the wire, whereas the non-topological state corresponds to a superconducting phase with no Majoranas or with an even number of pairs of Majorana modes. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality, but also allows having higher carrier density in the nanowire. Consequently, multiband nanowires are better-suited for stabilizing the topological superconducting phase and for observing the Majorana physics. We present a detailed study of the parameter space for multiband semiconductor nanowires focusing on understanding the key experimental conditions required for the realization and detection of Majorana fermions in solid-state systems. We include various sources of disorder and characterize their effects on the stability of the topological phase. Finally, we calculate the local density of states as well as the differential tunneling conductance as functions of external parameters and predict the experimental signatures that would establish the existence of emergent Majorana zero-energy modes in solid-state systems.

Zero-energy pinning from interactions in Majorana nanowires

“…Pinning, moreover, does not require a single channel regime. It also operates for any odd number of open channels, [38][39][40] as the physics of parity crossings is similar. Within the stabilized regions in parameter space with pinned Majoranas, the system becomes electronically incompressible (a related phenomenon of global incompressibility, albeit unconnected to zero-energy pinning and parity crossings, was discussed in Majorana nanowires in the limit of strong intrinsic interactions 18 ).…”

Microscopic theory for a ferromagnetic nanowire/superconductor heterostructure: Transport, fluctuations, and topological superconductivity

“…Indeed, recent theoretical works have addressed a multi-channel generalization of Majorana end states in quasi-one-dimensional structures with Rashba spin-orbit coupling. [81][82][83][84] The works show that the Majorana end states are realized in some parameter regime as long as an odd number of transverse sub-bands are occupied and the width of the wire does not greatly exceed the superconducting coherence length.…”

“…The N-replica KitaevMajorana model discussed here should apply to a quasi-onedimensional Co wire deposited on top of a three-dimensional W superconductor. In light of the multi-channel generalization for the Majorana end states, [81][82][83][84] Co nanowire does not necessary have to be in the strictly one-dimensional limit. In fact, in the presence of disorder Ref.…”

“…In fact, in the presence of disorder Ref. 84 have shown that an optimal nanowire system should have a few occupied sub-bands in order to create stable Majorana end states. Since Co is not a half-metal the question is also whether a ferromagnetic wire, with both majority and minority carriers, can still host an odd number of end Majorana fermions.…”

Nonlocality of zero-bias anomalies in the topologically trivial phase of Majorana wires

“…The semiconductor Majorana wire -the 1D version [15][16][17] of the semiconductorsuperconductor (SM-SC) heterostructure -represents a direct physical realization of the one-dimensional Kitaev model [5]. The observation of a sharp zero bias conductance peak (ZBP) in charge tunneling measurement has been proposed [15,[18][19][20][21][22] as a possible detection scheme for MFs localized near the ends of Majorana nanowires. The 1D SM-SC heterostructure and the associated ZBP measurements have recently attracted considerable experimental effort [23][24][25][26][27][28][29][30].…”