Observing Majorana bound States inp-Wave Superconductors Using Noise Measurements in Tunneling Experiments

Abstract

The zero-energy bound states at the edges or vortex cores of chiral p-wave superconductors should behave like Majorana fermions. We introduce a model Hamiltonian that describes the tunnelling process when electrons are injected into such states. Using a non-equilibrium Green function formalism, we find exact analytic expressions for the tunnelling current and noise and identify experimental signatures of the Majorana nature of the bound states to be found in the shot noise. We discuss the results in the context of different candidate materials that support triplet superconductivity. Experimental verification of the Majorana character of midgap states would have important implications for the prospects of topological quantum computation.

Majorana Fermions and Topology in Superconductors

“…192) Then, the systems is no longer in the eigenstate of γ 1 γ 2 , and the average of this operator leads to the vanishing of the correlation Eq.(116). 22) Concerning the last point, however, the situation is changed, when there is a finite overlap of the wave functions of two Majorana edge modes, and the topological degeneracy associated with the fermion number parity iγ 1 γ 2 = ±1 is lifted. In this case, the value of γ 1 γ 2 is determined by the lowest of the two states with n 12 = 0 and 1.…”

“…This is indeed the case for certain situations. 19,[22][23][24][25] To deal with this issue, we consider a simple toy model of a 1D topological superconductor with a Majorana zero-energy mode localized at the open boundaries of the system. (See Fig.9) We denote Majorana fields for these edge states at x = 0 and L as γ 1 and γ 2 , respectively.…”

“…[22][23][24][25] Two spatially well separated Majorana fermions exhibit a certain type of long-range correlation which is independent of the distance between them, and a phenomenon similar to teleportation can occur. These distinct features of Majorana fermions, fractionalization and non-local correlation, have not yet been experimentally established.…”

Quantum transport through a quantum dot structure side coupled with many quantum-dot and Majorana-bound-state pairs

“…Till now, many efforts have been made to detect and verify the existence of MBSs, and some innovative ideas, including the noise measurement, 8 the resonant Andreev effect, 9,10 and the periodic Majorana-Josephson currents, 11 have been proposed. Note that the quantum dot (QD) systems have been also suggested as the possible candidate for detecting the MBSs.…”

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].…”