Observability of surface Andreev bound states in a topological insulator in proximity to an s-wave superconductor

M Snelder,A Brinkman,Y Asano,A A Golubov

doi:10.1088/0953-8984/27/31/315701

Abstract

To guide experimental work on the search for Majorana zero-energy modes, we calculate the superconducting pairing symmetry of a three-dimensional topological insulator in combination with an s-wave superconductor. We show how the pairing symmetry changes across different topological regimes. We demonstrate that a dominant p-wave pairing relation is not sufficient to realise a Majorana zero-energy mode useful for quantum computation. Our main result is the relation between odd-frequency pairing and Majorana zero energy modes by using Green functions techniques in three-dimensional topological insulators in the so-called Majorana regime. We discuss thereafter how the pairing relations in the different regimes can be observed in the tunneling conductance of an s-wave proximised three-dimensional topological insulator. We discuss the necessity to incorporate a ferromagnetic insulator to localise the zero-energy bound state to the interface as a Majorana mode.

Highlights

S Online supplementary data available from stacks.iop.org/JPhysCM/27/315701/mmedia (Some figures may appear in colour only in the online journal)
Besides the possibility of hosting Majorana modes, topological materials are interesting for the study of unconventional p-wave superconductivity by itself. p-wave superconductivity gained renewed interest after the prediction that the p-wave pairing symmetry in He3 would lead to half-quantum vortices with potential application to the field of quantum computing [19,20,21]
We show the relation between odd-frequency pairing and Majorana zero-energy modes by using a Green function approach

Summary

Surface Andreev bound states and Majorana zero-energy modes

As we turn on the perpendicular magnetisation term, it follows from the dispersion relations that we have at Δ1, μ2 = v2 k 2+M2. F↿↿∼ 2Δeiθ (μ − M )(μ + M )3 /ZTI, F↿⇃∼ −2Δ(μ2 − M2)/ZTI, F⇃↿∼ 2Δ(μ2 − M2)/ZTI, F⇃⇃∼ −2Δe−iθ (μ − M )3(μ + M ) /ZTI. As soon as the time-reversal symmetry is broken the increase in M causes the p-wave component to become larger in magnitude than the s-wave component. This can be intuitively understood by notifying that a magnetic field aligns the spins parallel to the field. Spin triplet pairing is favoured above spin singlet pairing. It is possible to already observe dominant p-wave features in the regime M < μ

The ‘Majorana’ regime

Findings

Discussion and conclusion